Recursive SNE: Fast Prototype-Based t-SNE for Large-Scale and Online Data
Authors: Agil Aghasanli
Plamen P Angelov
Venue: Accepted by TMLR ()

Abstract: Dimensionality reduction techniques like t-SNE excel at visualizing structure in high-dimensional data but incur high computational costs that limit their use on large or streaming datasets. We introduce the Recursive SNE (RSNE) framework, which extends t-SNE with two complementary strategies: i-RSNE for real-time, point-wise updates and Bi-RSNE for efficient batch processing. Across diverse settings, including standard image benchmarks (CIFAR10/CIFAR100) with DINOv2 and CLIP features, domain-specific iROADS road scenes, neuroimaging data from the Haxby fMRI dataset, and long-term climate records, RSNE delivers substantial speedups over Barnes–Hut t-SNE while maintaining or even improving cluster separability. By combining a lightweight prototype-based initialization with localized KL-divergence refinements, RSNE offers a scalable and adaptable framework for both large-scale offline embedding and on-the-fly visualization of streaming data.

Published in Transactions on Machine Learning Research (10/2025)
Recursive SNE: Fast Prototype-Based t-SNE for Large-Scale and Online Data
Agil Aghasanli*
a. a.aghasanlil Slancaster.ac.
Lancaster Intelligent, Robotic and Autonomous systems (LIRA) Centre School of Computing and Communications
Lancaster University, UK
Plamen Angclov"
p.angelor@lancnsster..co uk
Lancaster Intelligent, Robotic and Autonomous systems (LIRA) Centre
School of Computing and Communications
Lancaster Universily, UK
Reviewed on OpenReview: openrevvee.. forum? id= 7UCPAPMDWN
Abstract
Dimensionality roduction techniques like t-SNE excel at visualizing structure high- dimensional data but ineur high computational costs that limit their use on large or streaming datasets. We introduce the Recursive SNE (RSNE) framework, which extends t-SNE with two complementary strategics: i-RSNE for real-time, point-wise updates and Bi-RSNE for elficient batch processing. Across diverse settings, including standard image benchmarks (CIFAR10/ (CIFAR1O/CIFARI00) CIFARR00) with DINOv2 and CL.IP features, domain-specific iROADS road scenes, neuroimaging data from the Haxby fMRI dataset, and long-term climate RSNE delivers substantial speedups over Barnes Hut t-SNE while maintaining or even improving cluster separability. By combining lightweight prototype-ban based initialization with localized KL-divergence refinements, RSNE offers a scalable and adaptable framework for both large-scale offline embedding and on-the-fly visualization of streaming data.
records,
1 Introduction
In the big data cra, high-dimensional datasets are standard in many fields, including finance Fann et al.
2011h, image processing, and biology (Wong) 2016). The "curse of dimensionalityy (Bellman 1957 Friedman 1997), which may conceal underlying patterns and structures, makes very difficult analyse and visualise such data. Dimensionality reduction methods have emerged essential tools for addressing these challenges by converting high-dimensional data into more manageable formats while maintaining crucial information. For example, in genomics, these techniques help identily significant gene expression patterns (Golub et al.
1999): in natural language processing, they help reduce the complexity of text representations (Pennington et al. 2014); ; in computer vision, they facilitate the extraction of meaningful features from images Turk & Pentland 1991).
Several mothods have been developed to address the challenges of high-dimensional data. Principal Component Analysis (PCA) (Pearson) 1901) widely used technique that transforms data into set of orthogonal components, capturing the maximum variance in the data. Linear Discriminant Analysis (LDA) (Fisher
1936 focuses on finding linear combinations of features that best separate different classes in the data space. The nonlinear method known as t-Distributed Stochastic Neighbour Embedding (t-SNE) (van der Maaten & Hinton 2008) attempts to maintain the probability distribution of pairwise similarities by modeling each high-dimensional data by a two- or three-dimensional position. Uniform Manifold Approximation and Projection (UMAP) (MeInnes & Healy 2018) emphasizes both local and global data structure, providing faster
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computation and often better preservation of global structures compared to t-SNE. Isomap Tenenbaum et al. 2000) extends Multidimensionall Scaling (Torgerson) 1952) by incorporating geodesic distances. capturing the intrinsic geometry of the data manifold. Locally Linear Embedding (LLE) (Roweis & Saul 2000) seeks to preserve local relationships by reconstructing each data point from its nearest noighbors.
Despite advances dimensionality reduction techniques, many methods face challenges when dealing with streaming or large-scale datasets. Traditional t-SNE, for example, requires reprocessing the entire dataset when new data points added, making it computationally expensive for real-time applications. To address this limitation, propose Recursive SNE (RSNE), an extension of t-SNE that allows for efficient updates with new data points without necessitating a complcte recomputation. Specifically, i-RSNE performs fast, point-wise updates ideal for streaming data, while Bi-RSNE handles large offline batches with vectorized operations. This approach is particularly beneficial for applications that involve dynamic or streaming data, where timely visualization and analysis are crucial.
In our experiments, Bi-RSNE processes trausformer-derived features from CIFAR1O (Krizhevsky et al. 2009 and CIFAR100 (Krizhevsky et all 2009) approximately five times faster than Barnes Hut t-SNE (van der Maaten 2013). while maintaining enhancing silhouette (Rousseeuw) 1987) and Davies Bouldin (Davies &
Bouldin 1979 scores across both DINOv2 (Oquab et al.) 2023) and CLIP (Radford et al. 2021 embeddings.
For instance, the batch method Bi-RSNE achieved comparable cluster compactness within roughly 40 % of the original computation time on CIFARI00. Meanwhile, i-RSNE integrates each new CIFAR sample in just a few milliseconds, over an order of magnitude faster than rerunning a full embedding, yet delivers virtually identical cluster layouts after a single gradient step. On the Nomain-speciff iROADS dataset, Bi-RSNE achieves around 3 times speedup and yields sharper, more semantically coherent clusters. On neuroimaging data from the Haxby fMRI dataset (Haxby et al. 2001), RSNE achieves up to 2.5x speedup over Barnes-Hut t-SNE while preserving embedding quality, making it suitable for interactive exploration of brain activity patterns. Finally, applied to a ten-year climate stream (Muthu 2017), RSNE reduces runtime by nearly 50 % while preserving cluster separation, undorscoring its offectiveness for both offline and real-time embeddings.
In this paper, we introduce RSNE and demonstrate its effectiveness in handling high-dimensional data in dynamic environments. Our contributions include:
Development of the RSNE framework, including i-RSNE for incremental updates and Bi-RSNE for batch updates, reducing computational overhead.
Comprehensive evaluation of RSNE's performance compared to Barnes-Huu t-SNE, highlighting its advantages in terms of efficiency and scalability.
Application of RSNE to real-world datasets, including CIFAR10, CIFAR100, IROADS, and climate data, to demonstrate its flexibility and practical utility.
2 Related Work
2.1 Overview of Dimensionality Reduction
Dimensionality reduction techniques are broadly categorized into linear and nonlinear methods (Cunningham) & Ghahramani] 2015). Linear methods, such as PCA (Pearson 1901) and LDA (Fisher 1936). assume that the data lies or linear subspace of the high-dimensional space. These techniques aim to find linear projections that capture the most significant variance (PCA) or that best scparate different classes (LDA). On the other hand, nonlinear mot are designed to capture more complex structures in the data that cannot be adequately represented by linear projections. Techniques like t-SNE (van der Maaten Hinton 2008). UMAP (MeInnes & Healy 2018), Isomap (Tenenbaum et al., 2000), and LLE (Roweis & Saul 2000) fall into this category, as they aim to preserve the intrinsic geometry of the data manifold by considering nonlinear relationships between data points.
