AutoDV: An End-to-End Deep Learning Model for High-Dimensional Data Visualization
Authors: Wei Dai
Jicong Fan
Venue: ICLR 2026 Poster (2026)
Keywords: High-dimensional Data Visualization
Deep Learning
Cross-dimension Generalization
Primary area: transfer learning, meta learning, and lifelong learning

Abstract: High-dimensional data visualization (HDV) plays an important role in data science and engineering applications. Traditional HDV methods, such as Autoencoder and t-SNE, require hyper-parameter tuning and iterative optimization on every dataset and cannot effectively utilize the knowledge from historical low-dimension representation, which lowers the efficiency, convenience, and accuracy in real applications. In this paper, we present AutoDV, an end-to-end deep learning model, for high-dimensional data visualization. AutoDV is built upon a graph transformer network and an invariant loss function and is trained on a number of diverse datasets converted into multi-weight graphs. Given a new dataset, AutoDV outputs the 2D or 3D embeddings of all data points directly. AutoDV has the following merits: 1) There is no hyper-parameter selection during the data visualization stage; 2) The end-to-end model avoids re-training or iterative optimization when visualizing data; 3) The input dataset can have any number of features and can be from any domain. Our experiments show that AutoDV can successfully generalize to unseen datasets without retraining with 89.37\% precision of t-SNE and 91.05\% precision of UMAP on the unseen CIFAR10 datasets. Compared with existing parametric data visualization deep models, our method obtains a significant improvement with 86.65\% precision gain. AutoDV can perform even better than t-SNE and UMAP on gene and UCI tabular datasets. The project is available at https://github.com/DryDew/AutoDV.

Published as a conference paper at ICLR 2026
AUTODV: AN END-TO-END DEEP LEARNING MODEL FOR HIGH-DIMENSIONAL DATA VISUALIZATION
Wei Dai
Zhejiang University of Technology, Hangzhou, China, The Chinese University of Hong Kong, Shenzhen, China, we weidai futizzzuuttco
www.jjtt.uuc...o edu.
Jicong Fan
The Chinese University of Hong Kong, Shenzhen, China, fan ccnnnccuuuh edu. en
ABSTRACT
High-dimensional data visualization (HDV) plays an important role in data sci- ence and engineering applications. Traditional HDV methods, such as Autoen- coder and t-SNE, require hyper-parameter tuning and iterative optimization on every dataset and cannot effectively utilize the knowledge from historical low- dimension representation, which lowers the efficiency, convenience, and accuracy in real applications. In this paper, we present AutoDV, an end-to-end deep learn- ing model, for high-dimensional data visualization. AutoDV built upon a graph transformer network and invariant loss function and is trained diverse datasets converted into multi-weight graphs. Given new dataset, Au- toDV outputs the 2D 3D embeddings of all data points directly. AutoDV has the following merits: 1) There is no prpee-prrameter selection during the data visual- ization stage; 2) The end-to-end model avoids re- re-training iterative optimization when visualizing data; 3) The input dataset can have any number of features and be from any domain. Our experiments show that AutoDV successfully generalize to unseen datasets without retraining with 89.37% precision of t-SNE and 91.99.... 91.05% precision of UMAP the unseen CIFARIO 10 datasets. Compared with existing parametric data visualization deep models, our method obtains a signifi- cant improvement with 86.65% precision gain. AutoDV can perform even better than t-SNE and UMAP on gene and UCI tabular datasets. The project is available at http:///gthubb.co///DyD//////u
number
INTRODUCTION
Extracting meaningful insights from high-dimensional and complex datasets (Fan 2025b) to support informed decision-making and drive innovation remains challenge in contemporary data analysis. High-dimensions data visualization (HDV) is a special dimensionality reduction (DR) technique that allows humans to intuitively interpret large, complex datasets by projecting them into two or three dimensions. This technique has demonstrated success across diverse scientific domains, such as genomics (Dorrity al. 2020), remote sensing (Li et al. 2022), and finance (Velykoivanenko & Korchynskyil (002). HDV is usually an unsupervised task. Formally, given a high- high-dimensional NN), where each data point æ; e Rd d is the dimensionality of the dataset, and N represents the number of data points, the goal is to find a corresponding low- dimensional representation Z [2), = ... )N where each z; E Rd², typically d' 2 or = such that the structural relationships in X are preserved
dataset X {21 ....... ........,,
Over the years, numerous algorithms for DR and HDV have been developed, broadly classified into linear and non-linear methods. Classical linear techniques, including Principal Component Analysis (PCA) (Abdi & Williams/ 2010), Multidimenssonal Scaling (MDS) (Saced et al. 2018).
"Coresponding author.

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Normllzed (par dalacit)
Normal NM0 (per dataset)
mnist
mn st
cifar10
cifar10
Campbell
Campbell
PBMC68K
PBMC68K
Human
Human
Mouse rečin
Mouse retina
TUNADROMD
TUNADROMD
PhilsILL
PhiUSII
10
30
80
60 100
Perplexity in t-SNEE
number neighbors UMAP
Figure 1: NMI Sensitivity under different hyperparameters for t-SNE (perplexity) and UMAP neigher)..). Note: The datasets are randomly sample to simulate various real-world un- seen datasets. Please see details in Appendix
and Linear Discriminant Analysis (LDA) (Balakrishnama & Ganapathiraju 1998), have established
foundational approaches but typically fail to uncover complex, non-linear latent structures inherent
in the data. Consequently, various non-linear approaches have emerged (Fan al. 2018), such
as Self-Organizing Maps (SOM) (Kohonen) 1982). Isomap (Tenenbaum et al. 2000). Kernel PCA
(Schölkopf et al., 1998). Principal Curves (Hastie & Stuetzle 1989), autoencoders Waag et al,
(016). Stochastic Neighbor Embedding (SNE) (Hinton & Roweis] 2002). Locally Linear Embed-
ding (LLE) (Roweis & Saul, 2000), and Laplacian Eigenmaps (Belkin Niyogi 2003). Despite their advances, these methods are not effective in visualizing real-world data with complex struc- tures. To address this, more sophisticated methods, like t-distributed Stochastic Neighbor Embed- ding (t-SNE) (Van der Maaten & Hinton 2008 Sun al., (023). Uniform Manifold Approximation and Projection (UMAP) (Mcinnes et al. 2018), TriMap (Amid & Warmuth] 2019), and PaCMAP WWnn et al. 2 explicitly optimize low-dimensional embeddings to maintain both local neigh- borhood structures and global data relationships effectively. Although the traditional methods and recent advances in HDV have facilitated substantial progress various domains, they face critical limitations in the following.
The traditional data visualization methods sen- sitive to hyper- apper-paraette selection, such as perplexity in t-SNE and the number of neigh- bors in UMAP and PaCMAP, also discussed by previous works (Wattenberg et al.) [016] selection will significantly change the vi-
Sensitive Syper-paramettr tuning:
Böhm et al. 2022). Different sualization results. As an empirical experiment presented in Figure T fixed or default hyper-parameter may not always lead to the best performance. The absence of labeled data in unsupervised tasks poses a unique challenge to tuning the HDV hyper-parameter.
Re-training overhead: They need re-run the training algorithm iteratively, i.e. training, on every new dataset. It brings significant computational overhead, especially when handling large number of datasets.
Lack of cross-domain and cross-dimension generalization: Some studies tried solve re-training overhead using a parametric model by optimizing the following problem: ming (=,,), z, 111 where f : Rd + Rd the HDV model. They still failed adapt the model from overfitting to the training datasets. They failed to effectively utilize the historical low-dimensional representations.
datasets with different domains and dimensions and suffered
To overcome these limitations, we propose AutoDV, a novel end-to-end visualization approach lever- aging graph neural networks (GNNs) (Kipf & Welling, (016) and graph transformers (Rampášck) et al. 2022). AutoDV builds a deep learning model using historical visualization results of la- beled datasets in meta-learning manner, effectively capturing the underlying data structure graph-based representations. Consequently, AutoDV generalizes robustly to unseen datasets with- out requiring re-training or additional hyper-parameter tuning during inference. Our contributions are summarized as follows:
We introduce AutoDV, an end-to-end data visualization method that eliminates the need for pyper-paramettr tuning and re-training when visualizing new datasets.
Compared with existing parametric visualization methods such parametric UMAP and inductive t-SNE, AutoDV can adapt to datasets varying dimensionality, exhibiting supe- rior generalization performance unseen datasets from any domain.
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selection when Published as a conference paper at ICLR 2026
Extensive numerical experiments real-world datasets demonstrate the effectiveness and superiority of AutoDV.
RELATED WORKS
As mentioned before, many insightful HDV methods have been proposed in the past decades (Hartono) 2020 Dehghani et al. 2024] Hartono al. 2014) but they incur high computational costs, particularly when projecting unseen test data. Techniques like Barnes- Hut t-SNE (Van Der Maaten 2014) and opt-SNE (Belkina et al. 2019) accelerate training but still require re-training on new datasets. Recently, end-to-end visualization models like parametric UMAP (Sainburg et al. 2021) and inductive t-SNE Rangel & Marchand-Maillee 2019) have been developed to avoid re- training overhead. These models use deep neural networks to map high-dimensional data directly to liw-dimessional spaces. Auto-encoder (Wang et al.) (016) and its successors, such as Geometric AE (Nazari et al., 2023) and GGAE (Lim al. 2024), also have the potential establish an end-to- end HDV model in a self-regression way. However, they still struggle to generalize across datasets with different dimensions or domains. In this paper. we resolve these challenges by utilizing graph neural networks and an affine invariant loss function design.
Another significant challenge in data visualization algorithms is the high sensitivity of hyper- parameter selection (Wattenberg et al. 2016, Böhm et al. (022). For example, the perplexity in t-SNE critically influences the visualization outcomes. Choosing an excessively large perplexity can result in meaningless spherical visualizations, while an excessively small perplexity might lead to clustering inconsistent with the true data labels, rendering the visualization practically meaning- less. Research addressing hyper-parameter optimization in visualization algorithms is still limited. Indeed, tuning syper-paremtert in unsupervised learning is always challenging (Fan et al. 2022).
Liao al. 2023) introduced Bayesian optimization-base framework to identify optimal hyper- parameters across various visualization performance metrics. However, these metrics rely heavily on ground truth labels, such classification accuracy, area under the ROC curve, and normalized mutual information (NMI), which are impractical to obtain for large, unlabeled datasets typical in real-world scenarios. Our proposed method does not intend optimize the hyper-parameters with- out accessing the ground truth label. Instead, we eliminate the visualizing new unlabeled datasets to further increase the efficiency.
PROPOSED METHOD
3.1 TASK DEFINITION OF AUTODV
Definition (AutoDV) Suppose we have labeled historical datasets (X1, y1). (X2, y2). (XL. yt). where X; E R.. R.Nix: i is the data matrix with N; samples and de features, and y; R.N. Let Ao be an effective data visualization algorithm, with hyper- parameters 0. For each X;, an optimal low-dimensional embedding Z; E N, is obtained by Zi =Ao; -X,;, where 0% denotes the optimal hyper-parumeters selected using y; with respect to some metric M. The goal of AutoDV is to train an end-to-end model fo RNNxd, + RR Nexd' from {(X,, H such that, for any unseen datasel Xnev E d with Zin = AoG (nne)). it
are the labels, = 1, 1,....I. L..
holds that
dist(f(((nev)) Ziew) S
where dist(;..) denotes some distance metric and > 0 is small constant.
In Definition I examples of As include t-SNE and UMAP. The evaluation metric M could be the normalized mutual information (NMI, which is a widely used index in clustering and dimensional- ity reduction. dist(;,-) could be the Frobenius norm. In most real scenarios, we hope to HDV methods to observe the potential cluster structures in the data and it not difficult to achieve large number of labeled datasets from diverse domains to train our model fa- That's why use labeled historical datasets to establish AutoDV.
Nevertheless, there are two challenges when solving problem 1
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CI Designing the end-to-end model fø is non-trine con-trivial, especially when the model is expected to handle imput datasets with different sizes and dimensions, i,c., N; # N, and de # dg for some and j.
C2 There exist multiple optimal low-dimension embeddings Z for the same input X; if we apply translation, rotation, and scaling to Z e.g., 2 and Z Q with any orthonormal matrix Q are equivalent in terms of visualization. This will result in a one-to-many problem and will be difficult to converge (Arridge et al. 2019).
To tackle these two challenges, present graph neural network (GNN) based model design and an affine invariant loss design in the following, respectively.
3.2 AUTODV MODEL DESIGN
Most deep neural networks are designed for fixed input dimensionality and therefore cannot be directly applied to datasets with different numbers of features, which is a main limitation of existing parametric data visualization models. To address this issue, AutoDV additionally exploits the graph structure of each dataset. Given historical dataset X,, we first construct weighted graph whose adjacency matrix is pairwise similarity matrix between samples. The similarity matrix is computed using a Gaussian kernel function (Wasserman) (2066). To preserve as much structural information as possible, we further generate k-scale graphs for each dataset by using different bandwidth parame- (kk)
ters in the Gaussian kernel, following (Long et al. 2015)) The resulting graphs, s s(?)
capture the data structure at different scales and are computed as follows.
s s( c] exp (-
X [u] - X.1ul11 Vj = 1,2, 1.2....,
7(0
where S [u, oj denote the entry in the u-th row and v-th column of (()) |X.[u] X rep- resents the squared Euclidean distance between u-th data point and the v-th data point in dataset X,, and 7(50 is the bandwidth parameter of the j-th scale graph. Consequently, dataset in Nxxd is transformed into multiple graphs represented by weighted adjacency matrices in RNNxN, This graph representation mitigates the constraints imposed by varying dataset dimensions on end-to-end visualization methods.
We employ Graph Neural Networks (GNNs) (Kipf & Welling 2016 to extract intrinsic structural features from the input graphs. GNNs, extensively studied in graph learning literature (Wu et al.) 2020), leverage message-passee passing and node-weight sharing mechanisms to handle graphs with vary- ing node counts effectively. Unlike typical graph learning tasks such as node classification (Yifan al. (2020), graph classification (Wang & Fan 2024), and graph clustering (Sun & Fan 2024 Fan 2025a). our input graphs do not inherently include node features, while GNNs often require node features for node aggregation. To solve this, we derive graph positional encodings (PE) (Grötschla et al., (024)) from the weighted adjacency matrices as node features, utilizing techniques such as Laplacian positional encoding (Belkin & Niyogi 2003) or random walk encoding (Perozzi et al,) 2014]. We denote the positional encoding as P. E R..xd,, where de is the dimensionality of the positional encoding. Then, for each dataset X,, we have
P(0) = M((())) vj=1,....
(3)
where h(-) is the function for extracting the positional encoding. In our experiment, we adopt singular value decomposition (SVD) positional encoding (Sium et al. 2023).
Our end-to-end AutoDV model extensively utilizes the popular GNN architectures, GIN (Xu al. 2018) and Graph Transformer (Rampášek et al. (022), as the model backbone. To utilize the k- scale graphs spawned from Eq. (2). we propose a individual GNN to process it. Then, we have k sets of node emheddings extracted by GNNs. By concatenating them together, a graph transformer is introduced to explore the inter-node relationship, and the final output of the model is produced by a multi-layer perceptron (MLP). The whole AutoDV framework is illustrated in Figure It processes an input dataset X, by first computing k similarity matrices {S(²) 1 } and extracting graph positional encodings [ | J==1- Then, inputs to the GINs, which perform feature extraction. The k outputs are concatenated new node
GNN. For each graph, there is an
get the final hidden node embedding for the input dataset. Finally,
= 1,2,... ... k, serve as
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HDV Algorithm A
Input Dataset
Positional Encodings
Graphs
GNNs
Graph Transformer
Bayesian Optimization
<D>
Z O
p
GIN, (P.".,
S
p.
GIN, GIN,(P, (P.))))))))
@
GT
MLP
Z min K, (d, A
S,
pm
GIN, (PII)
Training Only,
Figure 2: AutoDV framework. The imput datasets will first be converted into & graphs. Then, positional encodings are extracted from the graph. Fach graph is processed by an independent GIN network. The output node features of GINs concatenated and sent graph transformer. Finally, an MLP head is responsible for outputting the low-dimensional embedding. Ground truth label yi HDV algorithm A, and Bayesian optimization are only used at the training stage to produce Z
features and are fed into a graph transformer and MLP output low-dimensional visualization result Zg The AutoDV model fø is expressed as follows:
fo (((P()) ((PP)))s))))) ) MLP (T (G.N (D) S GIIG " (P())))()))))))) 1())
(4)
where represents the concatenation along the feature dimension, GIN, (+) is the j-th GIN net- work, = 1, ......... . and GT(-) is the graph transformer. Hence, we let fø to be a GNN model, RAXN, T N.d"" parametrized by & accepting unified dimensionality of node features.
3.3 MODEL TRAINING
Affine Invariant Loss Function To tackle the second challenge in problem 1 introduce affine invariant loss function for the AutoDV task. Instead of direct alignment between the output oow-dimesiional embeddings, align the geometric structure between the low-dinensional em- beddings. Specifically, construct pairwise squared similarity matrices A and A for Z, and Z i.c.,
| v] = (12 2.11122)
Aj
[4] Z (1]12))
(5)
where (-)) is a transformation function turning distance to a similarity. Then we present general training loss function as follows:
C
[u, v). A [u, v)),
(6)
where ..) denotes the Bregman divergence (Bregman 1967) with strictly convex function e and (2, y) = (xx) (yy) ( y) for any two scalers and y. By aligning the pair- wise distance matrices, the one-to one-to-many problem brought by translation and rotation is eliminated. To further realize the scaling invariant, we pre-process Z using 2-score normalization. Then, the training loss function an affine invariant function that effectively solves the one- one-to-many problem.
For the choice of a and vi, it depends the selection of .A spawning Z*. In this paper, consider t-SNE and UMAP since they are the most popular HDV methods currently, although other HDV methods be used in AutoDV. For t-SNE,
beebhackk--bbbeer divergence (KID) loss
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similar to the original t-SNE training process follows:
1 L
M,
P
Lisne
log u
(3)
1=1
qu,
(1 +
||
[1]
[u]l
(1 + [[ (,(01
Ext + Z [1/] 2 11
Eo,,. +1 (v11)))
Compared with t-SNE. Eq. does not have access to the original high- high-dimensional data, avoiding the selection of perplexity. It guides the model fg mimic the optimal low-dimensional embedding from t-SNE using KLD to ensure the outputs and ground truth Z" are from the same distribution.
As for Z' coming from UMAP, we consider both local structure and global structure consistency between 2 and Z" since the original UMAP algorithm focuses more on the local structure using "n_nei ghbors" hyper-parameter, leading to a sparse similarity matrix in the original data space. We present the training loss for UMAP as follows:
L
Lumap =
Σ
Σ (U.DEN
((u,)) + +((1)
((c..) (UN)EAG
Σ
L
and are two mapping the distance value into family of student-t distribution, X(t) is regularization coefficient decreasing as the training step t growing, NN is the index set of the k-nearest pairs in dataset X;, and the number of neighbors determined by Z" when searching the optimal nyper-parameters. i.e. "n_nei ghbors... We set = 1.93 and b 0.79, the same as the default hyper-parameters of UMAP. We linearly decay the A(t), i... A(t) = (1 - t/TT), where T is the maximum number of iterations. This term makes sure that the model focuses more the local structure consistency. We show that Eq. and Eq. (8) are special cases of Eq. (6) in Appendix C
where ((,,0) (1+0|12.[u] 2.(31113" - (w'']1 )
Eliminating Sign Ambiguity in PE In the proposed method, positional embeddings (PE) are de- rived using Eq. (3) via spectral techniques such as SVD or eigenvalue decomposition. A well-known challenge with these methods sign ambiguity (Lim et al.) 2022). If v is an eigenvector of S, then D is also an eigenvector. This inherent ambiguity can cause structurally similar graphs to produce significantly different positional embeddings simply due to inconsistent eigenvector signs, which clearly unreasonable. However, there is currently no principled way resolve this ambiguity or de- termine an optimal sign convention. To address the sign ambiguity, we propose a sign count-based method to decide whether to flip the sign of each dimension of PE or not. Specifically, if the major- ity value in one column of P is negative, we flip the sign of this column. Otherwise, we keep the sign. The process is illustrated in Appendix D Although the proposed sign flipping strategy may not completely solve the sign ambiguity problem, it is lightweight to implement and shows good performance in our empirical experiments.
3.4 COMPUTATIONAL COMPLEXITY ANALYSIS AND
EXTENSION
As shown by Table I AutoDV is more efficient than t-SNE and UMAP because it does not require iterative optimization on new dataset. More details are in Appendix F due to limited space.
Table 1: Computation complexity comparison for effectively visualizing a new dataset.
HDV Method
DutoDV
S-S
UMAP
Complexity
ON Wmmnx
ONN BT) ONNdd + Nr
As shown by the table, the quadratic complexity in terms of N₂ hinders the application of Au- toDV to very large datasets. One can use sparsification or other techniques to accelerate the computation of self-attention and graph convolution. We propose batch-based method to allow AutoDV scale to datasets with large sizes at the inference stage. Specifically, we split X; into
(x(1). x(!2) ..... x!4)3. where each subset is in Mxd, Then, we construct anchor subset A

