Title: Random Forest Autoencoders for Guided Representation Learning
Venue: NeurIPS 2025
Accepted: yes
Keywords: Manifold learning

Random Forest proximities

Regularized autoencoders

Semi-supervised visualization

Out-of-sample extension
Abstract: Extensive research has produced robust methods for unsupervised data visualization. Yet supervised visualization—where expert labels guide representations—remains underexplored, as most supervised approaches prioritize classification over visualization. Recently, RF-PHATE, a diffusion-based manifold learning method leveraging random forests and information geometry, marked significant progress in supervised visualization. However, its lack of an explicit mapping function limits scalability and its application to unseen data, posing challenges for large datasets and label-scarce scenarios. To overcome these limitations, we introduce Random Forest Autoencoders (RF-AE), a neural network-based framework for out-of-sample kernel extension that combines the flexibility of autoencoders with the supervised learning strengths of random forests and the geometry captured by RF-PHATE. RF-AE enables efficient out-of-sample supervised visualization and outperforms existing methods, including RF-PHATE's standard kernel extension, in both accuracy and interpretability.  Additionally, RF-AE is modality-agnostic, demonstrates strong robustness to hyperparameters, supports both classification and regression, and natively accommodates missing feature values. Our code is available at https://github.com/JakeSRhodesLab/RF-AE.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\n## Summary\n\nThe paper presents RF-AE, a novel framework for supervised dimension reduction method that addresses the limitations of the existing RF-PHATE method. It provides an explicit mapping function for out-of-sample extension, which is useful for handling large datasets and new data points. RF-AE combines autoencoders with the strengths of random forests and the geometric insights of RF-PHATE. It provides experiment results from comparing RF-AE with existing dimension reduction methods.\n\nSTRENGTHS AND WEAKNESSES:\n## Strength\n\nS1. This paper focuses on developing new algorithms for supervised dimension reduction, which is a timely research question. The proposed method is sound and novel.\n\nS2. The experimental design is comprehensive, using 20 datasets and comparing against popular dimension reduction algorithms such as tSNE and UMAP. The quantitative results look promising.\n\nS3. The paper is well-organized and easy to follow.\n\n## Major Weakness\n\nW1. One motivation for RF-AE is to accommodate new observations in during dimension reduction (L29). For example, the abstract and introduction highlight that supervised approaches like RF-PHATE can capture task-specific insights with auxiliary labels. However, section 4 doesn't seem to utilize any task-specific insights or expert labels.\n\nW2. One major benefit for UMAP is its speed and scalability. It is unclear how RF-AE compares to UMAP in these aspects.\n\n## Minor Weakness\n\nM1. How is new data defined? New data from the same distribution of the existing data, or totally out of distribution data?\n\nM2. The term \"data visualization\" in this paper can lead to confusion. This paper mainly focuses on dimension reduction instead of data visualization. I recommend changing it to dimension reduction.\n\nQUESTIONS:\n1. How is new data defined?\n2. How does RF-AE compare to UMAP in terms of speed and scalability?\n3. How can RF-AE incorporate task-specific insights?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a random forest inspired autoencoder (RF-AE), a supervised dimensionality reduction method that combines the \"geometric structure\" derived from Random Forest proximity kernels (RF-GAP) with the parametric capacity of autoencoders. The proposed framework enables out-of-sample embedding via a geometry-regularized encoder trained to preserve the label-informed structure captured by RF-GAP or RF-PHATE. The approach integrates a novel structural importance alignment metric to assess how well learned embeddings retain class-relevant features. A prototype-based approximation is also proposed to reduce input dimensionality and improve scalability.\n\nSTRENGTHS AND WEAKNESSES:\nS1: The paper is well-motivated to combine RF-derived proximity with AE training to address the shortcoming of out-of-sample mapping problem of RFs. It enables efficient parametric encoding and retain the supervised neighborhood structure.\n\nS2: It shows strong empirical performance in preserving class-relevant information across various datasets.\n\nS3: The paper is clearly written, well-organized, and provides sufficient implementation detail.\n\nW1: Despite the prototype approximation, the full proximity matrix is initially computed using all training points (L177). This may be prohibitively costly for large datasets. It would be better if more statistics and explanations related to scalability and computational cost could be discussed.\n\nW2: Although it is mentioned that this framework is agnostic to the kernel method. However, only results based on RF-PHATE are included, and it would be better to demonstrate that this framework works with other kernels. How does the selection of the kernel affect the quality of the final representation?\n\nQUESTIONS:\n1. The scalability of this framework, as mentioned above.\n\n2. Generalization Beyond RF-PHATE. Have the authors tested RF-AE with other embeddings? Empirical results would substantiate the generality claim.\n\n3. Impact of forest configuration: how sensitive is it to the configuration of RF, such as number of trees, max depth?\n\nLIMITATIONS:\nRebuttal content resolves my questions very well.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-06-30"}

comments: SUMMARY:
The paper proposes to build on top of a recent paper (RF-PHATE) to derive a framework for out of sample kernel based visualization. The paper provides a few empirical validations showing more interpretable visualizations.

STRENGTHS AND WEAKNESSES:
The entire motivation of the paper is unclear to me. Nonlinear visualization of data for out-of-sample has been tackled a long time ago by learning a parametric embedding model of the data and then doing a non-kernel based visualization based on those embeddings (this has been true for decades, even prior Deep Learning). There are also numerous specific papers looking at that problem, such as 
- Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering, Yoshua Bengio, Jean-Francois Paiement, Pascal Vincent Olivier Delalleau, Nicolas Le Roux and Marie Ouimet
- Supervised Deep Feature Embedding With Handcrafted Feature, Shichao Kan; Yigang Cen; Zhihai He; Zhi Zhang; Linna Zhang; Yanhong Wang

While it is possible that I missed the underlying benefits of the method, I believe that the abstract and introduction/background do not provide enough context and motivation which needs to be addressed.