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2.1.1 t-SNE and Its Limitations
t- t-Distributed Stochastic Neighbor Embedding (t-SNE) has become popular tool for visualizing high- dimensional data due to its ability to preserve local structures and reveal clusters. However, t-SNE has notable limitations, particularly concerning scalability and the handling of new data points. The algorithm's computational complexity ((N2) due to the pairwise similarity calculations, making it challenging to apply to large datasets. Additionally, it requires reprocessing the entire dataset when new data points are added, which is impractical for streaming data applications.
2.1.2 Barnes- Hut t-SNE
To address the scalability issue, Barnes-Hut t-SNE (van der Maaten 2013) was developed, which speeds up computations using a quadtree-based approximation. This approach reduces the computational complexity to (N log.N, making it more feasible to apply t-SNE to larger datasets. However, Barnes- t-SNE still requires reprocessing all data when new points are addod, limiting its applicability in dynamic or strcaming data scenarios.
2.1.3 Parametric t-SNE and FIt-SNE
Other techniques have been proposed to handle large-scale data and dynamic updates. Parametric t-SNE (van der Maaten] 2009) learns a mapping function via deep learning, allowing for the embedding of new data points without retraining on the entire dataset. However, this approach is limited by training complexity and may not capture the intricate structures in the data as effectively as non-parametric methods. FIt-SNE (Fourien-Ineerplatted t-SNE) [Linderman al. 2019) uses fast matrix operations improve computational efficiency but does not support stramnnng updates, it still relies on batch processing of dala.
2.2 Data Visualization Scale
Large datasets require visualization systems that can process and render millions of points without sacrificing interactivity or clarity.
Scalable frameworks typically preprocess data into multi-resolution hierarchies or employ on-the-fly aggregation that only subset of the data is rendered at any zoom level (Childs et al.] 2011). GPU-accelerated pipelines and parallel rendering engines further ensure that panning, zooming, and filtering remain fluid even as dataset size grows. Server-client architectures often couple lightweight front end with server-side data reduction layer, dynamically streaming only the detail needed for the current view.
Graph-based methods such as LargeVis construct an approximate Enearest-neighber graph once and then optimize a forco-directed layout via edge-centric stochastic updates (Tang et al. 2016). By decoupling neighbor search (e-g. using locality-sensitive hashing) from layout optimization, these approaches embed millions of nodes in minutes rather than hours. Asynchronous graph partitioning and parallel force computations further improve scalability on commodity hardware.
RSNE extends these ideas by performing only local, constant-time updates for incoming points, assigning them into existing clusters and refining their positions with a fixed number of gradient steps. This enables truly incremental graph expansions without re-running the full layout.
2.3 Manifold Learning for Temporal or Evolving Data
Many real-world streams, such sensor networks, neuroimaging, climate records, change continuously, requiring embeddings that evolve smoothly rather than abrupt shifts at each time step.
bidding-windww fMRI analyses, functional connectivity patterns drift along a low-dimensional manifold as cognitive states change (Hutchison et al. (2013). Traditional approaches recompute embeddings on each window or interpolate between static layouts, often resulting in abrupt visual discontinuities. Some methods introduce temporal regularization into the embedding cost., but still require expensive batch computations.
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Streaming manifold techniques update neighborhood graphs and cigenmaps incrementally, e.g., Streaming Isomap (Mahapatra & Chandola, 2017), to reflect evolving topology, but typically incur O(n log n) or higher per update. To improve speed, these methods sometimes prune old points or coarsen graphs, sacrificing long-range structure for performance.
RSNE maintains cluster summaries (means and variances) and applies a single KT-ddiergeecce gradient step per new point or batch, achieving constant-time updates that preserve both local neighborhoods and global manifold shape.
2.4 Visualization in Sppcifc Applications
Different application domains impose unique constraints on embedding quality and update speed. Geospatial analysis requires accurate spatial relationships, while biological imaging requires the preservation complex high-dimensional patterns.
Geovisualization systems layer thematic data traffic flows, pollution levels, demographic indicators on geographic maps, demanding that the embedded proximity reflect real-world distances (Tominski & Schumann 2020 Real-time sensor streams must be integrated without distorting existing clusters or misleading users, requiring incremental update strategies.
High-content microscopy produces feature vectors in the hundreds or thousands of dimensions, which are projected for tasks such as cell-type discovery or anomaly detection (Peng et al. 2010). When new image batches arrive (e.g., additional tissue sections or time-lapse frames), full re-embedding disrupts interpretability and delays analysis.
RSNE may let domain experts immediately visualize where they fall relative to existing clusters (see Section keeping the analytic pipelines responsive while preserving the semantic cluster structure.
2.5 Transformer-Basse Based Foundation Models
Transformer architectures have become foundational for generating rich, high-dimensional representations both vision and language domains. In computer vision, the Vision Transformer (ViT) treats image patches tokens in pure transformer model, achieving state-of-the-art performance large-scale image classification benchmarks (Dosovitskiy et al. 2020 Building on this idea, self-supervised variants such DINOv2 learn visual features without labels by aligning patch embeddings across views, resulting in semantically meaningful clusters in feature space (Oquab et al. 2023). CLIP extends the transformer paradigm to joint image text sctting, utilizing large-scale contrastive pretraining to align visual concepts with textual descriptions, thereby enabling zero-shot generalization (Radford et al. 2021).
On the language side, transformer models like BERT generate contextualized token embeddings that encode both syntactic and semantic information, markedly improving tasks such question answering and named- entity recognition (Devlin et al. 2019). Autoregressive transformers, such as GPT, demonstrate few- and zero-shot capabilities by training on massive text corpora, supporting diverse downstream applications with minimal or no fine-tuning (Brown et al. 2020). Because transformer-based embeddings often form well-separated clusters, which reflect object classes in vision or thematic groupings in text, many visualization pipelines now operate directly on these pre-trained features. RSNE leverages this structure by initializing a small set of prototypes drawn from a transformer embedding space and then refining locally via KL-divergence steps. This ensures that the global layout induced by DINOv2 CLIP remains intact while avoiding the need to rerun full t-SNE when new batches streaming data arrive.
2.6 Online and Recursive Update Methods
Many online learning and outlier-detection methods rely on recursive updates to avoid storing all past observations. One prominent example Recursive Density Estimation (RDE) (Angelov) 2012). RDE maintains a running mean and scalar summary (e.g., the sum of squared norms) so that the density istimate can be updated in current time instant from these summaries and the current sample. This exact,
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nonparametric formulation supports real-time novelty detection and clustering without retaining the entire data history.
Similar ideas are also present in streaming clustering and dimenniionallt--rduucii algorithms. Streaming K-means updates each centroid incrementally by combining the previous centroid with the new observation, avoiding full batch recomputation (Bottou & Bengio, 1994). Incremental principal component analysis (IPCA) maintains running covariance estimates via recursive formulas, adjusting principal components as new data arrive without re-computing cigenvectors from scratch (Weng et al.) 2003
RSNE integrates these recursive estimation principles directly into t-SNE. In the i-RSNE variant, each new data point is first assigned to its nearest high-dimensional prototype; that prototype's mean and variance are updated incrementally, precisely as in RDE, ensuring constant-lime updales. The corresponding low- dimensional centroid is also updated recursively before a single KL-divergence gradient step adjusts the new point's embedding. In the Bi-RSNE variant, prototype updates and affinity computations are vectorized across a mini-batch, yet still rely the same recursive summaries to maintain up-lo-date protolypes. As result, RSNE achieves efficient streaming and batch updates, which preserve both local neighborhoods and global layout without ever rerunning full t-SNE the entire dataset.