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with size smaller than M, where the intra-distance among points is small, ie., points in A belong to the same cluster. We simultaneously input A x J 1, 1.2, .....,99. for each j. The final low-dimensional embedding is the corresponding 2, U... U Z 2( We utilize fixed anchor set to calibrate -( from different outputs. The details are shown in Appendix
3.5 THEORETICAL ROBUSTNESS ANALYSIS FOR AUTODV
In this section, we analyze the theoretical robustness of AutoDV. It is to test how stable its outputs are when the input data contains noise, outliers, or small perturbations. A robust model will produce very similar low-dimensional visualizations even from slightly corrupted data, ensuring its results are reliable. This is crucial because real-world data is often messy.
Theorem Given a dataset X with n samples, let (P()),()) s with P(i) ())) E Raxde be the input of AutoDV model fΦr where the output is Z fa((P(), s6 } Denote X perturbed counterpart of X. where the output is Z = fo((P(), 111)) Suppose fo is Li-Lipschitz continuous, then
2n
cl0) +
Z - B|r S 2
|X X1E,,
max )
where cld)
2A
زفا) is the eigen gap between stD) and $11,, (i) is the maximum
8G)
X
min
eigenvalue of S(i), and A
is the minimum the de-th eigenvalue between S and St1),
The Lipschitz constant Lę is determined by the network structure and is usually OTI 122.. where D) denotes the maximum deepth of the neural networks and W; denotes the weight matrix of layer i. As shown by the theorem, proved in Appendix B if g(5) is large, de/A (3) is small, and 7(1 is large, our AutolVV is stable, provided that the neural network is not complex. The result also
indicates that, if new dataset is similar to training dataset, the visualizations should be similar too. This guarantees the generalization ability of AutoDV to some extent.
4 EXPERIMENTS
4.1 EXPERIMENTAL SETTINGS
Datasets We consider types of datasets from the real world. 1. Immae Data: We visualize image datasets via CLiP-extracted features (Radford et al.) 2021), common practice in deep learning (Hohman et al.] 2018; Huff et al. (001)) We use MNIST (Deng) 2012). Fashion-MNiSS (Xiao) 2017), and CIFAR-10 (Krizhevsky et al. 2009); each image is mapped
512-dim vector. MNIST and FMNIST are used for training, CIFAR-TO for testing. 2. Gene Data: We utilize four commonly used gene datasets in bioinformatics research. Baron Human (Baron et al. 2016). Mouse Retine Campbell (Campbell et al. 2017), and PBMC681 We set Mouse Retina as the testing set and the rest for training. We drop out the rare cells following (Wang et al., 2024) to ensure the class balance. 3. Tabular Data: We collect 26 real-world tabular datasets from UCI Machine Learning Library (Kelly et al.).. These tabular datasets are labeled for classification tasks. Categorical features are one-hot encoded. We drop the auto-increment attributes, such as date, time, and ID. We randomly split 30% for the testing. The detailed information of the datasets summarized in Appendix G
Baselines and Evaluation Metrics We compare the proposed AutoDV with two existing deep learning based parametric visualization methods, including parametric UMAP (p-UMAP) (AAUMAA)(Sania))) (Sainburg
'htpps//www.ncch nchi www.iiinnmiiiiiiii...mmmmmm....m htt.://wwwwggg/o/ccccccccccccc/p -tt.ooooo------taaadd----------- -stad--ardd-------- 1-1-0
hhtps://www. (Oxgenomics.o com.llatsee/iirrsii----p-ppmeeee
AAthoughh the gene data also belongs to tabular data, we in this work treat them separately because almost
all papers on gene data analysis use HDV, and gene data are often in higher dimensionllity with higher sparsity
than daily life labular data.

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NMI: 70.10, SC: 72.68
NMI: 10. SC: 73.11
NMI: 85.96, 73.73
NMI: 04.73, SC: 80.91
Class O
Class G Class
Class
Class
Class
Class
Class
(a) UMAP' on CIFARIO (b) AutoDV-UMAP on CI- (c) UMAP" on CIFARIO (d) AutoDV-UMAP on CI- with 120 points.
FARIO with 120 points. with 2759 points.
FARIO with 2759 points.
Figure 3: (a) and (b) are results of UMAP" and AutoDV-UMAP on the same small test subset of CIFARIO, where Au is better. (c) and (d) are results of UMAP" and AutoDV-UMAP on the same large test subset of CIFARIO.
et al. 2021 and inductive TSNE (i-tSNE) Cloman-Rangel & Marchand Maillet 2019 We man-
ually extend i-tSNE to UMAP as inductive UMAP (i-MMAP) for fair comparison. We also compare
the proposed method with PCA (Abdi & Williams 2010) and autoencoder (AE) (Wang et al., 2016). We also report the performance of the optimal cin-dimesioonal embedding from t-SNE and UMAP searched by Bayesian optimization as the ground truth performance of our method, denoted as t- SNE' and UMAP" respectively. The default (D.) t-SNE and UMAP are also reported. We evaluate the output low-dimensional embeddings using NMI with ground labels and the silhouette co- efficient (SC) (Rousseeuw (187), following (Qiao al.) 2025), detailed in Appendix H To validate whether our method can finish the AutoDV task in problem I we also report the relative precision of (M (2";)) y). M is NMI or SC. Note that the precision NMI and SC, which is calculated as (M y)
can be larger than 1 since the performance of Z can be better.
Training Data Preparation Due to the limited video memory size, directly inputting a graph with a large number of nodes is infeasible. To mitigate this, we randomly sample many subsets (sub-graphs) from very large dataset (graph) similar to (Zeng al. 2020). The detailed sampling process is in Appendix [ The maximum size of the subset is set to 3000. For each subset, we use Bayesian optimization (Jones al. 1998) and its ground truth label search for the optimal hyper-parameter and the corresponding low-dimensional embedding Z' setting .M to NMI. Note that AutoDV not limited by the choice of .M, and can accommodate various metrics for HDV depending on specific analytical objectives. We adopt NMI and SC, as they reveal cluster struc- tures that are more interpretable and perceptually aligned with human intuition in nigh-dimensional spaces. Finally, we drop out the subset with NMI less than 10% to ensure the quality of the train- ing data. For t-SNE, we search for the optimal perplexity. For UMAP, we search for the optimal seneiihhoors" Detailed implementation of our method is in Appendix J
4.2 RESULTS
Comparative Study with Baselines In the image data experiment, the feature dimensionality of training data and testing data is the same. So, we can compare the performance of our method and the baseline methods. We randomly sample 500 subsets from MNIST and FMNIST for training, and sample 50 subsets from CIFAR10 for testing. The comparison results are reported in Table 2 is seen that almost no baseline method can produce an effective low-dimensional embedding for unseen new datasets, indicating poor generalizability. For i-tSE and i-UMAP, due to the one-to- many problem, they are even underfitting on the training sets. In contrast, our method demonstrates superior performance unseen new datasets using historical results from t-SNE or UMAP.
Results on Gene and Tabular Data Since the dimensionalities of the training datasets and the test datasets are different, baseline methods cannot directly perform training. For
umap http://gggnnaaccoom///ee//a///ln
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Table 2: Comparative data visualization results on image datasets. Average NMI, NMI precision, SC, and SC precision are reported on the test set. 500 subsets of MNIST and FMNIST are sampled for training. 50 subsets of CIFAR- 10 are sampled for testing. The best performance on test sets bold. Selected visualization results are plotted in Figure 3
Methods
LSNEE
UMAP
D. FSNE D. UMAP
PCA
AE
P-UMAP HINE
1UMAP
AutoDV AUAADV-UMAP
Test NMI
77.04ga
80.45go.
11.71
79-72207
15.9716 6.8
15.58 5.38_a1
_.7
68.70_no
788.2M
Test NMI Prec.
100
100
18.5
10. 10.41
4.40-za
89.37275
91.00 91.05
Test SC
63.3229.
68.
47.24290 07.61 34.31 4280ga.7
43 43.84 30.4455
20.50.0.
65.15
70.41
Test
Prec.
100
100
62.634r2 62.65-xa
10
88.00
103.00 103.0
Table 3: Data visualization results on gene datasets. Average NMI, NMI precision. SC, and SC
precision are reported on the test set. 2918 subsets of Baron Human, Campbel, and PBMC68K are sampled for training. 113 subsets of the Mouse Retina dataset are sampled for testing. The best performance on test sets is bold.
Methods
USNE
UMAF
DAESNE D. UMAP PCA
AB
P-MAP
DISNE
FUMAF
UMAA
NMI
72.73
28
85
15.07
22
M.2
21.78
1.02xa
13.9827a
38.22
33.03-20.e
Test NMI Prec.
100
100
93.384729 35.42+20r
52.50+e11
102. 102.7
111.9
Test SC
31.43=4a
47.
27.98.22a
35.84
57.00
31
73.18
05.564153 51.70a14
01.11ss
47 17.11
47.98
Test Prec.
100
100
151.533 161.1.75 160.3
110.4ga0.1
112.5gaa.
these methods, we randomly project the input data into 512-dimension space. In the gene data experiment, we sampled 2918 subsets of Baron Human, Campbel, and PBMC68K for training and sampled 1 113 subsets of Mouse Retina for testing. All subsets have optimal NMIs higher than 10%. The results are reported in T In the tabular data experiment, we sampled 519 subsets total from 31 real-world tabular datasets. We split 30%. 156 subsets, for testing. The results are reported in Table In the results, we see that AutoDV has the best NMI on the test sets, and are even better than the optimal low-dimensional embeddings from the original t-SNE and UMAP. It indicates methods can better capture the structural information from the high-dimensional space. We observe that deep-learning baselines often yield high SC but very low NMI under our setting. suggesting the output representation collapses into a dense region due to optimization difficulties.
Cross-Domain Transferability of AutoDV To further validate the generalizability of the pro- posed AutoDV model, we conducted cross-domain experiments across diverse data types. Figure 4 summarizes the average NMI, with source domains represented along the columns and target do- mains along the rows. The results of SC are given in Appendix K AutoDV exhibits strong transfer- ability, especially when transferring from image or tabular domains to the gene domain. It surpasses even the optimal within-domain embeddings produced by t-SNE* and UMAP* Transfers into the image domain result in only slight reduction in performance, which may be attributed to the higher structural complexity or noise inherent in gene and tabular data.
4.3 RUNNING TIME COMPARISON
We compare the wall-clock running time among (-SNE, UMAP, AutoDV, and AutoDV with pre- computed PEs when visualizing a new dataset in 3000x512 using CPU core. The number of optimization iterations of t-SNE and UMAP are set to 2000. All runs are repeated 10 times. The results are Table is seen that AutoDV obtains significant acceleration compared with t-SNE. Although UMAP also consumes less time, it suffers from the hyper-parameter selection involving multiple retrainings, which results in unacceptable overhead.
Table 4: Data visualization results UCI tabular datasets. Average NMI, NMI precision, SC, and SC precision are reported on the test set. 519 subsets are sampled from 26 datasets, of which 156 subsets split for testing. The best performance on test sets bold.
Methods
E-NEE"
UMAP"
D. ESNE D. UMAP
PCA
AE PUMAP
H-NE
j-UMPP
AARRDV-ISNE AMRPD--UMPP
NMI
30.92.1:2
21.0
2 15.12
10.50-m13
Hillan 8:0--a 10.50::2.
33.4522
38.13
Test NMI Prec.
100
100
47.0 aasa 52.9 50.80
121
129.0.00.3
Test
44.42100
64.8
63.87 u 6181 10.
23.87-2m. 75.4
78.26 77.11::s 76.68.16.
48.25
64.28ea7
Test SC Prec.
100
171.24020 178.1g44 179.7440.
110.0g10.
1064gam.a