QUESTIONS:
Please see above.

LIMITATIONS:
Please see above.
TITLE: Official Review
CLARITY: 1
IMPACT: 2
ORIGINALITY: 1
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes Random Forest Autoencoders (RF-AE), a new framework for supervised representation learning, especially for out-of-sample (OOS) visualization.\nRF-AE integrates the geometry and supervision strengths of RF-PHATE with the flexibility and scalability of autoencoders.\nInstead of reconstructing the raw input, RF-AE reconstructs RF-GAP proximities, a supervised similarity metric derived from random forests, which allows it to learn embeddings aligned with the supervised structure of the data.\nA geometric regularization term ensures alignment between the latent representation and a precomputed RF-PHATE embedding.\nThe authors also introduce a prototype selection mechanism to reduce computational costs and memory usage by selecting representative training points via class-wise k-medoids clustering on RF-GAP dissimilarities.\nRF-AE consistently outperforms baseline parametric and nonparametric methods in terms of both classification accuracy and a novel Structural Importance Alignment (SIA) metric, which measures how well the embedding reflects the classification-relevant structure of the input features.\nRF-AE achieves strong trade-offs between local/global structure preservation and class separability, with robust performance across various hyperparameter settings.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n- The proposed RF-AE framework combines random forest-derived (RF-GAP) proximities with an autoencoder-based architecture. Reconstructing RF-GAP proximities, rather than original input vectors, within the autoencoder is a meaningful and novel departure from standard AE objectives.\n- The methodological foundation is strong, integrating insights from manifold learning, kernel regression, and autoencoder design in a coherent way. Key innovations include geometric loss regularization based on RF-PHATE embeddings and a prototype selection mechanism to enhance scalability.\n- The geometric loss, guided by RF-PHATE embeddings, ensures alignment between the supervised structure and the learned latent space, helping mitigate overfitting or trivial embedding solutions.\n- The Structural Importance Alignment (SIA) metric fills an important evaluation gap in supervised visualization by quantifying the extent to which embeddings preserve classification-relevant feature structure. This is a valuable and well-motivated contribution.\n- RF-AE ranks among the top across both local/global SIA and classification accuracy benchmarks. Ablation studies further demonstrate robustness to hyperparameter choices such as the geometric constraint weight ($\\lambda$) and number of prototypes.\n\n**Weaknesses**\n- As the authors acknowledge, a key limitation is the computational cost of computing RF-GAP proximities, which scales poorly with dataset size. Although prototype selection via class-wise k-medoids helps mitigate this, it still requires full computation of the RF-GAP proximity matrix which is posing a barrier for large-scale applications.\n- There are no concrete runtime or memory benchmarks demonstrating feasibility on large-scale datasets, although timing for the proposed method on a single dataset with varying prototype counts is reported.\n- The generalizability of the SIA metric may depend on the specific ensemble of classifiers and the perturbation heuristics used, which could introduce variance or bias across different data modalities or domains.\n\nQUESTIONS:\n1. While the authors acknowledge the computational cost of RF-AE, there is no concrete study and comparison on it, except the running time by different amount of prototypes. There should be training/inference time (and memory consumption) comparison with the other baselines compared across datasets, for a better understanding for practical considerations. \n2. How sensitive is the SIA metric to the choice of classifiers and perturbation schemes? Could the authors provide ablation results or sensitivity analyses with different classifiers or correlation thresholds? The authors may consider reporting SIA variation across: alternative classifiers or non-ensembled versions, different perturbation strategies, and/or datasets with weak label–feature correlation. \n3. Can we utilize unlabeled data also for training RF-AE, e.g., in a semi-supervised way? Unsupervised methods of course can handle all available data without using labels, and methods like UMAP, semi-supervised variants of t-SNE [1], ViVA [2], etc., can learn from both unlabeled and labeled data. In a realistic scenario, learning from labeled data only may reduce data efficiency.\n\n[1] Serna-Serna, Walter, et al. \"Semi-supervised t-SNE with multi-scale neighborhood preservation.\" Neurocomputing 550 (2023): 126496.\n\n[2] An, Sungtae, Shenda Hong, and Jimeng Sun. \"Viva: semi-supervised visualization via variational autoencoders.\" 2020 IEEE International Conference on Data Mining (ICDM). IEEE, 2020.\n\nLIMITATIONS:\nThe authors have done a good job acknowledging technical limitations, particularly about scalability due to the computational cost of RF-GAP proximities.\nHowever, they do not sufficiently address potential negative societal impacts of their method, especially considering its applicability in high-stakes domains like biomedical and healthcare.\nIt would be very helpful if the authors could discuss some potential pitfalls, for example (not must):\n- Risks in biomedical or clinical data visualization, such as over-interpretation of embeddings, model bias from supervised proximities, or misuse of visualizations in decision-making.\n- How the complexity of the RF-GAP kernel and the autoencoder might make the resulting embeddings even harder to interpret, especially by non-technical stakeholders.\n- What if the labels RF-GAP relies on encode social or demographic biases? Could this lead to skewed embeddings?\n\nAddressing those kinds of concerns, even briefly, would demonstrate awareness of broader impact and strengthen the paper’s maturity.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}