3 Methodology
Throughout this paper, we denote the original datapoint in the input space by x E RD, where D is the dimensionality of the original data. The corresponding low-dimensional embedding is denoted by y Rd where d < D is the dimension of the embedding space. We use X (2 2N, INZ for the dataset of N samples in the original space, and Y = {y1, ......, for their embeddings. Distances are Euclidean in both spaces.
3.1 i-RSNE
i-RSNE extends the initialization followed by updating paradigm to fully online setting, embedding new point at time while preserving the existing layout.
3.1.1 Initialization Phase
We first extract a small seed subset Xinit C of size a.N, where N the total number of data points (e.g. a 0.2). On this subset, Barnes-Hut t-SNE produces low-dimensional coordinates {uj that capture the global structure of the data. In parallel, K-means clustering in the original feature space yields high- (0) We then compute low-dimensional centroids
dimensional centroids f
(0) and variances 0g
10) Ky.k
1
(0)
C&
1/
iEC₁
where C₁ denotes the set of seed points assigned to cluster k. These paired high- and low-dimensional prototypes serve as the fixed foundation for all subsoquent updates, ensuring that the coarse manifold layout remains stable new data points arrive.
3.1.2 Incremental Phase
When a new sample Knew arrives, we first assign it to its nearest high-dimensionall prototype:
ks arg min |[
146 (t-
22-
This prototype search identifies the semantic region of the data manifold into which the new point most. naturally falls. We then warm-start the embedding by placing the new point near the corresponding low-dimensional centroid:
(t.0)
(1-1) py + e~ C0O, 0.1).
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This initialization prevents the new point from overlapping existing points and provides reasonable starting position for fine-tuning.
To keep our prototypes up to date without re-rumning K-means, we increment the cluster count ni- by one and update its high-dimensional mean and second moment in constant time:
(t-1) (t-1)
(t-1)
Ug
(t)
"k-
Pk
+
(8)
Tnows
ni (t--1)
(t)
(c) n2a
Fnew 1|2
n
The new high-dinenniioall variance then calculated as:
2
= Σ
||
To refine the new embedding, compute high-dimennsionll affinities
Pk
Pa exp( -1 - 12)111((0220))) Ps
Σm Pm
and low-dimensional affinities
Q
Qx (1+1ly
Mg, (1-1) 12)= Qx Σ m
Qm
These distributions quantify how strongly the new point prefers each prototype in both spaces. We then compute the gradient of the Kullback Leibler divergence,
K VyKL = Σ PP& Qk) 1=1
(t.0) (t-1) ynew
My
(1 (1-1)
+ ||
yy
and take single gradient step,
Vnew 17 KL
This step refinement corrects the new point's position to better align local neighborhoods. The gradient descent update only affects the embedding of the new point, while the embeddings of previous points remain fixed. By restricting to a single iteration, we keep each update at O(K (D + d)) cost, where is the low-dimensional embedding dimension, enabling real-time streaming performance.
Once the final embedding (l.*) is obtained, we update the low-dimensional centroid My,k for cluster k* in constant time:
(t-1) ni
(4)
(t..)
y.k-
+
(t)
Vnew
T
These constant-ting time updates in the low-dimensional space ensure that our centroids accurately track the evolving embedding without requiring full recomputation of cluster means.
3.2
Bi-RSNE
Bi- Bi-RSNE shares the same seed-set initialization as i-SSNE but replaces sequential, point-wise updates with a fully vectorized batch procedure the incremental phase.
3.2.1
Initialization Phase
Identical to i-RSNE, we extract seed subset Xinit> embed it with Barnes-Hui t-SNE to produce ()) and cluster the seed by K-means to obtain high-dimensional prototypes {4 (0) o (0)) and low-dimensional
centroids (0)) This shared initialization ensures both methods start from the same global layout.

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3.2.2 Batch Update Phase
For batch of B new points {a:) first compute the full B x K distance matrix ||: M* minimal entry in each row assigns to prototype k; and we collect these assignments into index sets IN = (i: k2 = kj. In one vectorized operation we update each high-dimensional centroid by
(t-1) 12. The
(1-1)
(t-1)
(1)
FR
(1-1)
+
Σ
Fi.
"
Σ IEIx
||aal1?
(t)
(1) 1
(8)
(2)
n
iEIx
nk
Th
where n. = k + Inl-
(t-1)
Next, we compute unnormalizod affinitics for all i,
A = expl -110, 1 11) o2 (2)2)))))) ()),,, Qi,k = (1 |10,1
(1.u)
-13)
normalize each row to obtain Pi,k and Qi,k, and compute the KT. gradient for each point:
K Σ
y; (/,w) (t-1)
V y. KL. = 4
(L. Qi,k)
1 llv,
((,0) (t-1)
k=1
A single vectorized gradient step
(t.*) (t,0) V KL
yi 1//
updates all B embeddings simultaneously. By expressing distances, prototype updates, affinities, and gradients as batched matrix operations, Bi-RSNE achieves O(B K (D+d)) runtime, fully leveraging hardware parallelism to handle large-scale batches efficiently, where is the batch size, D is the dimensionality of the original data, and d is the low-dimensional embedding dimension.
LB j are computed, we update each low-dimensional
Once the new low-dimensional embeddings {ul prototype Py.k in constant time for cluster k:
(t-1)
n
(1-1)
1)
Σ
9..
(t)
11
y,h
(e) y
n2
n2
IET,
Complerity. Both i-RSNE and Bi-RSNE have total cost
O RKDI ) O( nlog + O mK(D+d + ) seed clustering
t-SNE init
incremental updates
where n the seed size, I the number of k-means iterations, and m N a the number of incremental points. The difference lies in how the last term executed: i-RSNE processes one point at a time, repeating the ((D+d) work sequentially, whereas Bi-RSNE groups points into batches of size B and performs the same operations in parallel, exploiting vectorization and hardware acceleration. This makes Bi-RSNE practically faster, even though the asymptotic orders are identical.
4 Experiments
4.1 Datasets
CIFAR10 Dataset. The CIFAR10 datasct Krizhevsky et al. 2009) consists of 60,000 natural images in 10 classes (6,000 images per class), with 50,000 images for training and 10,000 for lesting. We extract 1024- dimensional feature vectors from each image using pre-trained DINOv2 ViT-L/14 and CLIP V/T-L/14 models. These transformer-basod embeddings capture rich semantic and visual information, providing challenging nigh-dimensional inputs. We evaluate both i-RSNE and Bi-RSNE on the train set of 50,000 images, comparing embedding quality (silhouette score, Davies Bouldin index) and runtime against. Barnes Hut L-SNE.