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Published as a conference paper at ICLR 2026
Avg. NMI t-SNE
Avg. NMI of UMAP
AutoDV-Image 68.70
46.53
23.37
AuteDV-Image
73.28
53.63
21.94
80
AutoDV-Gene 58.85
26.61
AutoDV-Gene
33.03
AutoDV-Tabular t-SNE"
AutoDV-Tabular
UMAP
28.85
Image
Gene
Tabular
Image
Gene
Tabular
Figure 4: Cross-domain transferability performance using t-SNE and UMAP. Each heatmap shows average NMI results for (left) t-SNE and (right) UMAP. Within each map, columns denote the source domain and rows the target domain for the first three rows; the fourth row ("TSNE** "UMAP*") reports the within-domain performance of the optimal low-dimensional embedding. Test sets for each domain are the same as in Tables and
92.56,
73.75, 63.25
Class
Class 2
Class
Class 2
Class
(a) AutoDV-UMAP CIFARIO (b) AutoDV-UMAP on CIFAR10 with 10000 points.
with 20000 points.
Figure 5: (a) is the result of extending AutoDV to a dataset with 10000 points by direct input. (b) is the result of extending AutoDV to a dataset with 20000 points by the batch-based method in 3.4
Table 5: Running time comparison for visualizing dataset.
HDV
AutoDV
AutoDV (precomputed PE)
1-SNE
UMAP
Time (s)
101.71
92.6716.2
763.30+1..01
103.3219.63
4.4 EXTENSION TO LARGE DATASET AND MORE RESULTS
We present results of two ways to visualize large datasets in Figure and show more results and an ablation study in Appendix
5 CONCLUSION
This paper proposed a new end-to-end parametric HDV method, called AutoDV. AutoDV avoids prper-parameter selection and retraining when visualizing new datasets. Furthermore, can be generalized to datasets with any number of features from any domain. Experiments on three types of datasets demonstrate superior performance in terms NMI and SC.
Limitations Although our proposed AutoDV tackles two challenges when designing parametric HDV models and avoids the hyper-parameter selection at the inference stage, it still has some limi- tations, such historical dataset dependency.
It requires historical datasets and their optimal low-dimensional embeddings. This common limitation of all inductive learning models.
In our empirical results, if the number of ground-truth classes of the dataset is large, the NMI will decrease compared with the optimal. This may be because the number training sets is small in our current experiments.
The strategy of extending to the large dataset using our method in Section 3.4 may not be optimal. We leave it as the future works.
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ACKNOWLEDGMENTS
This work was partially supported by the National Natural Science Foundation of China under Grant No.62376236, the Shenzhen Stability Science Program 2023, and the Natural Science Foundation of Zhejiang province, China, under Grant No. LMS26F030015. The authors would like to thank the group members and Prof. Tongkai Ji in the Institute of Data Intelligence at Zhejiang University of Technology for their support.
REFERENCES
Hervé Abdi and Lynne Williams. Principal component analysis. Wiley interdisciplinary reviews: computational statistics, 2(4):433 459, 2010.
Ehsan Amid and Manfred Warmuth. Trimap: Large-scale dimensionality reduction using triplets.
arXiv preprint arXiv:1910.00200 2019.
Simon Arridge, Peter Maass, Ozan Öktem, and Carola-Bibiane Schönlieb. Solving inverse problems using data-driven models. Acta Numerica, 28:1-174, 2019.
Suresh Balakrishnama and Aravind Ganapathiraju. Linear discriminant analysis-a brief tutorial. Institute for Signal and information Processing, 18(1998):1-8, 1998.
Maayan Baron, Adrian Veres, Samuel L Wolock, Aubrey L Faust, Renaud Gaujoux, Amedeo Vetere, Jennifer Hyoje Ryu, Bridget K Wagner, Shai Shen-Orr, Allon M Klein, et al. A single-cell tran- scriptomic map of the human and mouse pancreas reveals and intra-cell population structure. Cell systems, 3(4) 3(4):346-33 2016.
Mikhail Belkin and Partha Niyogi. Laplacian eigenmaps for dimensionality reduction and data representation. Neural computation, 1566):1373 2003.
Anna C Belkina, Christopher O Ciccolella, Rina Anno, Richard Halpert, Josef Spidlen, and Jen- nifer E Snyder-Cappione. Automated optimized parameters for t-distributed stochastic neighbor embedding improve visualization and analysis of large datasets. Nature communications, 10(1): 5415, 2019.
Jan Niklas Böhm, Philipp Berens, and Dmitry Kobak. Attraction-repulsion spectrum in neighbor embeddings. Journal of Machine Learning Research, 23(95):1-32, 2022.
Lev Bregman. The relaxation method of finding the common point convex sets and its applica- tion to the solution of problems in convex programming. USSR computational mathematics and mathematical physics, 7(3):200-217, 1967.
John Campbell, Evan Z Macosko, Henning Fenselau, Tune Pers, Anna Lyubetskaya, Danielle Tenen, Melissa Goldman, Anne MJ Verstegen, Jon M Resch, Steven A McCarroll, et al. A molecular census of arcuate hypothalamus and median eminence cell types. Nature neuroscience, 20(3):484-49, 2017.
Amirozhan Dehghani, Xinyu Qian, Asa Farahani, and Pouya Bashivan. Credit-based self organiz- ing maps: training deep topographic networks with minimal performance degradation. In The Thirteenth International Conference on Learning Representations, 2024.
Li Deng. The mnist database of handwritten digit images for machine learning research. IEEE Signal Processing Magazine, 441-)14 2012
Michael W Dorrity, Lauren M Saunders, Christine Queitsch, Stanley Fields, and Cole Trapnell. Dimensionality reduction by umap to visualize physical and genetic interactions. Nature commu- nications, 11(1):1537, 2020.
Jicong Fan. Graph minimum factorization distance and its application to large-scale graph data clustering. In Forry-second International Conference on Machine Learning, 2025a.
Jicong Fan. An interdisciplinary and cross-task review on missing data imputation. arXiv preprint 1..0v 196, 2025b.
11

---

Published as a conference paper at ICLR 2026
Jicong Fan, Tommy WS Chow, Mingbo Zhao, and John Ho. Nonlinear dimensionality reduction for data with disconnected neighborhood graph. Neural Processing Letters, 47(2):697-716, 2018.
Jicong Fan, Yiheng Tu, Zhao Zhang, Mingbo Zhao, and Haijun Zhang. A simple approach to automated spectral clustering. Advances in Neural Information Processing Systems, 35:9907- 2022.
J.N. Franklin. Matrix Theory.
Dover Books on Mathematics. Dover Publications,
2012. ISBN 9780486136387. URL https: httpppooooooooole.....oooooooo.. google. www...........keee.ek/o e eXOXwCDD9agC
Florian Grötschla, Jiaqing Xie, and Roger Wattenhofer. Benchmarking positional encodings for gnns and graph transformers. arXiv preprint WxXiv:2411112722 2024.
Nathan Halko, Per-Gunnar Martinsson, and Joel Tropp. Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review, 53 (2):217-288, 2011. doi: 10.1137/09077 1806.
Pitoyo Hartono. Mixing autoencoder with classifier: Conceptual data visualization. IEEE Access, 8:105301-105310, 2020.
Pitoyo Hartono, Paul Hollensen, and Thomas Trappenberg. Learning-regullted context relevant topographical map. IEEE transactions on neural networks and learning systems, 26(10):2323- 2335, 2014.
Trevor Hastie and Werner Stuetzle. Principal curves. Journal of the American statistical association, 84(446):502-516, 1989.
Geoffrey E Hinton and Sam Roweis. Stochastic neighbor embedding. Advances in neural informa- tion processing systems, 15, 2002.
Fred Hohman, Minsuk Kahng, Robert Pienta, and Duen Horng Chau. Visual analytics in deep learning: An interrogative survey for the next frontiers. IEEE transactions on visualization and computer graphics, 25(8):267--2633, 2018.
Daniel T Huff, Amy J Weisman, and Robert Jeraj. Interpretation and visualization techniques for deep learning models in medical imaging. Physics in Medicine & Biology, 66(4):04TR01, 2021.
Donald R Jones, Matthias Schonlau, and William J Welch. Efficient global optimization of expensive black-box functions. Journal of Global optimization,
1998.
Markelle Kelly, Rachel Longjohn, and Kolby Nottingham. The uci machine learning repository. https::/arrchvee ics. aaciedd Accessed: 2025-04-01.
Thomas N Kipf and Max Welling, Semi-supervised classification with graph convolutional net- works. arXiv preprint arXiv: 1609.02077 2016.
Günter Klambauer, Thomas Unterthiner, Andreas Mayr, and Sepp Hochreiter. Self-normalizing neural networks. Advances neural information processing systems, 30, 2017.
Teuvo Kohonen. Self-organized formation of topologically correct feature maps. Biological cyber- netics, 43(1):59-69) 69, 1982.
Alex Krizhevsky et al. Learning multiple layers of features from tiny images. Technical report, 2009.
Hongda Li, Jian Cui, Xinle Zhang, Yonggi Han, and Liying Cao. Dimensionality reduction and classification of hyperspectral remote sensing image feature extraction. Remote Sensing. 14(18): 2022.
Yin-Ting Liao, Hengrui Luo, and Anna Ma. Efficient and robust bayesian selection of hyperparam- eters in dimension reduction for visualization. arXiv preprint arXiv:2306.00357, 2023.
12

---

Published as a conference paper at ICLR 2026
Derek Lim, Joshua David Robinson, Lingxiao Zhao, Tess Smidt, Suvrit Sra, Haggai Maron, and Stefanie Jegelka. Sign and basis invariant networks for spectral graph representation learning. In The Eleventh International Conference Learning Representations, 2022.
Jungbin Lim, Jihwan Kim, Yonghyeon Lee, Cheongjae Jang, and Frank C Park. Graph geometry- preserving autoencoders. In Forty-first International Conference on Machine Learning, 2024.
Mingsheng Long, Yue Cao, Jianmin Wang, and Michael Jordan. Learning transferable features with deep adaptation networks. In International conference on machine learning, pp. 97-105, PMLR, 2015.
Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. In International Confer- ence on Learning Representations, 2017.
Liheng Ma, Chen Lin, Derek Lim, Adriana Romero-Soriano, Puneet K Dokania, Mark Coates, Philip Torr, and Ser-Nam Lim. Graph inductive biases in transformers without message passing. In International Conference on Machine Learning, pp. 23321-23337. PMLR, 2023.
Leland McInnes, John Healy, and James Melville. Umap: Uniform manifold approximation and projection for dimension reduction. arXiv preprint 1 2018.
Philipp Nazari, Sebastian Damrich, and Fred A Hamprecht. Geometric autoencoders: what you see is what you decode. In Proceedings of the 40th International Conference on Machine Learning, pp. 25834-25857, 2023.
Richard Nock, Aditya Menon, and Cheng Soon Ong. A scaled bregman theorem with applications. Advances in Neural Information Processing Systems, 29, 2016.
Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. 2017.
Bryan Perozzi, Rami Al-Rfou, and Steven Skiena. Deepwalk: Online learning of social repre- sentations. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 701-710 2014.
Dong Qiao, Xinxian Ma, and Jicong Fan. Federated t-sne and umap for distributed data visualization. In Proceedings of the AAAI Conference Artificial Intelligence, volume 39, pp. 20014-20023, 2025.
Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In International conference machine learning, pp- 8748-8763. PmLR, 2021.
Ladislay Rampášek, Michael Galkin, Vijay Prakash Dwivedi, Anh Tuan Luu, Guy Wolf, and Do- minique Beaini. Recipe for a general, powerful, scalable graph transformer. Advances in Neural Information Processing Systems, 35: 35:14501-14515. 2022.
Edgar Roman-Rangel and Stephane Marchand-Maille Inductive t-sne via deep learning to visualize multi-label images. Engineering Applications of Artificial Intelligence, 81:336-333 345, 2019.
Peter Rousseeuw. Silhouettes: graphical aid the interpretation and validation of cluster analy- sis. Journal of computational and applied mathematics, 20:53-65, 1987.
Sam T Roweis and Lawrence K Saul. Nonlinear dimensionality reduction by locally linear embed- ding. science, 290(5500):2333-2226, 2000.
Nasir Saced, Haewoon Nam, Mian Imtiaz UI Haq. and Dost Bhatti Muhammad Saqib. A survey on multidimensional scaling. ACM Computing Surveys (CSUR), 51(3):1-25, 2018.
Tim Sainburg, Leland McInnes, and Timothy Q Gentner. Parametric umap embeddings for repre- sentation and semisupervised learning. Neural Computation, 33(1 11:281-29907, 2021.
13