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Algorithm i-RSNE
Require: High-dimensional datasct X, seed fraction a, number of clusters K, learning rate
1: Select random seed subset Xinit C X of size X
2: Compute high-dimensional prototypes ())) of by running K-means on Xint
3: Run Barnes Hut t-SNE on Xinit to obtain low-dimensional points Y (0)
Compute low-dimensional centroids (0y, by averaging points in (() per cluster for each new sample Few arriving in the stream do
Find ncarest high-dimensional prototype index k arg ming || mell Initialize Unow by placing it near My,k- (plus small noise)
7:
8: Update uą- and o- to incorporate nnww in one step
9:
Compute affinitics between Tnew and cach μk, normalize to get Ps-
10: Compute affinities between Unew and each Py.k, normalize to get Qx
11:
Perform one gradient descent update on Vnew to reduce (T((P)IQ)
12:
Update Uy,k* to incorporate ynew in one step
Algorithm Bi-RSNE
Require: High-dimensional dataset X, seed fraction a, number of clusters K, batch size B, learning rate 17
1: Select random seed subset Xinit C X of size x|
2: Compute prototypes {Px (0), {{)) } via K-mcans on Xinit
3: Run Barnes Hut I-SNE on Xinit. to get (0) and centroids (py, (0))
4: for each incoming batch { do Compute x K distances between 2; and prototypes pk Assign each Ty to nearest prototype index k;
For each cluster k, update Mt: of using all x; assigned to k
8: Compute all high-dimensional affinities P. and low-dimensional affinities Qu,
9: Perform one vectorized gradient step on all y; to minimize batch KL divergence
10:
Update low-dimensional centroids Py.k using corresponding yi
CIFAR100 Dataset. The CIFAR100 dataset (Krizhevsky et al. 2009) extends CIFAR10 with 100 fine- grained classes (600 images per class), also split into 50,000 training and 10,000 testing images. We again extract 1024-dimensiooal features using DINOv2 VIT-L/14 and CLIP VIT-L/14 to evaluate RSNE's ability to handle increased class diversity and intra-class variability, Embedding results on the full 50,000 train set images assess how well RSNE preserves nuanced cluster structures relative to Barnes Hut t-SNE.
iROADS Dataset. The iROADS dataset (Rezaei el al. 2018 comprises approximately 5,000 road-scene images collected from diverse driving environments (urban, suburban, rural). From each image, we extract. 1024-dimensional feature vector using the pre-trained DINOv2 VIT-L/14 model (Oquab et al.) 2023), capturing high-level semantic information such road type, weather conditions, and object presence. These deep features form challenging high-dimensional input, well suited to test the scalability and representational power of our methods. We evaluate embeddings of the full set to compare t-SNE and Bi-RSNE, and we measure how well clusters corresponding to annotated road conditions are preserved.
Climate Dataset. The climate dataset (Muthu 2017) contains daily measurements from 50 meteorological stations over 10-ycar period (2006-2016), yielding roughly 182,500 samples. Each sample records features such temperature, humidity, wind speed, and precipitation, resulting in a 10-dimensional input. We use monthly batches (e.g., April 2008, May 2008, June 2008) to simulate streaming environment for Bi-RSNE, and we also evaluate full-dataset embeddings for i-RSNE. Due to the continuous nature and overlap of weather variables, this dataset presents a difficult scenario for any clustering-based embedding, making it a strict test of our recursive update mechanisms. The weather conditions are categorized into five classes: clear, partly cloudy, mostly cloudy, foggy, and rainy.
Haxby 2001 fMRI (Visual Object Recognition). We use the widely studied Haxby 2001 Haaxy et al. 2001) visual object recognition dataset, block-design MMRT experiment targeting ventral temporal (VT)
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cortex responses to eight categories (faces, houses, cats, bottles, scissors, shoes, chairs, scrambled pictures). The full release includes 6 subjects with 12 runs per subject; each run presents eight 24-s stimulus blocks separated by rest, acquired at TR=2.5 (120 volumes per run). We rely on the standard Nilearn distribution of this datasct (subject 2) and extract per-volume VT-masked voxel patterns (samples x voxels). In our experiments we treat. each 2.5 volume as one sample; selecting the first. 7 runs and excluding "rest" yields nearly 500 labeled samples spread over the eight categories, which convenient for comparing t-SNE and RSNE on a modest, well-annotated neuroimaging benchmark.
4.2 Baseline
Barnes Hut t-SNE. Barnes Hut t-SNE (yan der Maaten 2013 accelerates the original t-SNE by using a quadtree approximate the interactions of distant points, reducing the run time to O(N log log.). Although this makes it feasible to embed large datasets in single batch, still requires full re-embedding when new data points are added, preventing its use in real-time streaming scenarios.
In contrast, our RSNE framework updates existing embeddings with only partial or batch recomputation, bridging the gap between dynamic online use cases and large-scale offline processing.
4.3 Evaluation Metrics
We evaluate embedding quality and computational performance using the following quantitative metries:
Runtime. The total embedding time is measured as the sum of:
Tint = Initialization time (e.g., Barnes-HHel t-SNE on the first 20% of samples),
(1)
T Tundate = Update time for new data points (processed individually or in batches).
(2)
Tiotal Tinit + Tupdate-
(3)
measures how well each point lies within its cluster versus its nearest neighboring cluster. Values range from (poor separation) +1 (well-separatod clusters), with higher scores indicating clearer cluster boundaries.
Silhouette Score. The silhouette coefficient (Rousseeuw] 1987
Davies Bouldin Index. This index @Davies & Bouldin 1979) quantifies the average similarity between each cluster and its most similar counterpart, with lower values signifying better cluster compactness and separation.
Together, these metrics provide a holistic picture of how well the embeddings balance fidelity, cluster structure, and computational cost.
4.4 Implementation Details
Hardware Configuration. Feature extraction was performed using an NVIDIA GeForce RTX 3080 GPU with 16GB of VRAM. All other experiments, including Bi-RSNE, i-RSNE and full Barnes-Hut t-SNE ovaluation, were conducted on a system equipped with an Intel Xoon CPU 22.20GHz and 52GB of RAM.
Hyperparameters. For both RSNE and Batch incremental RSNE (Bi-RSNE), the high-dimensional input space is set to D 784, while the low-dimensional embedding space is d = 2. We employ K-means clustering with K = 200 clusters for all datasets except CIFARI00, where we use K = 1000 to account for its finer class granularity. The learning rate is fixed at 10 to ensure stable updates during oplimization. Each update step applies a single gradient iteration to adjust the embeddings efficiently. For Bi-RSNE, a batch size of 100 is used to process multiple samples simultancously, balancing computational efficiency with accuracy. Additionally, different initialization percentages are tested analyze trade-offs between computational overhead and embedding quality.
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4.5 Results
4.5.1
CIFAR10
We begin our evaluation on the standard CIFARIO benchmark using features extracted by two state-of- the-art vision transformers: DINOv2 ViT-L/14 and CLIP ViT-L/14. Tables | and report silhouette scores, Davics-Bouldin indicos, and runtimes for Bi-RSNE, i-RSNE, and full Barnes Hut t-SNE under two initialization fractions (20 % and 50 %).
DINOv2 Features. On DINOv2 features, Bi-RSNE with only 20 % initialization embeds all 60 000 images in 36.04 8, which is over a 6.9x speedup compared to Barnes Hut t-SNE's 247.45 s, while achieving a silhouette of 0.5074 and a Davies Bouldin index of 0.6894. These metrics indicate substantially tighter and more separated clusters than t-SNE's 0.4278 silhouette and 0.7659 DB. When the seed set is increased 50 %, Bi-RSNE's runtime grows to 79.43 but the silhouctte only slightly decreases 0.4793, with the DB remaining at 0.6962, showing that the method maintains global structure even with more extensive initialization. i-RSNE at 20 % initialization achieves the highest silhouette (0.5269) and lowest DB (0.6661) in 44.70 s, demonstrating that per-point recursive updates can marginally improve local cluster fidclity at a modest computational cost. However, at 50 % initialization i-RSNE's runtime increases to 85.03 and its clustering metrics regress toward those of Bi-RSNE, suggesting diminishing returns for larger seed fractions in the incremental setting.
CLIP Features. On CLIP VIT-L/14 features (Table 2 the trends are very similar, with some nota ble differences in clustering tightness. Bi-RSNE at 20 % runs in 36.17 and attains silhouette of 0.5244 and DB of 0.6882, slightly improving over DINOv2's compactness while matching its speedup. Increasing to 50 % initialization extends runtime to 86.29 and yields silhouette of 0.4883 and DB of 0. 0.7558, indicating that CLIP features form slightly looser clusters as the seed grows. i-RSNE at 20 % achieves a peak silhouette of 0.5251 in 48.24 s, closely mirroring the Bi-RSNE result and demonstrating that one-step updates suffice to preserve local structure. Full Barnes Hut t-SNE on CLIP takes 260.92 s (silhouette 0.4493, DB 0.7903), confirming that RSNE's cluster-based initialization and local refinements generalize across different transformer embeddings, consistently delivering 7x speedups with minimal loss or often gains in clustering quality.
Table 1: Comparison of embedding methods on CIFAR10 features extracted With DINOv2 VIT-L/14. Metrics include silhouette score (t), Davies-Bouldiy index (4), and runtime in seconds. Embedding visualizations are provided in Appendix A
Method Init.%
Visualization
Silhouette (1)
Davies-Bouldin (1)
Runtime (s)
Bi-RSNE
20%
Fig.
2a
0.5074 + 0.0007
0.6894 + 0.0001
36.72 #0.32
i-RSNE
20%
Fig.
0.5269 +0.0006
0.6661 +000002
44.70 = 0.22
Bi-RSNE
50%
Fig.
2b
0.4793 0.0003
0.6962 1: 0.0002
79.43 + 0.81
i-RSNE
50%
Fig.
2d
0.4669 + 0.0002
0.7204 # 0.0001
85.03 = 0.67
Barnes-Hue t-SNE
Fig-
0.4278 0.0000
0.7659 + 0.0001
247.45 + 1.42
4.5.2 CIFAR100
Scaling up to CIFAR100, with its 100 fino-grained classes, presents considerably more challenging embedding task. The increased class diversity and intra-class variability demand both expressive representations and robust layout algorithms to reveal meaningful cluster structure in two dimensions.
DINOv2 Features. Table 3 reports detailed results on DINOv2 VIT-L/14 features for both recursive and full t-NNE methods. With only 20% initialization, Bi- Bi-RSNE embeds all 000 images in 158.27s. yielding a silhouette of 0.1847 and Davics-Bouldin index of 3. 1302 roughly 57% of Barnes Hunns--utttio t-SNE's 278.20s 20s runtime, but with lower cluster separation. Increasing the seed set to 50% incurs a negligible time penalty (160.42s) while boosting the silhouette to 0.2325 and tightening the DB to 2. 2.6058, indicating much better
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Table 2: Comparison of embedding methods on CIFARIO features extracted with CLIP VIT-L/14. Metrics include silhouette score (t), Davics-Bouldin index (4), and runtime seconds. Embedding visualizations are
provided in Appendix A
Method
Init.%
Visualization
Silhouette (1)
Davies Bouldin (1)
Runtime (s)
Bi-RSNE
20%
Fig.
2e
0.5244 + 0.0006
0.6882 +000007
36.17 +0.35
i-RSNE
20%
Fig.
0.5251 1..0007
0.7055 + 0.0005
48.24 = 0.22
Bi-RSNE
50%
Fig.
21
0,4883 + 0.0004
0.7558 = 0.0006
86.29 = 0.56
i-RSNE
50%
Fig.
2g
0.4891 0.0003
0.7486 + 0.0008
90.78 = 0.48
Barnes-Hut t-SNE
Fig.
2j
0.4493 0.0001
0.7903 + 0.0004
260.92 + 1.25
quality-time trade-off. 80% initialization, Bi-RSNE completes in 167.79s and achieves a silhouctte of 0.2674, surpassing full t-SNE's 0.2615, and a DB of 3.0342. In the incremental setting, i-RSNE with an 80% seed attains the highest silhouette overall (0.2751) and DB of 2. 2.6328 in 205.61s, demonstrating that one-step updates can further refine cluster compactness at the cost of higher runtime. Reducing the seed to 50% gives a silhouette of 0.2509 and DB of 2.4436 in 245.69s, whereas 20% seed yields a silhouette of 0.2164 and DB of 3.9259 in 266.266 Full Barnes Hut t-SNE remains the slowest (278.20s) with a silhouel of 0.2615 and DB of 3.0632.
Table 3: Comparison of embedding methods CIFAR100 features extracted with DINOv2 VIT-L/14. Metrics include silhouette score (t), provided in Appendix
index (4), and runtime in seconds. Embedding visualizations are
Method
Init.%
Visualization
Silhouette (t)
Davies Bouldin (1)
Runtime (s)
Bi-RSNE
20%
Fig.
3a
0.1847 0.0011
3.1302 + 0.0008
158.27 +0.39
Bi-RSNE
50%
Fig.
3b
0.2325 1 0.0008
2.6058 1 0.0007
160.42 + 0.75
Bi-RSNE
80%
Fig.
0.2674 0.0003
3.0342 = 0.0005
167.79 0.93
-RSNE
80%
Fig.
3d
0.2751 +-0.0002
2.6328 + 0.0005
205.61 + 0.88
iRSNN
50%
Fig.
3e
0.2509 1 0.0006
2.4436 10.0006
245.69 + 0.94
i-RSNE
20%
Fig.
31
0,2164 0.0010
3,9259 + 0.0008
266.26 + 1.17
Barnes- Hut t-SNE
Fig.
3m
0.2615 + 0.0001
3.0632 + 0.0005
278.20 + 1.66
CLIP Features. Results CLIP ViT-L/14 features (Table reveal that very small seed fractions fail to capture CLIP's semantic structure: Bi-RSNE with 20% initialization finishes in just 127. 127.75s but yields a silhouette of 0.0001 and DB of 5.0068. A 50% seed improves silhouette to 0.0509 and DB to 4.4623 in 138.63s. With 80% initialization, Bi-RSNE matches Barnes-Hun t-SNE's silhouette (0.1324 vs. 0.1309) in 172.93s, though DB remains higher (3.8542 vs. 3.7263). the incremental regime, i-RSNE 80% seed achieves silhouctte of 0.1066 and DB of 4.9388 in 197.45s, while 50% and 20% scods yield progressively lower silhouettes (0.0647 and 0.0125) and higher DBs (4.8345 and 5.6213) in 216.13s and 259.55s, respectively. Full Barnes-Huu t-SNE CLIP features requires 278.00s, with silhouette of 0.0309 and DB of 3.7263. These patterns indicate that CLIP embeddings demand larger seed set to form reliable prototypes, but that Bi-RSNE and i-RSNE can still recover comparable clustering quality at substantial runtime savings.
Interestingly, for i-RSNE, the 80% seed variant completes faster than the 20% variant, contrary to the trend observed in CIFARI0. This inversion is attributed the significantly larger number of clusters used for CIFAR100 (K=1000). With fewer clusters (e.g., K=200 in CIFAR10), lower seed fractions usually lead faster runtimes.