---

Published as a conference paper at ICLR 2026
Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller. Nonlinear component analysis as a kernel eigenvalue problem. Neural computation, 10(5):1299-131) 1199119999,,,, 1998.
Yonas Sium, Georgios Kollias, Tsuyoshi Idé, Payel Das. Naoki Abe, Aurélie Lozano, and Qi Li. Direction aware positional and structural encoding for directed graph neural networks. In ICASSP 2023-2023 IEEE International Conference Acoustics, Speech and Signal Processing (ICASSP), pp. 1-5. IEEE, 2023.
Gilbert W. Stewart and Ji-guang Sun. Matrix Perturbatiin Theory. Computer Science and Scientific Computing. Academic. Boston, 1990. ISBN 0126702306 9780126702309. URL https: /tt:://wwwww. worldcat
909 946968
Yan Sun and Jicong Fan. MMD graph kernel: Effective metric learning for graphs via maximum mean discrepancy. In The Twelfth International Conference on Learning Representations, 2024.
Yan Sun, Yi Han, and Jicong Fan. Laplacian- based data visualization. ACM Transactions Knowledge Discovery from Data, 18(1):1-22, 2023.
t-sne for nigh-dimensional
Joshua Tenenbaum, Vin de Silva, and John Langford. global geometric framework for nonlinear dimensionality reduction. science, 290(55000 2000.
Laurens Van Der Maaten. Accelerating t-sne using tree-based algorithms. The journal of machine
learning research, 15(1):3211-3245 2014.
Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(11), (1,,, 2008.
Halyna Velykoivanenko and Vladyslav Korchynskyi. Application of clustering in the dimensionality reduction algorithms for separation of financial status of commercial banks in ukraine. Universal Journal of Accounting and Finance, 10(1):148-160, 2022.
Minjie Wang, Da Zheng, Zihao Ye, Quan Gan, Mufei Li, Xiang Song, Jinjing Zhou, Chao Ma, Lingfan Yu, Yu Gai, Tianjun Xiao, Tong He, George Karypis, Jinyang Li, and Zheng Zhang. Deep graph library: graph-centrie, highly-performant package for graph neural networks. arXiv 2019.
preprint
Xiaoying Wang, Maoteng Duan, Jingxian Li, Anjun Ma, Gang Xin, Dong Xu, Zihai Li, Bingqiang Liu, and Qin Ma. Marsgt: Multi-omics analysis for rare population inference using single-cell graph transformer. Nature Communications, 15(1):338, 2024.
Yasi Wang, Hongxun Yao, and Sicheng Zhao. Auto-encoder based dimensionality reduction. Neu- rocomputing, 184:232-242 2016.
Yingfan Wang, Haiyang Huang, Cynthia Rudin, and Yaron Shaposhnik. Understanding how dimen- sion reduction tools work: an empirical approach to deciphering t-sne, umap, trimap, and pacmap for data visualization. Journal of Machine Learning Research, 22(201):1-73, 2021.
Zixiao Wang and Jicong Fan. Graph classification via reference distribution learning: Theory and practice. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024.
Larry Wasserman. All of nonparametric statistics. Springer Science & Business Media, 2006.
Martin Wattenberg, Fernanda Viégas, and Ian Johnson. How to use t-sne effectively. Distill, 1(10): e2, 2016.
Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and S Yu Philip. A comprehensive survey on graph neural networks. IEEE transactions on neural networks and learning systems, 32(1):4-24 2020.
Han Xiao, Kashif Rasul, and Roland Vollgraf. Fashion-mnist: a novel image dataset for benchmark- ing machine learning algorithms. arXiv preprint arXiv: 1708.07777 2017.
14