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Table 4: Comparison embedding methods on CIFAR100 features extracted with CLIP VIT-L/14. Metrics include silhouette score (t), Davics-Bouldin index (4), and runtime in seconds. Embedding visualizations are
provided in Appendix A
Method
Init.%
Visualization
Silhouette (1)
Davies Bouldin (1)
Runtime (s)
Bi-RSNE
20%
Fig.
3g
0.0001 + 0.0009
5.0068 + 0.0007
127.75 +0.43
Bi-RSNE
50%
Fig.
0.0509 0.0006
1.4623 1 0.0005
138.63 + 0.73
Bi-RSNE
80%
Fig.
31
0.1324 =0.0002
3.8542 = 0.0008
172.93 + 0.91
i-SNE
80%
Fig.
31
0.1066 0.0001
4.9388 + 0.0006
197.45 1.04
IRSNE
50%
Fig.
3k
0.0641 + 0.0006
1.8345 + 0.0007
216.13 + 1.22
i-RSNE
20%
Fig.
3j
0.0125 + 0.0008
5.6213 + 0.0009
259.55 + 1.45
Barnes-Hue HutessHuu&&& t-SNE
Fig.
3n
0.1309 0.0001
3.7263 +0.0004
278.00 = 2.10
4.5.3 iROADS
We evaluated RSNE on the iROADS driving-scene dataset by embodding the full set of 656 images using 1024-dimensional DINOv2 ViT-L/14 features. Table reports results for both Bi-RSNE and i-RSNE at 20% and 50% initialization alongside full Barnes Hut t-SNE. With seed, Barnes Hut t-SNE requires 9.96 to produce an embedding with silhouette 0.3038 and Davies Bouldin (DB) index 1.0085. These moderate clustering metrics reflect the dataset's seven annotated scene conditions, but come at the cost of nearly 10 of compute time.
Bi-RSNE with a 20 % seed set cuts runtime to just 3.26 8, over three times faster, while dramatically improving cluster separation (silhouette 0.6852, DB 0.4369). In comparison, i-RSNE with the same 20 % seed runs in 4.13 s (still more than twice fast as full t-SNE) and yields silhouette of 0.6302 and DB 0.5041, demonstrating that ono-step, point-wise updates additional cost. Increasing the seed fraction to 50 % raises Bi-RSNE's runtime to 6.02 (silhouette 0.4281, DB 0.8094), still 40 % speedup over t-SNE. In that setting, i-RSNE completes in 7.31 s with silhouette 0.4113 and DB 0.8344, indicating that larger seeds diminish the benefit of per-point updates but remain faster than a full re-embedding.
also produce tight clusters with only modest
We also test a setting where - 1 points were used for initialization, and only one incremental update was performed for the remaining sample. This provides stringent test of whether the initialization and update mechanism approximate, even surpass, the quality of embeddings obtained by full t-SNE optimization. itanvie results on DINOv2 features of the iROADS dataset reveal that the incremental approach not only matches but slightly improves the embedding quality. Specifically, our method achieved a Silhouette score of 0.3092 compared to 0.3088 from full (-SNE, and a Davies Bouldin Index of 1.0007 compared to 1.0070. These results indicate that even with a single update step, the incremental procedure preserves inter-cluster scparation while improving intra-cluster compactness. This demonstrates that the proposed initialization and update strategy can provide embeddings that at least. reliable as those from the standard full (-SNE run, while being more efficient and better aligned with continual streaming data scenarios.
Overall, these iROADS results demonstrate that both RSNE variants exploit clear semantic modalitics in a modestly sized, real-world dataset: Bi-RSNE's batch updates achieve the best clustering metrics at minimal runtime, while i-RSNE's one-step refinements offer a middle ground, which is more accurate than Barnes-Fil Hut t-SNE and easily adaptable to streaming data, with only a slight time penalty relative to Bi-RSNE.
4.5.4 fMRI (Haxby 2001)
We evaluated RSNE on the Haxby visual object recognition fMRI dataset using the standard ventral temporal (VT) mask and per-volume features across the eight object categorics. Under the same preprocessing and initialization protocol as our t-SNE baseline, both Bi-RSNE and i-RSNE achieved clear runtime reductions while preserving overall embedding quality: silhouette and Davies Bouldin scores remained similar to
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Table 5: Comparison of embedding methods on iROADS (4 656 samples) with DINOv2 ViT-L/14 features. Metrics include silhouctte score (f), Davies Davies-Bouldin index (L), and runtime seconds. Visualizations are in
Appendix A
Method
Init.%
Visualization
Silhouette (1)
Davies Boulldin (1)
Runtime (s)
Bi-RSNE
20%
Fig.
4a
0.6852 =0.0003
0.4369 +0.0005
3.26 +0.12
i-RSNE
20%
Fig.
1c
0.6302 + 0.0003
0.50.1 0.0004
4.13 + 0.08
Bi-RSNE
50%
Fig.
4b
0.4281 + 0.0002
0.8094 = 0.0005
6.02 = 0.35
i-RSNE
50%
Fig.
4d
0.4113 + 0.0001
0.8344 0.0006
7.31 0.42
Barnes Hut I-SNE
Fig-
Me
0.3038 + 0.0001
1.0085 0.0002
9.96 + 0.77
Barnes- Hut t-SNE. This outcome is consistent that VT representations are distributed and overlapping, which typically limits strong cluster separation; nevertheless, RSNE maintains the same qualitative structure at lower computational cost, making it practical for rapid fMRI exploration and iterative analyses.
Table 6: Comparison of embedding methods on Haxby fMRI (subject 2, VT mask; ~ runs, non-rest volumes).
Method
Init.% %
Silhouette (t)
Davies Bouldin (4)
Runtime (s)
Bi-RSNE
20%
00.997 + 0.0096
26.1182 + 2.3087
0.486 =0.052
i-RSNE
20%
00.051 +: 0.0061
25.7151 +: 2.1954
0.642 0.066
Bi-RSNE
50%
-0.0765 10.0056
25.6565 + 1.7633
0,880 0.038
i-RNEE
50%
-0.0779 + 0.0047
26.1999 +1.6205
1.065 0.031
Barnes-Hie Hut t-SNE
-0.0831 + 0.0042
25.4699 + 1.2609
1.202 0.102
4.5.5 Streaming Data Integration on Climate Dataset
To evaluate RSNE's performance in an online setting, we simulated streaming scenario on the Climate dataset, which comprises approximately 182 500 daily measurements from 50 meteorological stations over ten years. We first embedded 20 % of the data with Barnes- t-SNE to establish initial layout, then applied Bi-RSNE and i-RSNE to incorporate three subsequent monthly batches (April June 2008). Table summarize the quantitative and qualitative results.
and Figure I
Full re-embedding of all 182 500 samples via Barnos-Hut t-SNE requires 508.09 s, yiclding a silhouctte of 0.0676 and a Davies Bouldin index of 8.2827. These metrics reflect the inherently overlapping nature of climate variables, where distinct clusters are difficult to separate. By contrast, Bi-RSNE with only a % seed reduces total runtime to 83.79 (an 83 % reduction), while producing a silhouette of 0.0806 and Davics-Bouldin index of 8.9379. Although the silhouette degrades slightly and DB increases modestly, the quality- time trade-off is highly favorable for interactive or iterative analyses. In the same 20 % setting, i-SNE embeds the stream in 147.14 with silhouette -0.0803 and DB 8.9509, showing that one-step, point-wise updates can nearly match Bi-RSNE's clustering metrics at the cost of additional runtime.