---

Published as a conference paper at ICLR 2026
Ruibin Xiong, Yunchang Yang, Di He, Kai Zheng, Shuxin Zheng, Chen Xing, Huishuai Zhang, Yanyan Lan, Liwei Wang, and Tieyan Liu. On layer normalization in the transformer architecture. In International conference machine learning, pp. 10524-10533. PMLR, 2020.
Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful graph neural networks? In International Conference on Learning Representations, 2018.
Hou Yifan, Zhang Jian, Cheng James, Ma Kaili, Ma Richard TB, Chen Hongzhi, and Yang Ming- Chang. Measuring and improving the use of graph information in graph neural network. In The Eighth International Conference on Learning Representations (ICLR 2020), Addis Ababa, 2020.
Yi Yu, Tengyao Wang, and Richard Samworth. A useful variant of the davis-kahan theorem for statisticians. Biometrika, 102(2):315-322 2015.
Hanqing Zeng, Hongkuan Zhou, Ajitesh Srivastava, Rajgopal Kannan, and Viktor Prasanna. Graph- saint: Graph sampling based inductive learning method. International Conference on Learning Representations, 2020.
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A LIMITATION OF AUTODV
It requires historical datasets and their optimal low-dimensional embeddings. This common limitation of all inductive learning models.
In our empirical results, if the number of ground-truth classes of the dataset is large, the NMI will decrease compared with the optimal. This may be because the number of training sets is small in our current experiments.
The strategy of extending to the large dataset using our method in Section 3.4 may not be optimal. We leave it as the future works.
B
PROOF FOR THEOREM
Before we prove Theorem 1 we provide 2 lemmas.
Lemma The Gaussian kernel function in Eq. depending different choice of 7(1)) We have
2 is Lg Lipschitz continuous with Lg
Vot0o
2n
|| - $ s 2 eg(i) |x 1|p..
(10)
Proof: Here we repeat some key notations and definitions.
[14 X
x
|X x
S(1) [u, u/
exp
$100 wl exp
(11)
7(11
[xx112) 7
Consider the Gaussian kernal function g(x) exp
the gradient Vg(x)
-2/y e/ppexpp( (1x12//)xx Then, the norm of the gradient
2 e
V 2/>l|x (- (-11x|1/h)
(12)
with the maximum value of Vg(x) obtained when ||x 3.2 Hence, g(-) is Lipschitz continuous with ())
2
.9
Then, for a graph j.
(| - 56) Σ
s [u. v| - 500
[u, u < (6) 1.
Σ
X [u]
X [w]]le + [[]] [x]]l2)
u.3
21 (1) I (
[1 X [MI1 + |
4mL()) 1
X x11111 = - 1 11
Hence,
|86] - S00 < 22 - *1| = 2/
2n eg(l)
x
x-
(13)
Q.E.D.
Lemma For the perturbed positional encoding p(), if the SVD positional encoding adopt, satisfies
2x11
de
| .65)
|S - -00
(14)
865)
2
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where 815) is the eigen gap between S and S10,, (i) is the maximum eigenvalue of SG), and X is the minimum the de-th eigenvalue between 8 and SG)
Proof:
Let ( and (ú3) perform truncated SVD with first de singular value.
5 = و v , = -6 عا
(15)
Then,
p() = U del [Wi|: de:: del a de V
p()) = T6 delv E00 des: del a
de] أها),
50)
da
V
d,
(16)
We have
pQ) p =|IU/0
-يا0) v / 1|
de
V
de
1 U63) V 5 - -U% v 2
T6
D. - V 50
+
de
(17)
F
110 - / Ex
+
V
1
For the first term,
U1 ( U2 2 < -
V
50 de
-V
VV
U
-.60
F²' (18)
where X is the maximum eigenvalue of StD).
Here, we consider a simplified case that SVD process follows a consistent rule where no sign or rotation ambiguity exists. It is possible realize we propose a sign-flipping strategy. Based on Davis-Kale Kahan theorem (Stewart & Sun 1990 Yu et al. 2015). we have
2/2)00) 561||F
|0
1 S
(19)
86)
where 8(3) is the eigen gap between s and $6) The eigen gap is formally defined as 8(6)
= inf { - - ( (&L), 2(21, 30) E (-x, (0) + U (Ai, oo) ).( and are the i-th
largest eigenvalue of ((i) and $(1). Then, we have
2v ())
| )
) 2
S
|| (55)~)0)) -500 |F
(20)
5()
For the second term,
|
(1)
V
d
())
A
de
8
(j)
v 12
For each i,
(a(2) -Va("0)
(
2
( min
( min(1 (1) ((1)) i.c ( is the minimum the de-th eigenvalue between s and
where
50) Hence,
| 1
50
1
Σ/
5000
(21)
2V
X
(3)
F
According to Weyl theorem theorem(Franklin 2012).
(x(()) ا66'
S <||$0] - -S Then,
\V 9) - /362
vdle
|S S10122 5 Vdle
|| 100 F.
(22)
2/ A
2 ()
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Published as a conference paper at ICLR 2026
Now, combine Eq. 20 and Eq. 22 and plug them in Eq.
17
have
2v
2
dde
p p S
+
|| - -5
815)
2/x00
2
Then, we finish the proof.
Q.E.D.
Proof of Theorem II
Proof: Since AutoDV model consists ht separate GINs with the same network structures, we assume the GIN -ip-Liiscchtzz continuous. Denote H GIN, (P6), (ú)) and HÚ)
GIN, S()), we have
p(3) [SG)
[P0
H
H (K)
H
(K)
S
>> j=1
Lo1
(5G)
<kLo1 max (1|P() p
|| - -|(0)] -5011e))
Suppose GT and MLP together are Log-Lipschitz continuous, we can have
1 2 S Lug
H ..... H60] HT)) Fr 1|
SkLoL max (1 - pl |I + - (1
Let T.p Tup l.g2 and use the results Lemma
2 We have
2v 2x
I 2 r S kLg max
do
+1 ||50) - -S ||-
(23)
3
5()
2
x A
Now, plug in the results of Lemmal
We have
1| Z11E S 2kL max
2v 2
vd.
+ 1)
1)
2n
X
1||
(24)
8(5)
2 1
Let c(5)
21 8(3)
we finish the proof.
Q.E.D.
22
A
Remark B.1 From the intermediate result Theorem we can have the following result.
2
2x(3)
Vde
|| 2|r & kLS max
+
[|5() -5:0)
(25)
3
8G)
2 Xain
It indicates that if two input graphs are similar to graphs in the training set, the visualization results should be similar.
It is possible that very different X produce similar S because datasets can have similar internal relation structures. Hence, it guarantees the cross-domain generalization ability to some extent.
C PROOF OF LOss DESIGN
We first show Eq. 7 special case of the Bregman divergence.
Proof: Let a [u] Z.[u]lii E.,, (1+ - which is normalized similarity
(1+ (1+ M Z, (-)l)))
value, applying to 2; and Z,- Let (x(x)) = x log( we have
K(x,v) = x log(rr) - y ylog(v) (1 + log(z)) = <olo((
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We that the Bregman divergence is reduced to the KLD loss. Hence, Eq. is special case of Eq.
(6).
Q.E.D.
Then, show Eq. (8) is special case of the Eq.
Proof: Let (xx) THazt Let (xx) = 3 which is strictly convex. We prove bu, is a reduced
form of Bregman divergence in the following. Let (xxx) _=²²" we have
1 K(z, v) "²² -/- -
(y. v) - y)²
We see that the Bregman divergence is reduced the MSE loss. Hence, Lu, is a reduced form of Bregman divergence. Since A(t) is constant during the loss calculation. Eq. (8) is linear combination of Bregman divergence by using properties in (Nock et al. 2016).
Q.E.D.
D SIGN-COUNT BASED SIGN FLIPPING ALGORITHM FOR POSITIONAL. ENCODING
The detailed process is shown in Algorithm D
Algorithm Sign-Count based Sign Flipping for Positional Encoding
Input: positional encoding E R Nxd. from Eq. 33;
I: for E (1.....d ) do
2: v t P(;
3: n_pos sum(bool > 0)); Mcount the number of positive elements in
4:
n_neg f s sum(bool (v < 0)); /ccount the number of negative elements in w
5:
if pos < n neg then
6:
<- - v
7:
end if
8:
P u; 8: end for
9:
Output: Sign Flipped Positional Encoding P.
E EXTENDING TO LARGE DATASETS
There are two methods to utilize our AutoDV on large datasets. The first one is directly inputting the large dataset into the model. This method is limited by the memory space. example result is in Figure 6a| The second method is the proposed batch-based method. The method is scalable in large datasets. As described in Section 3.4 The process is detailed in Algorithm An example of visualizing CIFAR10 with 20000 points in Figure 6b
Algorithm 2 Batch- AutoDV for Extending to Large Datasets
Input: Trained AutoDV model fa. input dataset X, anchor size MA;
I: [x())Xt)
X (4)} split(X, .); // split dataset into q chunks.
2: c + X.size/ /MM;
3: A KMeans (X,c)
4: Z+0 +-0: 0;
5: for E {1..... q} do
6:
Xin = A AUX (
7:
(P), (5) t- Extract PEs and similarity matrix from X
8:
Zout + fo((P) (S})
9:
Ž x-2 Ž U Zout [M :]
end for
Output: Low-dimensional embedding for large dataset 2.
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NMI: 92.56, SC: 84.16
NMI: 73.75, SC: 63.25
Class 0
Class 1
Class 2
Class 0
Class 2 Class
Class 1
(a) AutoDV-UMAP on CIFARIO with 10000 (b) AutoDV-UMAP on CIFARIO with 20000 points.
points.
Figure 6: (a) result extending AutoDV to a dataset with 10000 points by direct input. (b)
the result of extending AutoDV to dataset with 20000 points by the batch-based method in section 3.4
F DETAILS OF COMPUTATIONAL COMPLEXITY ANALYSIS AND COMPARISON
In the training stage, the process involves Bayesian optimization for searching the optimal hyper- parameter of the HDV algorithm, graph conversion, PE calculation, and model training. For t-SNE. the complexity for the searching is ONN?d, + BTN?d'). where B is the number of runs for searching the optimal hyper-parametens and T the number of iterations for training. For UMAP, the complexity is O O(N2d, + rr', where is the number of neighbors used in UMAP. The time complexity for & PEs calculation is (N + &. by utilizing randomized SVD (Hakko al. 2011). Let Wmax represent the maximum width of the hidden layers in the L-layer AutoDV model. The complexity of AutoDV forwarding for one dataset is at most dd since the transformer block has complexity in O(N3). The complexity of training loss calculation is (N?dd). Hence, the final training complexity of AutoDV is O( (BT + Wmax)) as k. de, d', and I. are usually set as fixed constant.
In the inference stage, AutoDV only involves PE calculation from k-scale graphs and model for- warding. Then, the inference complexity is ONN Wmux). A comparison between AutoDV, t-SNE, and UMAP when processing a new dataset is summarized in Table Furthermore, the complexity of our method can be lowered by batch operation, i.e., splitting large graph into qi sub-graphs with M nodes and visualizing them one by one. The complexity will be OKNN, N, More im- portantly, PEs in our method can be pre-computed, which further accelerates our method practice.
G EXPERIMENT DATASETS SUMMARY
Table 6 lists the details datasets used in this paper, including name, size, number of classes, and dimensionality. Here, mentioned in Section 4.1 MNIST, FMNIST, and CIFAR10 are features in latent space extracted by CLIP. Campbell, PBMC68K, Baron Human, and Mouse_reting are filtered the rare cells.
H EVALUATION METRIC DETAILS
Normalized Mutual Information (NMI): NMI evaluates how well the clustering results match the true labels. quantifies the amount of mutual information shared between the cluster assign-
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Table 6: Dataset Summary.
Name
dims
n class
60000)
512
10
FMNIST
60000
512
10
CIFARI0
50000
512
10
Campbell*
13289,
26774
6
PBMC68K*
66332
32738
8
Baron Human
7771
20125
6
Mousc_retina"
8352
6198
5
Palmer Penguins
333
3
Leay_Soobee___Cieee from. Subsequent
9
40
Cirrhosis Patientt Predictio
312
776
3
PIRvision Pori presence detection
15302
56
3
Auction Verification
2043
2
Period Changer
1177
2
SUPPORT2
332
64
2
Wine
178
13
3
Iris
150
4
3
Cryotherapy
90
2
Phishing Websites
11055
2
Sirtuin6 Small Molecules
100
6
2
Land_Mines
338
3
5
Z-Alizadeh.San Sani
606
78
2
NHANES
2278
2
Differentiated.Thyriid. wtwp:eeee.ooooooo..eeeeeeeeeeeee Recurre.e
383
2
RT-IoT2022
123117
94
12
Apeedttiicc
780
31558
2
DARWIN
174
624
2
TUNADROMD
4465
241
3
Toxicity
171
1203
2
Drug
597
196
2
MetroPT-3
1516948
15
2
Accelcrometer.co SaapotterGGroooMooo MorroMMobi__PPaa Phone
31991
6
2
Caesarian Section. Classification Datttc
5
2
NPHA
714
14
3
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ments and the ground truth. To measure the quality of the HDV results, first perform K-Means clustering upon the output low-dimension embeddings. Then, we calculate the NMI of the clustering results. The higher NMI, the better, because objective of HDV is to show the clustering structure within the high-dimensional dataset.
Let U be the set of ground truth labels and V be the clustering assignments. The Normalized Mutual Information is defined as:
2. -TUUV) V)
NMI(U, = H(U) + H(V)
where I [U; V) the mutual information between U and V. and (U) and (V) denote the entropy of U and V, respectively. Concretely,
P(u,v)
I(UV))
ΣE P(u, v) log NEU NEV
P(u)
H(U) - Σ DEU
log P(u), H(V)= = Σ eEV
lou) P(o)
Silhouette Coefficient (SC): SC is also a metric of clustering. It quantifies how well a point is clustered, i.e., how similar it is to own cluster compared other clusters.
For each data point i, define a(i) as the average intra-cluster distance (distance to other points in the same cluster), and b(i) the average nearest-cluster distance (distance to the closest neighboring cluster). The silhouette coefficient s(i) is given by:
b(i) a(i)
sii)
max(a(1), b(i)
The overall silhouette coefficient for the dataset is the mean value of s(i) over all samples:
SC =
s1)
DATA PREPARATION DETAILS
Due to the limited video memory during the training, randomly downsample the datasets to generate several subsets if the number of points in the dataset is less than 3000. To increase the diversity of the training subsets, we first randomly select a number classes, then randomly sample 10 subsets with different sizes from the selected classes. The detailed process is in Algorithm 3 Note that the maximum number of points of subsets is 3000. Since the total number of classes used in the experiments is smaller than 10, we go through all combinations of the selected classes. For image data experiments, we randomly select 500 subsets from MNIST and FMNIST for training, and randomly select 50 subsets for testing. For gene data experiment, we filtered out the NMI less than 10 of the optimal low-dimensional embedding for training and testing. For tabular data experiments, we do the same filtering. Then, we randomly split the whole sampled subsets into training and testing, where 30% is for testing.
We list additional training details not mentioned in Other training details and justifications: the main text in the following.
At the training stage, we pre-computed PEs for all k-scale graphs in advance saving the processing times.
We perform 50 times Bayesian optimization searches for both t-SNE and UMAP.
We list the following justifications for potential questions:
Why filter out NMI less than 10% when generating Z We observe that if the NMI is very small, the results of t-SNE and UMAP will collapse into one dense area. It usually means the training fails at this dataset for t-SNE or UMAP. These datasets are harmful for the AutoDV training since they are meaningless.
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Why filter out the rare cell in gene data experiments? The rare cell is usually present in small portion of the gene data. The portion is usually smaller than 3% according to (Wang at 2024). It could be considered as noise information and hence harmful for the AutoDV training. So, we filter out them. We leave a AutoDV training that robust to the noised structure dataset in the future work.
Algorithm Dataset Downsampling in Training Data Preparation
Input: dataset X, the number of class C, maximum subset size Nmazi
1: Dirain t 0;
2: for E (I....,C) C) do
3: C Catmmiintiinnn....
4:
X, select all points with label in C;
5:
+- Linespace(100, NN 10); // generate 10 subsets with different sizes.
6:
for j E f1...., 10) do
7:
NO f- random(s[]], s + 1]);
8:
X' randomly downsample N' samples from Xa;
9:
Drain <- D U (x'):
10: end for
end for
Output: All sampled subsets Dirain-
J IMPLEMENTATION DETAILS
All experiments are implemented by Pytorch (Paszke et al. 2017) with Deep Graph Library (Wang et al. 2019) NVIDIA GeForce RTX 4090 and Intel Xeon Gold 5117 platform. We set k = 5 and set y0) as [0.1, 0.5, 2, 5] times the median value of the pairwise distance matrix. We utilize SVD as the positional encoding and set de = 64. For GNNs, we utilize a 3-layer GIN with 128 hidden dimensions and 8 8-layer graph transformer with 4 heads and 2048- 1448-dimensional feed-forward layer. A 2-layer MLP head is appended for the dimensionality reduction. All layers are activated by SeLu (Klambauer al. 2017) and layer normalization (Xiong al.. 2020). Unless specified, the model trained for 100 epochs by Adam (Loshchilov & Hutter (017). The learning rate is set 1 x 10 4 with cosine anneal decay. During each batch, there are 18000 nodes processed. The results of (-SNE and UMAP are trained separately. For baseline methods with deep neural networks, we use 10-layer MLP network for fair comparison with ours.
K MORE TRANSFERABILITY RESULTS
We report the SC results in Figure 7 consistently shows a good transferability of AutoDV.
L ABLATION STUDY
Due to limited resources, design simplified experiment setting, where only 5 training subsets are randomly sampled from MNIST, FMNIST, CIFARIO. They are MNIST with class labels in [0, 1, 2, 3. 4], MNIST with class labels in [5, 6, 7, 8, 9], FMNIST with class labels in [0, 1, 2, 3, 4J, FMNIST with class labels in [5, 6, 7, 8, 9], and CIFARIO with class labels in [0, 1, 2, 3, 4]. There is only subset sampled from CIFAR1O. which is CIFAR10 with class labels in [5, 6, 7, 8, 9]. All subsets are with 3000 points. This is the simplest toy experiment setting, where the test dataset remains unseen during the training. We test different types of PE in AutDDV-SNEE, including Laplacian PE (LapPE), non-negative matrix factorization (NMF), random walk (RRWP) (Ma et al., 2023). SignNet (Lim et al., 2022), and SVD. In this line of testing, there is no sign flip- ping strategy for SVD and LapPE. We test two variants of LapPE, using only eigenvectors of graph Laplacian matrix (LapPE-V V) or both eigenvectors and eigenvalues (LapPE-VS), The results are re- ported in Figure Sal where SVD PE performs the best. Although SignNet claims it can handle the sign ambiguity problem well, instead is harmful to our AutoDV model training and inefficient when N; and d, is large.