When the seed fraction is increased to 50 %, Bi-RSNE's runtime grows to 228.49 with silhouette -0.0911 and DB 5.7680, indicating that a larger seed can capture slightly more compact clusters (lower DB) at the expense of higher compute. In this setting, i-RSNE completes in 268.40 and achieves silhouette 0.0916 and DB 76662 closely matching Bi- Bi-RSNE's DB but at roughly 18 % longer runtime. Even with 50 % seed, both RSNE variants remain nearly 45 % faster than full t-SNE, demonstrating RSNE's flexibility in balancing speed against embedding fidelity.
Figure visualizes the embedding progression: the top panel shows the initial 20 % layout, and the subsequent panels illustrate the integration of cach monthly batch. New points (outlined black) slot into their nearest cluster prototypes with minimal distortion of the existing structure, highlighting the stability and responsiveness of both Bi-RSNE and i-RSNE update mechanisms.
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Initial embedding (20%)
Smowd
Month (2008-04)
Month 2 (2008-05)
Month (2008-06)
Figure 1: Progression of Bi-RSNE embeddings over time on the Climate dataset. Starting from an initial 20 % layout, three monthly batches are integrated incrementally. New points (outlined) are assigned into cxisting clusters with minimal perturbation.
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Table 7: Streaming integration performance on the Climate dataset. Metrics include silhouette score (t),
Mavies-BBuldd index (4), and total runtime.
Method Init.%
Silhouette (1)
Davies Davies-Bouldin (4)
Runtime (s)
Bi-RSNE
20%
0.0806 + 0.0005
8.9379 0.0012
83.79 10.51
i-RSNE
20%
-0.0803 + 0.0004
8.9509 = 0.00013
147.14 + 0.62
Bi-RSNE
50%
"0.0911 + 0.0002
5.7680
0.0009
228.49 + 1.02
i-RSNE
50%
00.916 +: 0.0002
5.7662 +.000110
268.40 1: 1.31
Barnes Hut t-SNE
-0.0676 #0.0001
8.2827 0.0008
508.09 + 3.45
4.6
Discussion
4.6.1
Embedding Quality in Foundational Model Feature Spaces
RSNE is well suited for visualizing high-dimensional features from foundational models like DINOv2 and CLIP.
These models produce embeddings that are often organized in meaningful groupings, such object classes in DINOv2 semantic similarities in CLIP. RSNE captures these groupings effectively by first placing representative samples using clustering and then adjusting the rest of the points in a way that respects the overall structure.
One of main advantages of RSNE this context that keeps the global layout stable while gradually adding new points. This makes it easier to see consistent patterns across different types of features, even when those features vary in how tightly they group (e.g., more compact in DINOv2, more spread out in CLIP). RSNE helps maintain this structure with much less computation than re-running full t-SNE, making it especially useful when working with large embedding sets or during model development, where updates and comparisons are frequent.
4.7 Ablations
Table 8: Ablation over gradient steps and learning rate 7) performed on the iROADS dataset with DINOv2 VIT- L/ 14 features and 20% initialization size. Higher Silhouette better; lower DB Index better. Initialization time was between 2.0-2.8s depending on r,. Reported runtimes are incremental update times only.
7
Steps
Time (s)
Silhouette
DB Index
0.6530
0.4966
5
0.7
0.6378
0.5120
10
10
0.9
0.6375
0.5123
full
4.6
0.6442
0.5056
1
0.8
0.6858
0.4207
5
0.9
0.6937
0.4097
10
1.0
0.6963
0.4052
full
4.1
0.6912
0.4079
1
0.8
0.6757
0.4639
5
0.8
0.6763
0.4630
0.1
10
1.0
0.6776
0.4610
full
5.5
0.6884
0.4407
0.5
0.6614
0.4689
5
0.8
0.6607
0.4698
0.01
10
0.9
0.6604
0.4700
full
5.5
0.6654
0.4635
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We conducted an ablation study to examine the effect of two key hyperparameters: the number of gradient descent steps per incremental update and the learning rate 7)- Results on the iROADS dataset with DINOv2 VIT-L/14 14 features and 20% initialization size are summarized in Table S Across all settings, we observe that the mothod is relatively stable with respect to the number of gradient steps. In fact, even a single step yields embeddings of comparable quality to full convergence, confirming that the proposed proolyye-based initialization provides a strong starting point that requires only minor refinement.
The learning rate 77 also inffuences performance. While very small values (e.g., n 0.01) slow convergence and provide limited gains, moderate values (17 = 1) achieve the best overall trade-off, delivering the highest Silhouette scores and lowest DB indices with efficient runtime. Larger values (1 10) are more sensitive, sometimes degrading quality slightly despite reduced time per update. These results validate the robustness of our approach and highlight that a modest learning rate with minimal update steps sufficient to achieve strong embedding quality with low computational cost.
We further assessed how protolypes are chosen for Bi-RSNE on iROADS, comparing centroids from k-means ("clustering") to uniformly sampled data points ("random"), Using the same 20% and 50% initialization sizes, clustering- baased prototypes consistently yielded better separation (higher Silhouette, lower DB) with only a small runtime overhead relative to random selection (Table Db Intuitively, clustering produces centroids that minimize within-eluster squared distortion and act as effective anchors that cover dense regions of the feature space, yielding more stable hearest-prototype assignments and better preservation of local neighborhoods in the prototype-afinity step of RSNE; random prototypes lack this coverage and increase assigument noise.
Table 9: Prototype selection ablation on iROADS (DINOv2 VIT-L/14): Bi-RSNE with clustering vs. random prototypes under two initialization sizes. Metries are mean + std.
Prototype selection
Init.%
Silhouette (t)
Davies-Bouldin (1)
Runtime (s)
Random
20%
0.6586 + 0.0004
0.4662 + 0.0006
3.12 + 0.09
Clustering
20%
0.6852 + 0.0003
0.4369 + 0.0005
3.26 + 0.12
Random
50%
0.4132 + 0.0002
0.8203 + 0.0004
5.88 + 0.12
Clustering
50%
0.4281 + 0.0002
0.8094 + 0.0005
6.02 + 0.35
4.8 Overall Findings and Implications
Our results highlight several key ad advattages of the RSNE framework across a range of datasets and embedding types.
Faster, High-Quality Mapping: Bi-RSNE provides a clear trade-off between runtime and embedding quality. By adjusting the initialization fraction, usors can significantly reduce computation lime, often by 50% or more, while still achieving results that are close quality to full t-SNE. This makes RSNE well suited for fast, large-scale visualization.
Efficient Streaming Integration: i-RSNE supports incremental updates by embedding new points individually without reprocessing the entire dataset. This is useful for applications where new data arrives continuously, such as monitoring or interactive data exploration.
Consistency Across Embeddings: RSNE works reliably across different feature types. Whether using DINOv2 or CLIP embeddings, it captures the main structure of the data while preserving both local and global relationships. This makes flexible tool for analyzing features from various deep learning models.
Scalability and Practical Use: Because RSNE updates depend only on a small portion of the data and a limited number of steps, it remains fast and efficient even as datascts grow. It avoids the high computational cost of traditional t-SNE, making it practical for both offline and real-time settings.
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5 Limitations
Although RSNE achieves clear runtime advantages over Barnes-Hut t-SNE, few limitations should be noted. First, the efficiency of i-RSNE can degrade when the number of prototypes K is very large, since each new sample must sequentially compute affinities against all prototypes. This behavior is visible in Table 3 (K= = 1000), where i-RSNE becomes slower relative to Bi-RSNE. In contrast, Bi-RSNE processes entire batches in vectorized manner, amortizing prototype comparisons across many points and maintaining faster runtimes. For smaller prototype sizes (e.g., K 100 in Tables 2 this effect is much less pronounced.
Second, like other prototype-based based methods, RSNE assumes some degree of cluster structure in the data, When the structure is weak, prototype initialization is less effective, though our ablation with random prototypes (Table 9) shows that the method still degrades gracefully and remains efficient.
6 Acknowledgement
This work is supported by ELSA- European Lighthouse on Secure and Safe AI funded by the European Union under grant agreement No. 101070617. Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or European Commission. Neither the European Union nor the European Commission can be held responsible.
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Figure 2: 2D emboddings of CIFAR10 features extracted with DINOv2 and CLIP ViT-L/14 under varying initialization ratios using Bi-RSNE, i-RSNE and full Barnes-Hut t-SNE.
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Figure 3: 2D embeddings of CIFAR100 features extracted with DINOv2 and CLIP VIT-L/14 under varying initialization ratios using Bi-RSNE, i-RSNE and full Barnes-Hut t-SNE.
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Reviews:
[{"review_id": "lLiZv4ir8j", "reviewer": "Reviewer_2GWp", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Please note that I'm unfamiliar with t-SNE and my review is an educated guess.\n\nThe empirical results provided seem to be quite strong. In particular, the reduction in runtime is quite significant.\n\nOn the other hand, the description of the algorithm is quite unclear to me, perhaps because I'm unfamiliar with this line of work.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors extend the t-SNE dimension-reduction algorithm to handle online updates either in the form of an individual sample or a batch of samples. Using these modifications reduces the runtime of processing additional data while improving performance in different metrics.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "* I think it would be helpful if you could state what the mathematical objective of t-SNE is. Then, are there any guarantees that your method is achieving the same objective? In particular, is just one gradient step sufficient?\n\n* Isn't i-RSNE a special case of Bi-RSNE? Are there any advantages to i-RSNE when there is a small number of updates?\n\n* If you're mathematically solving for the same objective as Barnes-Hut t-SNE, how can your performance in terms of Silhouette and Davies–Bouldin metrics be noticeably better, e.g. in Table 5? Is there an explanation/intuition for this?", "broader_impact_concerns": "Not applicable.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "ILfpRu9CVY", "reviewer": "Reviewer_Mg1i", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- The paper is well written and easy to read.\n- There is an extensive related work section with an overview of the field.\n- The presented algorithm is easy to understand and implement.\n\nWeaknesses:\n- There are design choices that are not explained theoretically or explored empirically.\n    - There is no direct comparison of the original t-SNE algorithm to the the proposed algorithm to give the reader an idea of what is being traded off for improved computational efficiency.\n    - It is not clear how exactly the choice of the small seed subset impacts the final performance.  While the authors do vary the initialization subset size with 3 choices (20%, 50% and 80%) in the experiments and do see that performance increases with larger initialization subsets, it is not clear how exactly this choice could affect performance because sometimes the experiments with small initialization sizes were the top performers.\n   - The paper does not justify why a single gradient update is used to improve the embeddings (other than for computational reasons).  How much would the performance change if the optimization is run to completion or if a fixed number of gradient updates were used?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper presents a variant of the t-SNE algorithm for dimensionality reduction that is designed for fast incremental updates with applications for large-scale datasets and streaming data.  The authors state their new algorithm and evaluate its performance in terms of both computational efficiency and clustering performance on various datasets.  The results confirm that the new method is faster than the leading t-SNE algorithm on large datasets, without sacrificing performance in the metrics that the authors evaluated.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Critical changes:\n- Compare how the final embeddings obtained by the proposed method compare to the embeddings obtained by standard t-SNE.  For example, compare the embeddings obtained by t-SNE on a dataset size of N compares to the embeddings obtained by the proposed method using an initialization size of N-1 and 1 incremental update.\n- The experiments section would be greatly strengthened by repeated experiments with different random seeds so that the results tables provide error bars with the results.\n- More extensive evaluation of the design choices such as the size of the initialization set and the number of gradient updates.  The former could be displayed with a curve where the x-axis is the size of the initialization set and the y-axis is a performance metric on a dataset.", "broader_impact_concerns": "There are no broader impact concerns.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "cU8wOuuJZu", "reviewer": "Reviewer_KBDs", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\nThe paper is generally well-written, the idea is simple, and the results are promising. \n\n\nWeaknesses\n\nThe idea of running only one GD step is not justified. I understand it in the context of efficiency. However, what is the intuition behind it? Is this an approximation of another method?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "In this paper, the authors propose an economic version of t-SNE, which also allows to handle streaming data. The main idea is to select a subset of the original dataset, and run t-SNE on this data, while in parallel computing k-means clusters in the original space. When a new point is to be embedded, the closest centroid in the high-dimensional space is computed, and the low-dimensional vector of the new point is initialized in the corresponding low-dimensional centroid. Then one step of gradient descent of the Kullback-Leibler divergence (of the preference of the new point to clusters in the high and low dimensional spaces).\n\nA version for batch processing is also presented.\n\nThe methods are tested in CIFAR10/100, iROADS, and a Climate Dataset. The 2d visualizations are shown, and the Silhouette score and Davies-Boulding Index are reported. The results are very good in general.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "## Critical \n\n - I was expecting a couple of ablation studies, related to each other. Namely:\n\t - You do only one GD step. How does the number of steps affect the result? \n\t - Maybe more important, and related to one point mentioned above. Would it be desirable to minimize the KL all the way? (GD until convergence) I would like to see some results and comparisons related to this. If the results are worse, what is the intuition behind he proposed method working\n\n - What happens when the original data is not clustered? For instance, consider the example mentioned in the paper: streaming resting-state fMRI data for a patient.\n\n - Table 3 shows that for Bi-RSNE, increasing the size of the seed set impacts the runtime, suggesting that the clustering step is the most time-consuming part.\nOn the other hand, for i-RSNE the behaviour is reversed. \nA follow-up experiment on this would be nice.\n\n - Also, based on this last fact, I wonder whether for larger datasets the runtime of (B)i-RSNE is still better than Barnes-Hut t-SNE.\n\n - On page 7, first paragraph. The runtime of Bi-RSNE is O(BK(D+d)). Please detail this order. Also, what is the (total) order for i-RSNE? It only says O(Kd) per update, and with these orders, I don't see why doing the batch procedure is way better than doing B times the i-RSNE. Is it the order? The constant?\n \n## Strengthen the work\n\n - Since, at the end of the day, this is a method to use as an alternative to pure t-SNE, it would also be nice to include other methods in the comparison (UMAP, and other methods mentioned in the paper).\n\n - Add a paragraph for setting the notation throughout the paper. For instance, $x$ will be used for the original datapoint in the original dimension $D$, and $y$ for the embeddings, etc. The notation $d$ for the dimension of the embedding space is defined at the end of the presentation of i-RSNE!\n\n - On page 6, it says \"while leaving the rest of the embeddings essentially unchanged\". Why \"essentially\"? The GD update only affects the embedding of the new point, right?\n \n  - A reorganization of Section 2 may be needed. Also, based on Section 2.3, I was expecting an application to fMRI data.", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)