Effectiveness of PE
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Avg. SC of L-SNE
Avg. SC of UMAP
75
AutoDVV Image
71.17
AutoDV.
70
70
Image
65
65
AutoDV Gone
67.69
47.11
76.11
60
AutoDV- Gene
52.02
47.98
63:24
53
50.89
76 97
48.25
AutoDV-
51,84
53.80
64.28
34.43
50
Imape
Gene
Tabalar
Image
Gane
Tabular
(a)
(b)
Figure 7: Cross-domain transferability performance using t-SNE and UMAP. Each heatmap shows average SC results for (a) t-SNE and (b) UMAP. Within each map, columns denote the source domain and rows the target domain for the first three rows; the fourth row ("TSNE** or "UMAP**) reports the within-domain performance of the optimal low-dimensional embedding. Test sets for each domain are the same as in Tables and
Types
on Different Sign Flippings
80
80
70
70
NMI (%)
50
50
NMI
40
20
20
RRWP
LapPE
LapPE-45
NRF
5VD
Sign
Randem
0
Stm
KLD
BCE
L-fuem
Lando
MSE
(a)
(b)
(c)
Figure 8: Results of ablation studies using different (a) PEs, (b) sign flipping strategies, and (c)
training loss functions.
Effectiveness PE Sign Flipping We fix the PE as SVD and test various sign flipping strategies in AutoDV-(SNE, including random, summation, lo. é1, lz. and fxc. lo is the default SVD result by numpy in Python. Random means that we randomly flip the sign of each dimension of PE. Summation decides the sign based on the sign of the column Algorithm f, f2, and foo are variant of &o by using different norms line 3 and 4. The test setting the same above. The results are presented in Figure 8b Among the strategies compared, the sign-count-bas -baund (fo) flipping method achieves the highest NMI. Although the summation approach yields comparable performance, we adopt the Eo strategy due its intuitive interpretation that the majority sign dominates the overall direction.
of S. En is the adopted strategy in
Effectiveness of Loss Design We test the performance of AutoDV-UMAP under different loss designs, including KLD, binary cross entropy (BCE), local only (L-Lumap), global only (G-Lumup), and mean square error (MSE). MSE is loss similar to i-tSNE (Roman-Rangel & Marchand-Mailn 2019). KLD is the same Lise- BCE is similar to KLD but utilizing the cross entropy. The test setting is the same as Table The results are shown in Figure Sc The proposed loss function Lumap Eq. [aahhives the highest NMI. In contrast, using only the local loss results poor performance, as the initialized model tends to collapse all points into close proximity. This collapse leads to an artificially small local loss value, ultimately causing training failure.
Sensitivity of PE Dim. de: Due to limited time, keep the experiment settings the same described in "Effectiveness PE", where there are only 5 datasets for training and dataset for testing. The results of AutoDV-ISNE are listed below.
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Table Results of different PE dimensions compared with I-SNE.
PE dim.
8
16
32
64
128
t-SNE#
train NMI
76.83
77.70
78.52
78.18
78.12
80.39
train SC
57.43
57.75
57.10
57.34
57.24
54.23
test NMI
78.41
77.15
81.78
82.48
73.24
86.28
test SC
64.61
61.50
62.30
62.43
60.07
67.25
It is seen that setting PE dim. to 32 64 is good choice. If PE dim. is small, the structural information may loss. PE dim. is large, the model could face the problem of underfitting or receive more noisy structural information.
Sensitivity of the number of graphs (k): Since the choice of k will directly affect the model running cost, we tested k 5, show the effectiveness of multi-scale graphs. The detailed selection of sigmas is here.
Table 8: Sigmas used for different & values.
k sigmas
7
9
0.5, 1,2
0.1, 0.5, 1,2,5 00.05, 0.1, 0.5, 1, 1,2,5, 0.01, 0.05, 0.1, 0.5. 2, 10, 20
The results of AutoDV-ISNE varing different k are listed below.
Table 9: Results of different values compared with t-SNE.
k
3
5
7
9
t-SNE*
train NMI
38.32
76.75
78.18
77.86
36.23
80.39
train SC
42.20
58.32
57.34
57.25
53.64
54.23
test NMI
59.83
75.54
82.48
74.08
53.27
86.28
test SC
45.79
57.60
62.43
56.41
48.12
67.25
is seen that less or more will lead to a very low training NMI. is small, the structural information is limited to train the model. If k is large with too large sigmas and too small sigmas, the structural information will become noisy leading to difficult convergence.
Justification of Hyper-pand parrmmere Selection during AutoDV Training: As shown above, al- though there still are hyper-parameter selections for AutoDV, two core dyper-parametens de and k. can be reasonably decided. For other syper-parametery such learning rate, hidden dimension, etc. All deep learning-based methods need to tune these hyper-parameters. In AutoDV, luckily, we can also tune these hyper-parameters, including d, and k:, by spliting the original training into training and validation sets. Then, the papee-paraeeeess can be tuned according to the model per- formance on the validation set, which is the same any supervised learning. Hence, the training stage, AutoDV will not meet the hyper-paramett tuning challenge in the unsupervised setting as discussed in Section 2
M MORE QUALITATIVE VISUALIZATION RESULTS
We here present more visualization results on training set and test set. For image data from CLIP, the results on the training and testing set are in Figure 2 to 10 and Figure II to [2] respectively. We show the results that contains 2 to 8 classes. It is seen that AutoDV is little underfitting when the number of classes becomes large. It may be because training data with large number of classes is small. Such imbalance leads a biased training. This problem can be solved by carefully generating the subsets for training. Nevertheless, the performance of Au on dataset with a small number of classes is visually acceptable and can be well generalized to the unseen test dataset.
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1-SNE, NMI 100 00, SC: 66.12
UMAP", NMIL 100.00 00, SC: 66.32
AubaDWiSNE, NMI: 100,00, SC: 100,00 NuboDVUMAe, NMI 100 00, SC: 100.0C
(a)
(b)
(i)
(k)
USSEE NMI
UHAP", 83 S5, SC: 65.9
AutoDI-ISNE, NMU: 62.08, SC: 62,08
AutoDV-UNAP, NMI: 31, SC: 75.31
(m)
(n)
(0)
(p)
ISNE: NME. 76.24. SC: 57.39
UNAP: NME 77.15, SC: 57.39
AutoDV-LSNE NME: 72.13, SC: 72.13
AutoDV-UNAP, NMI: 77.54, SC: 77.54
(g)
(r)
(L)
Figure Visualization of t-SNE", UMAP" AutoDV-LSNE, and AutoDVUMMAP on training datasets of image data experiments. Each row represents the different number of classes.
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ISNE:, NMI. 80.31, SC. 55.42
UNAP", NMI: 80.93, SC: 55.42
AutoDV-tSNE, NML 75.26, SC. 75.26
AutsDV.UMAP, NMI: 80.30, SC: 80.30
(a)
(b)
UNAP: SC:
AutoDViUNAP,
Figure 10: Continued visualization of t-SNE", UMAP", AutoDV-ISNE, and AutoDV-UMAP on training datasets of image data experiments for 7-class data and 8-class data.
ISNF
AutsDI-ISNE, 59.16,
(b)
(c)
1:SE"" NMI 84.37, SC 67.61
UNAP" NML 88 96, SC: 67.61
AutoDi-ISNE, NML: 80.92, SC: 80.92
AutoDi-UNAP, NMI: 83.82, SC: 83.82
(e)
(f)
tSNE", NMLL 86.86. SC. 65.78
UNAP", NMI: 88 92, SC: 65.78
AutoDV 1SNE. NML: 83.89, SC: 83.89
AutoDV-UNAP. NMI: 80.78, SC: 80.78
i
kk)
(I)
Visualization of t-SNE*, UMAP" AutoDV-ISNE, and AutoDV-UMAP on testing datasets of image data experiments. Each row represents the different number of classes.
Figure 11:
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ISNET. NMI 62.
UNAP", 88 61, SC: 62.78
AutoDX-ESNE, NM:: 76. 80, 76,80
AutoDVAUNAP, NMI: 56, SC: 74.56
(a)
(b)
(c)
ISNE:, NML 84.02. SC 62.24
UNAP: NML 94,90, SC: 62.24
AutoDV NML 66.70, SCI 66.70
AutoDV-UNAP. NMI 74.67, 67, SC: 74.67
(c)
())
(h)
tSNE", NML. 79-19, SC. 56.49
UMAP" NMI: 83-23, SC: 56.49
AutoDV-ISNE, NMLL 66,90, SC: 66.90
AutsDVIUMAP, NMI: 73.49, Sc: 73.49
(i)
(k)
UMAP", SC:
AutoDAAISNE, 60.17,
AutoDV-UMAP, 68,
(m)
Figure 12: Continued visualization of t-SNE UMAP" AutoDV-ISNE, and AutoDV-UMAP on test datasets of image data experiments from 5-class data 8-class data.
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N USE OF LARGE LANGUAGE MODELS
We use LLM to polish our verbal writing as is really useful.
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O TRAINING DATA DIVERSITY STUDY
We conduct series of experiment to study how the training data diversity affect the model perfor- mance and generalization ability. It includes structural diversity, training sample size, dimensional- ity, domain diversity.
How do the number of training data and the diversity jointly affect the performance? We keep the same setting as that in the Table Then, we vary the number of training data in [10, 50, 500, 1000], and see how the performance changes on the AutoDV-UMA. Note that if we increase the number of training data under such setting, both training sample and training diversity will be increased because the training data are uniformly subsampled. The results the same test data are shown below in Table 10
Table 10: Training Sample Size and Diversity v.s. test NMI/SC
training size
10
50
500
1000
UMAP#
test NMI
57.19
58.72
73.28
74.17
80.45
Test SC
51.11
52.01
70.41
71.30
68.54
In the results, we see that if the training sample size becomes large, the performance a fixed testing set will become better.
To further understand how the training sample size and training sample diversity affect the model performance separately, we conduct the following studies.
How does training-data structural diversity affect performance? We define training-dat data di- versity terms of geometric structural diversity. We construct a family of synthetic datasets with controlled structures, where the geometric structural diversity is controlled by the variety of cluster structures present in the training set.
Concretely, we generate datasets from mixtures of Gaussian components in 20-dimension space, so that each dataset contains exactly c well-separated clusters. We vary from to 9, and refer to these datasets c-cluster datasets. Thus, each value of corresponds to a distinct geometric structure.
To study the effect of structural diversity, gradually enlarge the set of structures used for training. Let the structural coverage of the training data the set of cluster configurations included it. We consider sequence of training regimes where the coverage increases from {1-cluster), { (1-cluster, 2-cluster),
(1-cluster, ..., 8-cluster).
In other words, the k-th regime (k = 1...., 8) uses all datasets whose number of clusters c satisfies 1 S c < k. so that the structural diversity of the training data increases with k. We then evaluate how the model's generalization ability changes as this structural diversity grows. The training sample size fixed at 10. For the testing data, we use a dataset from 9-cluster datasets. We use AutoDV-UMAP with 10 epoch training. Qualitative and quantitative results are reported in Figure 13
It is seen that AutoDV-UMAP training with 1-cluster data can generalize a lot on 9-cluster data but is not perfect. As the coverage or structural diversity increased, the generalization ability gets better and better. On the one hand, indicates AutoDV cannot generalize well if the geometric structure of the test data is never seen. One the other hand, the results indicate the more diverse in the training data, the better the generalization.
How does the number of training data solely affect the performance? Here, we use training data from (1 (1-cluster, 2-cluster) with different number of training samples in [10, 50, 100, 250, 500, 1000]. The test data is the same above, i.e, dataset from 9-cluster. The performance curve in terms of test NMI is illustrated Figure [4] The result indicates that increasing the number of training sample can help the generalization, but it is very limited. Compared with the result in the bottom right in Figure [ the performance can easily increase to 1.0 by increasing the training data diversity. However, here the number of training data is increased to 1000, the performance still lower than 0.98. means solely increasing the training sample cannot efficiently help the model performance.
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Auto UMMPP- SC
NUTSOV-UMAP. 2C
AUAPDVUNAP: SC
AUTODV UMAP: 4C
UMAP Embediing of SCluster
-0-1
10.75
0.50
3.25
IA)
(C)
Auto Daw.--AAAIAPPPPPM SC to 9C
AutaCVAIMAP: 6C
AutoDNuIMAP: 7C to 9C
AutaDALMMP: BC 9C
Diversity vs. Test NMI
-0
Teal Wiltion on Clusse
6.5
-0.
6.4
-0.
0.0
22
6-
0.2
02
0.1
06
0.8
08
0.6
6.4
0.2
26
0.2
0.1
Covcroge
Figure 13: Figure (A)-(H) are qualitative visualization of different coverage. The upper right corner the UMAP visualization of the test datasets. The bottom right corner is NMI performance curve varying training data diversity.
Number of Training Datasets v.s. Test NMI with Fixed Structural Diversity
1.00
0.98
Test MMI on 9 Cluster Data
0.96
0.94
0.90
600
Number of Training Datasets
Figure 14: Performance curve of varying the different training sample size with fixed structural diversity. Training data coverage 2-clusstr
How does the dimension of training data affect the performance? Here, we study the problem by varying the dimension of 2-cluster datasets. We test the performance of AutoDV-UMAP trained on 2-cluster datasets in [2, 4, 8, 16, 32, 64, 128, 256, 512] dimensional space. The test data is from 2-cluster and 9-cluster in 2-dimension space and 1024-dimension space, separately. The results shown in Figure [5 In the results, as expected, the dimensionality of training data will not affect the performance if the test data share the same geometric structure with the training data though they are in different dimensions (Figure 15]a) and I5fc)). In addition, it is of interest to find that when the training data come from higher-dimennionall space, the model generalizes poorly lower- dimensional test data (Figure 15 (b)). In contrast, when the training data are low-dimensional and model evaluated on higher-dimensional data, the generalization performance remains strong (Figure 15 (d)). This asymmetry may be related to the fact that, as the dimensionality increases, pairwise distances between samples drawn from a Gaussian distribution tend to grow, altering the geometry of the data manifold.
How does the domain diversity of training data affect the performance? We argue that the domain diversity is not the key to affect the performance, while the structural diversity still the most important factor. To understand this, we illustrate results of AutoDV-ISNE on image data.
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Number Dimension Test NMI with Fixed Diversity
Number ber Dimension Test NMI with Fixed Diversity
1.05
Rest MM1 on 24 Cluster Data
2.00
0.850
0.825
0.775
0.750
0.725
100
200
300
400
500
100
200
300
400
500
Number of Dimension
Number of Dimension
(a) Transfer from 2-cluster to 2d 2-cluster data.
Transfer from 2-cluster 2d 9-cluster data.
Number of Dimension Test with Fixd Diversity
Number of Dimension Test Fixed Diversity
1.05
Test NM on 1024d Cluster Data
1.00
3.1
1024d
100
200
300
400
500
100
200
300
400
500
Number of Dimension
Number of Dimension
(c) Transfer from 2-cluster to 1024d 2-cluster data. (d) Transfer from 2-cluster 1024d eluluseer data.
Figure 15: Performance on different dimensions and geometric structures varying training data di- mensions with fixed training diversity.
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CIFARLO S-dass Test NKI: O 6940
CIFARIO S-class Test MM: 0.3156
1.2
1.0
10-
0.6
0.2
15-
-0.4
-0.6
-0.6
-02
02
-20
-13
20
(a)
(b)
Figure 16: Visualization and test NMI on 5-class CIFARIO dataset. (a) Performance of model trained on 2-class data from MNIST and FMNIST. (b) Performance of model trained on 5-class data from MNIST.
Due to limited time, conduct toy example. First, randomly sample 2-class datasets from MNIST and FMNIST for training. The training data is with high domain diversity. Second, we randomly sample 5-class solely from MNIST to train another model. The corresponding training data is with low domain diversity. Finally, we compare the testing results on a 5-class dataset from CIFARIO. 10. The results shown in Figure [6] seen that increasing the domain diversity does not help with model generalization ability.
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P ADDITIONAL METRICS FOR EVALUATION
We provide results using more evaluation metries of Table The distance rank correlation cal- culated by spearman rank correlation. The triplet preservation is consistent with Wang et al. (2021) The result are in Table T t-SNE* and UMAP*
It is seen that our method can obtain comparable performance with
Table 11: Performance comparison on Image data (values mean, subscript indicates = variance, all in %).
Metric
t-SNE*
UMAP"
Default t-SNE
Default UMAP
AutoDV-ISNE
AutoDV-UMAP
Trust
93. 13.18_.60 58.991
94.3211.61
93. 20.47
95.0611.19
87.34
88.6211.99
Trust
92.32_4.91
93.92+1.62
91.95
94.46.1.50
87.6221184
88.7821.00
Trust@50
92.24_3.9
92.8442.35
91.30
93.31:1..0
88. 24
89.41
Continuity@
95.58-2.02
97.53+1.20
14.79
98 18.03=20.51
93.34=1.32
93.97
Continuity 10
94.59_2202
95.35+1.44
93.68 68.6882..0
95.77-00.0
92. 92.10=11.6
92.92+
Continuity @ 50
93.84_1.90
93.21
92. 89
93.73:11.30
91.38 38.88...7
92.21
Rank Correlation
65.58 15.74
62.17
62 08 14778
64.86.1..e
62.90 10.15
65.19
Triplet
22.41
72.48
73.06 1.98
73.49.1.89
73.19 3.66
74.20
CA-knn @
10.60
90.45
86.95 9:.09
89 89.99.44.56
82.90 82.99_10.33 10.37
86,23 58
CA-knn @
89.77
92.41 92.41
89. 2.373
92.69 1:3.79
86.61 do
89.29
CA-knn@05
88.63_9.0
91.49
88.54 14.14
91.53
86.08
88.3217.14
NMI
77.04
80.4510.64
71.71
79.72
68.70 2..04
73.28
SC
63.32_0.c2
68.5446.58
47 47.24=0.91
67.61
55.15=6.67
70.41
KNN Overlap@
8.17
8.91 1:3.0
10.67 11.80
10.9614.1s
2.05
2.441/200
KNN Overlap 10
21.61 21.61 28.54
26.43
2..02
29. 29.62 17.77
12.4446.78
50
41.36=11.02
42.00+9.63
41.51=99.0
43.29
29.33=11.54
31.84+12441
Jaccard
8.17
8.91
10.67 11.83
10.96
2.0511.73
2.44
@accard 10
13.33_a.07
16.60
15.02=4.87
18.88
6.27
7.28
@accard@50
27.96
28.084a.5)
27.93
29.21+a.16
18.59
20.57+10.62
The results of Gene data with metries are in Table 12
that the results are basically consistent with the results in Table 3 AutoDV-ISNE and AutoDV-UMAP outperforms t-SNE and UMAP terms of many metries such Rank Correlation and Triplet preservation.
Table 12: Performance comparison Gene data (values are mean, subscript indicates + variance, all in %).
Metric
E-SNEF
UMAPE
Refaulre-SNE
Default UMAP
AutoDV-SNEE
AutoDV-UMAP
Trust 1
36.46-25227
53.67 24.88
33..442..6
54.34g-477
53.632-.12
53.75
Trust@
35.8825.54
28.
23.59-4.02
54.01 92
54.4724.00
54.32+4.77
T0
58.7627.30
55.20
55.65
55.121s.0
57.7225.88
56.6815.50
Continuity @
74.24-0.80
48. 18.20
68.7 688.7=144.5
63.53+11
89.06=33.12
65.27+9.90
Continuity 10
74.52225.65
G6. 79..99.2. 1
69. (89.52-13.77
66. 66.4827.22
70.33 70.33
60.0126.05
Continuity 50
26.03
61.82 2.678
14.44
63. 63.744..50
73.79 23.79
62.7315.92
Rank Conrelation
12..55
10.44
23. 23.28
3.07=11.88
48.67 11.11
20 20.37 13.35
Triplet
63.29
54.02=5.21
38. 38.07 =7.30
52.63
64.044.3.10
58. 03.00322..5
CA-knn
90.3426.24
85.54_7.02
81.16
85.4746.78
U1.37=5.ar
02.89444225
CA-knn 10
92.81 42.11
00.35=44.4
87.08=6.20
90. 90.20+4.70
02.58
94. 04.27 +3.377
CA-knn@ 50
91.02=4.51
90.01+4.87
86.31
89.89
91.23
92. 02.154-4.00
NMI
32,75 32.73=30.76
28 34.744
15.67 22.9
22. 22.45
33.22=25.77
33. 33.03::24.99
SC
34.43+44.6
47.98=20.10
35.8 15.84=13.33
47.98+24.0 91
47 47.11=10.82
47.98
KNN Overlap@
0.7010.46
0.91 10.74
0.32....34
1.55
0.21 10.22
0.14
KNN Overlap 10
2.83
3.06
1.97
3.87=22.4
2.07
1.74
KNN Overlap@50
13.24=9.26
10.16477.58
9.96
10.12#7.27
11.05
9.02
@accard
0.70
0.91 10.74
0.32
1.55
0.21
0.14
Jaceard @ 10
1.82
1.70
1.19
2.16
1.364n.59
0.99
Jaccard 50
9. 9.76+6.92
5.65
6.4446.8
3.62
8.43+60.25
5,31
The results of the Tabular data is in Table 13 Similarly, it is seen that AutODV-SNE/UMAP out- perfoms t-SNE/UMAP not only in terms of NMI and SC, but also many metries such as CA-KNN, Rank Correlation, and Triplet preservation.
We noticed that despite AutoDV can obtain good CA-knn performance indicating a fairly good local preservation, the KNN Overlap and Jaccard not good enough. This problem can be solved by adding new regularization term during the training to further pay attention to the local structure. We leave this for future improvement.
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Table 13: Performance comparison on Tabular data (values are mean, subscript indicates + variance,
all in %).
Metric
ESNEE
UMAP#
Defanit F-SNE
Detault UMAP
AutoDV-ISNE
AUDDV-UMAP
Trust
98.41 11.1
91.11=9.00
98.23
97.7821.21
91.31
86.50g11
Trust 10
97.56 1..5
90.18_9.81
97.39 a3.31
97. 27.26
90.2249.66
84.17+11.88
Trust@50
45.4743.55
10.07
95.77+3.87
94.1245.90
89.39+9.71
81.98
Continuity @
98.5121.05
93.22_6.31
98.52g1.07
98. 22.8822..11
95.9045. 10
93.11
Continuity @ 10
97. 1..9
89.99_7.96
97.9 97.944
97. 07.60
94.75446.06
90.10+7
Continuity @0
96. 96.3043.04
84.67
96.85 26.85
93. 03.58
93.25
86, 49.29
Rank Correlation
55. 22.201
35.19 06
65.43194.08
40. 20.99
38.59 58
40.10 26
Triplet
72.33+9.52
11.17=11.94
+10.68
12.11
73.93+9.25
67.32+12.8
CA-knn 6
94.61
94.26_s.30
24.34
93. 93.77
94.49
94.69
CA-knn 10
93.88210.0
94.25
93. 33.59
93. a0.001
94..77
94.39
CA-knn
91.95 10.47
91.36 11 56
91. 91.81
11.11
92.67
93.20
NMI
80.92.80+12.20
24.80_16.2
23.58
13:12.0
33.445221.00
35.15:10455
SC
44.42
64.46 in
43.87 43.87
61.81 :19.1
48 18.25
64.28
KNN @verlap@)
30.0 30.01
9.45
31.18+10.06
17 17.30
21.76
19.51
KNN Overlap@1 10
117.66
28.56
47.46218.4
43.09
31 31.64422.58
24:31 2::.000000
KNN Overlap@ 50
58. 14.604
38.40
59.72
54.81
16.30
13.
Jaccurd I
30.01:15.82
9.45
31.18+40.96
17.30+0.08
21.76426.01
19.51
Jaccard 10
35.74417..10
20.23=15.01
36.50 36.50=11.00
31.59.14.07
24.49421.83
18.44
Jaccurd @
45. 16.
26.97=18.29
46.71
41.26::1.98
35.07
23.48
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AUDIEN brrbodd Cirid
AUDSY USAP Exbeddingg diee
-24
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-1
-38
-25
33
60
05
Emozading Crcle
Irioadingg
15-
-4
(a)
(b)
Figure 17: Visualization on Circle dataset. Circle samples 5000 points uniformly on the unit circle and then bin them by angle into 10 equal angular sectors (arcs). (a) Performance of AutoDV-ISNE and default t-SE. (b) Performance AutoDV-UMAP and default UMAP.
Q GENERALIZATION BOUNDARY AND FAILURE CASE ANALYSIS
We analyze how far away our model can generalize to a new unseen dataset. The experiment re- ported so far using classification centric datasets, where these dataset may share some intrinsic structurally similarity. So, can generalize well. We would like to see whether it has any fail- case. Here, we further explore the generalization boundary of our models by answering two questions.
Q1: Can AutoDV trained on image data generalize to non-classification centric dataset? Rather than testing AutoD-UUMP and AutoDV-ISEE on classification centric datasets, we test AutoDV-UMAP and and AutoDV-ISNE trained on image data on some dataset focusing on mani- fold structure, such as Circle, Lineage, Mammoth, which is also used in Wang et al. (202T). The results are compared with default UMAP and default t-SNE. The results of Circle is in Figure [7 is seen that AutoDV can successfully generalize the circled structure. The results of Lineage is in Figure 18 It is seen that AutoDV can allocate the point a line though they are not a straight line. In contrast, t-SNE and UMAP fail do The results of Mammoth is in Figure [9 It is seen that our model finally fails to generalize to datasets emphasizing manifold structure and local patterns.
AutoDV fails to generalize to Mamooth because the training data is classification centric. The model does not learn the manifold structure during the training. The problem can be solved by training an AutoDV model using data emphasizing manifold structure such as Swiss Roll and Swiss Hole. Then, further conduct the experiment where an AutoDV model is trained by default t-SNE results of Swiss Roll and Swiss Hole. We report the test results newly sampled Swiss Roll and Swiss Hole, and Mammoth in Figure 20 [T] 2nd It seen that AutoDV can successfully showing the roll and hole in the Swiss Roll and Swiss Hole. In addition, AutoDV can correctly allocate the legs and body of the mammoth with local structure preserved. Note that Mammoth is totally new to the AutoDV model showing strong generalization ability of our method.
Q2: Can AutoDV model generalize to dataset with high-noise, or overlapping clusters, or even random noise? We select AutoDV-UMAN model trained 20 2-cluster datasets for the analysis. The definition of 2-cluster data is described in Appendix O
High-noise: We study global noise and local noise. Specifically, we randomly sample noise from uniform distribution in the test data the global noise. We randomly perturb
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MANDH-SNE brbbeding of ur Greage
KROOHUMPP Smrecd Livoage
-056
-146
-20
-22
18
-00
-53 -12
(a)
(b)
Figure 18: Visualization Lineage dataset. Circle is bunch of Gaussian blobs arranged in straight line high-dimensional space. (a) Performance of AutoDV-SSNE and default t-SNE. (b) Perfor- mance of AutoDV-UMAP and default UMAP.
66
-2
ESRE Emtbedd to of Nanmeth
UWAP Erboiding Farmsth
(b)
Figure 19: Visualization Mammoth dataset. (a) Performance of AutoDV-ISNE and default t-
SNE. (b) Performance AutoDV-MMAP and default UMAP.
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Tretnnding
b-SH Frbbedding
AstID)-ISM Embedding
13-
23.
00-
Figure 20: Visualization on newly sampled Swiss Roll dataset. (left) Performance of default UMAP. (middle) Performance of default t-SNE. (right) Performance of AutoDV-ISNE trained Swiss Roll and Swiss Hole.
Eniostlling of
Eribaciding
Astotkiche trlleiding
66
Figure 21: Visualization on a newly sampled Swiss Hole dataset. (left) Performance of default UMAP. (middle) Performance of default t-SNE. (right) Performance of AutoDV-SNE trained on Swiss Roll and Swiss Hole.
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Exriccddnng Embbeddnn Eribeldingg
-10
Figure 22: Visualization Mammoth dataset. (left) Performance of default UMAP. (middle) Per- formance of default t-SNE. (right) Performance of AutoDV-ISNE trained on Swiss Roll and Swiss Hole.
AutoDV-UMAP: 9Cluster with global uniform noise
UMAP: 9Cluster with global uniform noise
0.55
12.5
0.50
10.0
0.45
7,5
0.40
5.0-
2.5
0.30-
0.0
0.25
2.5-
0.20-
5.0
Figure 23: Visualization of 9-Cluster dataset with global noise using AutoDV-UMAP trained 2-Cluster data (a) and UMAP (b). Red points indicate the noise.
each points within radius using a uniform noise for the local noise. The test set is a 9- cluster dataset with 1500 points in 1024 demension space. The results of global noise is Figure 23 The results of local noise with small radius and large radius are in Figure 24 and Figure 25 respectively. It is seen that if the data contains global noise, our AutoDV model can effectively recognize the noise and keep the original cluster structure. For the local noise, the AutoDV model can correctly show the location of the noise.
We show results of the overlap cluster in 3 degree, low, middle, and high. For better understanding. we use 2-dimension 2-Cluster data for testing. The original data is also illustrated. The results are presented in Figure 26 27] and In the results, AutoDV can still illustrate the 2-cluster structure while UMAP tend to split the cluster due to the overlapping.
Overlap cluster:
Random noise: We directly visualize 3 types of noise with zero mean, Gaussian noise, uniform noise, and Laplacian noise. The results are shown in Figure 29 30 and 31 It is seen that AutoDV tends to form a 2-cluster structure. It is because the model is trained with 2-cluster datasets. However, it is better than UMAP terms of showing randomness.
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AutoDV-UMAP: 9Cluster with local uniform noise
UMAP: 9Cluster with local uniform naise
0.55
0.50-
15
0.45-
0.35-
S-
0.30-
0.15-
6.2
0.0
0.2
19
(b)
Figure 24: Visualization of 9-Cluster dataset with small radius local noise using AutoDV-UMAP trained on 2-Cluster data (a) and UMAP (b). Red points indicate the noise.
AutoDV-UMAP: 9Cluster with local uniform noise
UMAP: 9Cluster with local uniform noise
15-
0.2
0.0
0i2
0'4
0.6
-10
-5
5
10
15
(6)
(b)
Figure 25:
Visualization of 9-Cluster dataset with large radius local noise using AutoDV-UMAP
trained on 2-Cluster data (a) and UMAP (b). Red points indicate the noise.
AutoDV-UMAP: Overlap 2Cluster
UMAP: Overlap 2Cluster
original: Overlap 2Cluster
7.5
5.0
0.0
0.2
-2.-
-3
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-5.0
-0.55
0.00
0.25
0.50
0.75
10
-5.0
-2.5
0.0
2.5
5.0
(b)
(c)
Figure 26: Visualization of 2-Cluster dataset with low level overlap using AutoDV-UMAP trained on 2-Cluster data (a) and UMAP (b). (c) is the original cluster allocation.
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AutoDV-UMAP: Overiap 2Cluster
UMAP: Overlap 2Cluster
original: Overlap 2Cluster
15
0.6
0.4
0-
5-
-0.2
-5-
-0.5
0.0
0.5
5 (b)
10
2
(c)
Figure 27:
Visualization of 2-Cluster dataset with middle level overlap using AutoDV-UMAP trained on 2-Cluster data (a) and UMAP (b). (c) is the original cluster allocation.
AutoDVAUMAP: Overlap 2Cluster
UMAP: Overiap 2Cluster
original: Overlap 2Cluster
0.8
12.5
0.6
10.0
7.5
5.0
-2.5
(a)
(b)
(c)
Figure 28: Visualization of 2-Cluster dataset with high level overlap using AutoDV-UMAP trained on 2-Cluster data (a) and UMAP (b). (c) the original cluster allocation.
AutoDV-UMAP: Gaussian Noise
UMAP: Gaussian Noise
original: Gaussian Noise
0.5-
10
0.3
0-
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0.00
0.25
050
-5
10
(b)
Figure 29: Visualization of 2D Gaussian noise using AutoDV-UMAP trained on 2-Cluster data (a) and UMAP (b). (c) is the original Gaussian noise allocation.
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AutoDV-UMAP: Uniform Noise
UMAP: Uniform Noise
original: Uniform Noise
15
15
1.0
0.5
0.0
0.2
0.0
-0.2
5-
-0.50-0.25 0.25 0.50 (a)
(b)
(c)
Figure 30: Visualization of uniform noise using AutoDV-UMAP trained on 2-Cluster data (a) and
UMAP (b). (c) the original uniform noise allocation.
AutoDV-UMAP: Laplace Noise
UMAP: Laplace Noise
original: Laplace Noise
12.5
10.0
7.5
5.0
2.5
0.0
-2.5
(a)
(b)
(c)
Figure 31: Visualization of Laplace noise using AutoDV-UMAP trained on 2-Cluster data (a) and
UMAP (b). (c) the original Laplace noise allocation.
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Entedding
Emberding
AutHRMARCA Emtediing
6
45.
10
Figure 32: Visualization a Swiss Hole dataset. Performance of PCA. (b) Performance of default t-SNE. (right) Performance of AutoDV-PCA trained on Swiss Roll.
PCA Scheedillingg mammeth
3SME Erddadddngg mammothh
ALt:PWiP Embedding olimmmmcth
170
100
12-
-100
-108
Figure 33: Visualization Mammoth dataset. (a) Performance of PCA. (b) Performance of default
t-SNE, (right) Performance of AutoDV-PCA trained on Swiss Roll.
R EXTEND TO LINEAR DIMENSION REDUCTION METHODS
We further explore how good AutoDV is if it is supervised by linear DR method, such as PCA. Due limited time, we conduct the experiment using synthetic dataset similar Q1 in Appendix Q Specifically, train AutoDV-PCA model using Swiss Roll and test the performance Swiss Hole and Mammoth datasets. The results are shown in Figure 32 and 33 is seen that AutoDV-PCA has similar result to the original PCA validating proposed Autoly framework.
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Delecd: I-NNE N4M:: 0.3996
AsteDi-iSEE NMH: 0.7502
Deleadi LIMAP, NMN 6,7439
NAtDVVIKAP. NMI: 0.7764
Figure 34: Visualization of Mouse Retina subset with 3 classes. (a) Default t-SNE, (b) AutoDV.
ISNE, (c) Default UMAP, (d) AutoDV-UMAP.
S MORE VISUALIZATION ON GENE AND TABULAR DATA
We select some representative results in Gene and Tabular experiments, and compare the visual- ization with the default t-SNE and default UMAP. The results of Mouse Retina with classes are in Figure 34 The results of PhiUSIIL with 2 classes are in Figure 33 The results of Wine with 3 classes are in Figure 336 It is seen that both AutoDV-SNN and AutoDV-UMAP show a better cluster structure than default t-SNE and default UMAP. For datasets with classes, present the results of RT-IoT2202 with 12 classes and Forty Soybean Cultivars from Subsequent Harvests with 40 classes in Figure 37 and Figure 38 respectively.
In some cases, the proposed AutoDV can be better than the default I-SNE/UMAP or even than /USPP, can be understood from perspectives.
Both t-SNE and UMAP build a single neighborhood graph (or similarity matrix) on the target dataset and optimize embedding directly from that graph. Their behavior is there- fore controlled by one neighborhood scale (perplexity or n_neighbors) and by the local sampling density of the current data, which makes the result sensitive to noise, density variations, and hyper-parameters, and limits their ability to capture complex geometric structures in real-world datasets. In contrast, AutoDV converts each training dataset into multiple k-scale graphs with different bandwidths and trains a neural network to map these multi-scale similarity patterns to dow-dimeniional representation. Trained diverse set of datasets, this network learns a data-driven prior that reconciles different structural scales and is robust spurious local connections. So, AutoDV yields more stable and expressive embeddings
The local-noise noise experiment in Figures 24 and 25 in Appendix Q) illustrates this difference concretely. t-SNE and UMAP treat all points symmetrically and do distinguish "noise" from "normal" points; they only try to preserve high-dimensional neighbor rela- tions. Local uniform noise points typically lie close so they enter the KNN graph as strong neighbors of the cluster points. In the t-SNE KL objective and the UMAP cross-entropy objective, breaking these nigh-dimensional neigh- bor edges incurs a large penalty, whereas accidentally adding extra neighbors is penalized much less. Therefore, it always cheaper for default t-SNE/UMAP to pull the noisy sam- ples into the clusters than to isolate them, which explains why the noise is visually mixed with the cluster cores in the default UMAP embeddings. In contrast, AutoDV is robust to such spurious local connections, and can correctly visualize the shifting caused by local noise. When facing datasets with more complex structure, such property can better reflect the pair- wise relative position in high dimension.
cluster in the original space,
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10
20
6.3
-14
-35
-24
(9)
Figure 35: Visualization PhiUSIIL with classes. (a) Default t-SNE, (b) AutoDV-LSNE, (c) Default UMAP, (d) AutoDV-UMAP.
Default L-SNE, NMI: 0.3757
AsteDIASNEE, NMI: 0,2078
Defeudt USAP. NME:-.3996
ActeDHAAMAA.. NMME: 0.8050
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Figure 36: Visualization of Wine with classes. (a) Default t-SNE, (b) AutoDV-SSNE, (c) Default
UMAP, (d) AutoDV-UMAP.
Detbult E-EEE NMI: 3453
AUFRON-INEE, AM): 0.912
Defoult UMAP, 0,3342
AUTODN-UMAP. NMI: 0.3537
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Figure 37: Visualization of RT-1oT2022 with 12 classes. (a) Default t-SNE, (b) AutoDV-SNNE, (c) Default UMAP, (d) AutoDV-UMAP.
45

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Published as a conference paper at ICLR 2026
Delaul L-SNE, NME 0.5308
AuteDVASNE, NMI: 0.5395
Defecd USAP, NME:0.5399
AutODK-LNAAP, MML 0.6691
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Figure 38: Visualization of Forty Soybean Cultivars from Subsequent Harvests with classes. (a) Default t-SNE, (b) AutoDV-SNN,, (c) Default UMAP, (d) AutoDV-UMAP.
46


Reviews:
[{"review_id": "zcEeIkgAS7", "reviewer": "Reviewer_hD97", "summary": "The authors propose an automated way of learning to embed whole datasets similarly to a specific prescribed embedding algorithm, without the need of choosing its hyperparameters. The hyperparameters, used to generate each embedding, are different for each dataset and are chosen based on the labels of the dataset. These labels are used the validate the quality of the embedding, and are not used throughout the embedding process. Then, at inference time, the model produces an embedding that should correspond to an embedding with hyperparameters selected in the same manner for this dataset.", "questions": "1. NMI. How did you choose the number of K in K-means when you calculated the NMI? I am wondering whether you allowed K to be much larger than the number of clusters as the problem is related to Manifold Learning and not only to Clustering.\n\n2. Same bandwidths used across all datasets. The optimal bandwidths may vary in orders of magnitudes between different datasets (and even within the same dataset). It can depend on all kind of factors, like the number of samples and the type of the data (e.g., curvature, density) . In a lot of cases, even z-scoring wouldn't remove this phenomena. How did you tackle this problem, or maybe this problem did not occur in your data as it had very similar characteristics (like in the image data that used the clip embedding space) ?\n\n3. How many samples are there in each subset within the training data?", "limitations": "", "rating": 2, "confidence": 3, "soundness": 1, "presentation": 1, "contribution": 1, "strengths": "The fact that the neural network was able to produce an embedding based on the test data is interesting.", "weaknesses": "1. The terminology is not consistent with the manifold learning field. The authors propose to generate \"k -view graphs\", where in each of the k graphs they use a different bandwidth parameter. There are a whole field that deals with multi-view dimensionality reduction, where each view considers a different source. Here on the other hand, we get the same source. The more suitable term here will be multi-scale, as the algorithm generates the similarity matrix over the data in multiple scales of bandwidths. \n\n2.  Paper aims to solve too many tasks altogether. If I understand correctly, the paper aims to solve two problems together, including: (A) Extract good hyperparameters (and their corresponding bandwidth/s) for a given dataset, and (B) Generate an embedding based on these bandwidths. Each of these tasks are non-trivial, and I would expect the authors to show their superiority on each task independently.\n\n3. Quantification metrics. The training data includes datasets along with their corresponding embeddings, which are the result of applying the same embedding algorithm with different hyper-parameters. These hyper-parameters were chosen based on some supervised metric. I wonder why the authors do not compare the embeddings they got from test data with the true embedding (of the embedding algorithm) using its \"optimal parameters\", one approach to do so is through their graphs.\n\n4. Unsupervised bandwidth selection. The problem of unsupervised bandwidth selection is studied in the context of different embedding algorithms, and in other related contexts such as KDE. I did not see any discussion about this field.\n\n5. Missing clarification about choices related to the neural network. For example, why is the SVD positional encoding good for this case, and why do embedding algorithms such as the ones considered in this paper relate to them. Going even further than that, you can then ask how this encoding corresponds to the initialization of the selected embedding algorithm.\n\n6. The paper will really benefit from generating even a synthetic dataset, which will be easy to understand, and then the generated embeddings along with the scores can better illustrate the algorithm's output more clearly. \n\n7. Theoretical Configuration. The configuration of the problem is not well defined.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "LXgitBs3SR", "reviewer": "Reviewer_gpJd", "summary": "This paper introduces AutoDV, a high-dimensional data visualization algorithm which leverages a graph transformer network to embed datasets into lower dimensional spaces. Datasets are first converted into a similarity graph, which is passed into a graph transformer, which is trained to predict the ground truth TSNE/UMAP values under optimal hyperparameters. The paper highlights two challenges in performing this end-to-end modeling task: different sizes/dimensions for the input points, and the presence of multiple ground truths for each underlying input (under rotation,  scaling etc.). To solve the first challenge, the paper ignores the dimensionality of the points, and relies on taking as input a similarity graph under a gaussian kernel function (Following Long, 2015). This makes it possible to apply a GNN to encode the graph, and reproduce it in a lower dimension. To solve the second challenge, the paper introduces an affine-invariant loss function, which attempts to align the pairwise squared similarity matrices in the lower dimension under a Bregman divergence (using either KL divergence for T-SNE or a structural similarity, given in Eq. 8, for UMAP). \n\nThe paper is evaluated across several image datasets (MNIST, Fashion-MNIST, CIFAR-10), as well as several datasets for bioinformatics (Baron Huntman, Mouse Retina, Cambell and PBMC68K), and tabular data (UCI Machine Learning).  Evaluations of the NMI and Silhouette Coefficient show that AutoDV approaches, and sometimes exceeds the representation performance of the baseline approach across almost all results, while being somewhat faster than the existing methods (Particularly an un-optimized TSNE).", "questions": "- How are the optimal parameters for TSNE/UMAP chosen (I might have missed this in the appendix)? It seems like while AutoDV is trained to approximate these methods, the optimal parameter choice chan highly influence the final outcomes.\n- Are there any scaling properties? Does the AutoDV model have to be a particular size to achieve this performance? \n- Does the model generalize beyond classification datasets? How much does the underlying manifold have to change in order to break the hyperparameter approximation of this method? \n- Is this any different than just learning good initial hyperparameters for TSNE/UMAP? Does it outperform such methods?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "This paper tackles an interesting problem in data visualization: can you learn a function which end to end approximates t-SNE or UMAP (or really any of the dimensionality reduction methods), which doesn't require tuning the hyperparameters. AutoDV is a step towards that: there's no hyperparameter selection, and it generates what are numerically better visualizations of underlying data. The theoretical stability results are nice (albeit somewhat weak), and the method is much more efficient than un-optimized t-SNE, which means that there are potential gains here as well.", "weaknesses": "While there are some strengths, the paper does have significant weaknesses:\n- For a paper on data visualization, there is very little actual visualization in the paper. It would be good to demonstrate qualitative results for several different datasets (Ideally beyond those in Figure 4), which honestly do not look remarkably similar to the underlying optimal TSNE/UMAP examples (even under transformation). What about visualizing some more classic datasets (swiss roll, lines, etc.)? \n- It's also not clear here that the learned parameters are that much better than defaults (For example, for Figure 4, how well does a single learned default parameter perform?) - Could you have a similar baseline, perhaps, that just uses the TSNE* data to inductively learn the optimal dataset-specific parameters? \n- It's not entirely clear if this model will generalize to new datasets, and the paper does little . While the paper does show that it generalizes from MNIST and FMNIST to CIFAR, it's not entirely clear how far that generalization goes: will a pre-trained AutoDV model generalize from CIFAR to a Genetic dataset? Or from CIFAR to something like the swiss roll? It would be really good for this paper to explore the extent of generalization - how far away to the datasets have to be structurally before the models start failing (CIFAR 10 has 10 classes, for example, which is shared with MNIST). There's also no datasets here that are not classification centric (i.e. all datasets have some larger class structure), which means that it's hard to tell if an AutoDV model will generalize between underlying manifold structures.\n- There's a pretty large limitation in that the model can only handle 3000 point datasets (L364). It's a proof of concept, but it seems pretty bad, especially given the potential scalability of UMAP/TSNE.\n- There's not really much analysis of the failure cases of the model - are there any? How does the model perform in situations where there are high-noise, or overlapping clusters, or even on random noise? \n- There are some really confusing wordings in this paper, which make it quite challenging to read, for example, the following sentence: \"To allow a deep neural network to accept different input dimensionalities directly is barely possible, which is what the existing parametric data visualization models suffer from.\" which motivates the design of the paper. \n- The paper is lacking some fundamental motivation/ablations: Why were the base architectural choices made? Are there scaling properties to the AutoDV metric? The practical choices for $\\mathcal{K}_\\psi$, and particularly $\\psi$ are not particularly well motivated - and no alternatives are explored. There's also no ablations on the different loss components (with/without something affine aware, with/without sign ambiguity, etc.).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "SwAaeU6V8m", "reviewer": "Reviewer_kZK1", "summary": "This paper addresses the practical pain points of high-dimensional visualization (HDV): methods like t-SNE and UMAP require dataset-specific hyperparameter tuning and iterative optimization, and their results vary across domains and input dimensionalities. The authors propose AutoDV, an end-to-end model trained once to produce 2D/3D embeddings for unseen datasets without per-dataset tuning. The key idea is to learn from historical, high-quality visualizations and generalize that “visualization know-how” to new data.\n\nTechnically, AutoDV first graphizes any dataset—regardless of its original feature dimension—into multiple similarity graph views (e.g., Gaussian kernels at different bandwidths). It then computes graph positional encodings and processes each view with a per-view GNN; the view outputs are concatenated and fed to a Graph Transformer, followed by an MLP that yields the final low-dimensional coordinates. Training is supervised by “optimal” target embeddings obtained from conventional HDV (e.g., t-SNE/UMAP selected via Bayesian optimization on labels/metrics). Instead of matching raw coordinates, AutoDV minimizes an affine-invariant divergence between pairwise similarity structures of its prediction and the target, eliminating rotation/translation/scale ambiguities and stabilizing learning.\n\nThe paper’s main limitations are the dependence on historical “optimal” targets (which may require labels and careful tuning to curate) and potential quadratic costs from pairwise structures (mitigated by batching/anchors). Nonetheless, AutoDV offers a compelling step toward set-and-forget visualization: a single trained model that produces stable, near-optimal embeddings for diverse new datasets without per-dataset fiddling.", "questions": "1. How do you expect the user should choose AutoDV over UMAP in practice?\n\n2. What is the neighour-preserving rate between the high and low dimensional data?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The idea of learning a mapping from multi-view graph topology to a low-dimensional layout is novel. It decouples from raw feature dimensionality, uses affine-invariant supervision, and targets cross-dataset generalization without per-dataset tuning.\n\n2. The authors demonstrate strong command of related work and discuss it thoroughly. They situate the approach against classical DR (PCA/MDS), modern manifold learners (t-SNE/UMAP and variants), and parametric/inductive methods, clearly motivating the gap.\n\n3. The experiments are extensive across many datasets and modalities. Image (with pretrained features), gene-expression, and tabular benchmarks are covered with multiple metrics, offering broad evidence for robustness and generalization.", "weaknesses": "1. Unclear data requirements for learning from historical visualizations. \n\nIt is not specified how much and what diversity of historical visualizations are required for AutoDV to reliably replace UMAP in practice. The paper should quantify sample complexity and coverage (e.g., number of datasets, domain diversity, class balance, feature dimensionality ranges) and provide learning curves/ablation studies (performance vs. amount and variety of historical supervision).\n\n2. Evaluation relies heavily on NMI, which can be a coarse proxy. \n\nWhen high-dimensional features (or labels) are imperfect, cluster labels are not a reliable indicator of visualization quality. The paper should include neighbor-preservation metrics and rank-based fidelity measures—e.g., kNN overlap/Jaccard@k, Precision/Recall@k, Trustworthiness/Continuity, triplet preservation, and (optionally) global distortion/stress or distance rank correlations—to demonstrate that local and global neighborhood structures are faithfully preserved.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "elESUJkTy6", "reviewer": "Reviewer_dtQX", "summary": "This work proposes an end-to-end high-dimensionality reduction that generalises to unseen datasets with various feature sizes without retraining. Given some historical dimensionality reduction representations as the learning example, the proposed mechanism acquires meta-knowledge of how to capture the structure of high-dimensional data and preserve it in the low-dimensional representation.\nTo the best of the reviewer's knowledge, this ability is rarely studied, and thus, this work is novel.", "questions": "1. In pg. 3 subsection 3.1, the authors wrote: \\theta^*_i denotes the optimal hyper-parameters selected using y_i (the labels). However, in the experiments, the proposed AutoDV was trained using historical DV, t-SNE, and UMAP, which are unsupervised DRs that do not account for dataset labels. So the statement does not reflect the experiments well.\n\n2. The term \"historical datasets\" can be confusing. The term \"historical low-dimensionality representations\"  is better. Please review the usage of this terminology.\n\n3. To further show the meta-learning ability to capture the preserved structure of high-dimensional data, it will be interesting if the authors can run additional experiments against t-SNE with various perplexity values (or UMAP with various numbers of neighbors). It is of interest to observe that, for a perplexity that generates poor maps, it will still be possible for AutoDV to capture the preserved structure.\n\n4. pg. 2, \"Lack of cross-domain....\": min_theta E_i|f(x_i).....| ->  min_theta E_i|f_theta(x_i).....|\n\n5. Fig.1 is too small to see\n\n6. Some novel DR methods may benefit the depth of this paper. Please consider including them in the discussion and for future experiments to further argue the proposed method's generality\n\n- A. Dehghani, et al.,Credit-based self organizing maps: training deep topographic networks with minimal performance degradation, ICLR 2025, https://openreview.net/pdf?id=wMgr7wBuUo\n\n- P. Hartono, Mixing autoencoder with classifier: conceptual data visualization, IEEE Access, Vol. 8, pp.105301 -105310 (2020) DOI: 10.1109/ACCESS.2020.2999155\n\n- P. Hartono, P. Hollensen, T. Trappenberg, Learning-Regulated Context Relevant Topographical Map, IEEE Trans. on Neural Networks and Learning Systems, Vol. 26, No. 10, pp. 2323-2335 (2015). DOI:10.1109/TNNLS.2014.2379275", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "This is a very solid work, supported by strong theoretical arguments and valid experiments.\n\nThe strengths of this proposed algorithm are as follows:\n1. It offers an end-to-end DR mechanism that generalises across many not new data points, but new datasets. It frees users from the need to retrain the DR method.\n2. It does not need any hyperparameter tuning.", "weaknesses": "The reviewer found no significant weaknesses in this work.\n\nThe proposed algorithm was trained only on historical low-dimensional representations from t-SNE and UMAP. The reviewer understands that this is due to the page limitation. However, the proposed work's generality will be further strengthened if the authors can train AutoDV using other DR algorithms. Specifically, t-SNE and UMAP are non-linear and unsupervised DR methods. Hence, it will be interesting to observe the generality of the AutoDV against a linear DR such as traditional PCA or MDS, and against a supervised linear DR such as LDA.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)