List of Papers Browse by Subject Areas Author List
Abstract
Learning unsupervised representations of medical imaging cohorts can reveal anatomically meaningful prototypes without expert labels, which are often noisy and fail to capture true pathological heterogeneity. However, existing deep latent-variable models estimate Gaussian mixture priors via Euclidean averaging, producing prototypes that drift off the curved data manifold and degenerate as the number of sub-populations grows. We propose a manifold-anchored variational framework built on a geometry-aware Expectation-Maximization (EM) algorithm, whose M-step selects each sub-population prototype as the graph medoid with the highest diffusion centrality on a heat-kernel-weighted latent graph, ensuring that every prototype remains on-manifold. A Dirichlet energy regularizer enforces geometric smoothness of the latent space, and a per-sub-population uncertainty score enables label-free quality assessment. The manifold-anchored EM is a general-purpose geometric tool that extends standard EM and applies readily to other latent-variable models beyond this setting. On cardiac scar and brain MRI benchmarks, our framework attains the highest accuracy among all compared methods, produces the sharpest prototypes reported to date, and remains stable at large sub-population counts where all baselines degenerate. The Code and implementation details are available at https://github.com/jr-xing/On-Manifold-Variational-Learning-with-Heat-Kernel-Priors.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/4033_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/jr-xing/On-Manifold-Variational-Learning-with-Heat-Kernel-Priors
Link to the Dataset(s)
N/A
BibTex
@InProceedings{XinJia_OnManifold_MICCAI2026,
author = { Xing, Jiarui AND Zeevi, Tal AND Wu, Nian AND Wang, Jian},
title = { { On-Manifold Variational Learning with Heat-Kernel Priors } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16896},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
Authors in their paper propose a unified framework bridging probabilistic latent clustering with spectral manifold geometry for label-free stratification of medical images.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
Authors in their paper presented a clustering framework that eliminates offmanifold drift by selecting cluster prototypes as heat-kernel medoids on the latent manifold. Experiments were performed on various datasets confirming its enhanced clustering accuracy and effectiveness.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
Limited novelty of the methodology, lack of statistical methods to ensure the results, lack of information regarding the complexity of the approach
- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission has provided an anonymized link to the source code, dataset, or any other dependencies.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
The paper is interesting. However, I have main concerns regarding the following:
1) The novelty of this paper is not sufficiently explained. What is the superiority of the proposed framework, compared to other relevant approaches? It is not clear to me. 2) There is lack of statistical tests. Have the authors tested the validity of their results? 3) Contributions of this work are mentioned to some extent, but need to be improved. Both in abstract and Introduction, authors should have clarified their novelty and contributions in a clear way. 4) What are the limitations of this work? There is no such discussion to this paper. 5) What is the computational complexity of this algorithm? 6) Is it faster or not in the execution compared to the rest approaches?
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The paper has an impact on the scientific community and has an interesting topic. However, my main concerns are that there is lack of novelty, statistical tests and and that some information is missing regarding the complexity of the proposed approach.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
Although the majority of concerns have not been adequately explained, I would suggest that this manuscript be accepted and further optimized based on the reviewers’ suggestions, as it includes interesting research and has an impact on the scientific society.
Review #2
- Please describe the contribution of the paper
The paper proposes a manifold-aware probabilistic clustering framework that avoids unrealistic cluster representatives by ensuring prototypes lie on the underlying data manifold. It builds a heat-kernel graph over latent embeddings and uses graph Laplacian and Dirichlet energy to regularize the latent space, preserving its intrinsic structure. Used in the standard VAE, it leads to improved clustering accuracy, uncertainty estimation and applicability to unlabeled medical datasets.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
The key idea of avoiding off-manifold drift addresses a limitation of standard clustering. This idea is fully integrated into an end-to-end variational framework. Moreover, this label-free approach is highly relevant for medical imaging with scarce annotations. Also, we can produce well-calibrated uncertainty estimates with this method. Additionally, the code is publicly shared.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
Mini-batch approximation: as described, the graph structure is computed locally within mini-batches, which may not fully capture the global manifold geometry. It would be helpful to clarify how batches are constructed, as this could affect performance. And it isn’t clear if the method can be applied to any type of manifold. Limited discussion of failure cases or challenging datasets: so, a more detailed analysis of the method’s limitations would improve the paper.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission has provided an anonymized link to the source code, dataset, or any other dependencies.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(5) Accept — should be accepted, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
An elegant manifold-aware clustering framework that improves clustering, but relies on assumptions about latent geometry that may limit robustness.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
The paper presents a technically interesting framework, rebuttal clarifications are presented, although some reviewer concerns can be only partially addressed.
Review #3
- Please describe the contribution of the paper
1.Proposes a manifold-aware deep clustering framework that replaces Euclidean centroids with heat-kernel graph medoids to keep prototypes on the data manifold. 2.Introduces spectral (Dirichlet energy) regularization to preserve latent-space geometry and improve cluster structure. 3.Provides per-cluster uncertainty estimation for label-free quality assessment, achieving more stable and clinically meaningful clustering.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.The paper introduces a fundamentally different approach to latent clustering by replacing Euclidean centroids with heat-kernel graph medoids, ensuring prototypes remain on the data manifold. This directly addresses the well-known issue of off-manifold drift and cluster collapse in GMM-based deep clustering, which is both theoretically well-motivated and practically impactful. 2.The use of heat-kernel affinities and Dirichlet energy regularization provides a strong geometric foundation for preserving intrinsic structure in the latent space. This combination of probabilistic modeling with manifold/spectral methods is elegant and generalizable beyond this specific task. 3.The method is validated across multiple datasets of increasing complexity (MNIST, synthetic cardiac, and real brain MRI) with consistent improvements in clustering metrics (ACC, NMI, ARI) and qualitative results. The comparison against strong generative baselines (VAE-GMM, Diffusion-GMM) strengthens the empirical claims.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1.From Fig. 2(a–c), comparisons are mainly against VAE-GMM and Diffusion-GMM, both closely related generative methods. There is no comparison with strong non-generative clustering baselines (e.g., DEC, SCAN, spectral clustering), making it unclear whether improvements are due to the manifold idea or simply the model class. 2.In Fig. 2(c) and Fig. 3 (top), the claimed “sharper” cluster centers are visually apparent but not strongly distinct from baselines. The sharpness metric is shown, but lacks statistical testing or perceptual validation, making the improvement somewhat subjective. Fig. 2(d) and Fig. 3 (bottom) show more structured uncertainty, but there is no quantitative evaluation of uncertainty quality (e.g., calibration, correlation with errors, or clinical relevance). It is unclear whether the uncertainty is truly meaningful or just visually different. 3.The method relies on graph construction and heat-kernel computations, but the figures do not provide evidence of scalability (e.g., runtime, memory) for larger datasets, which could be a practical limitation.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission has provided an anonymized link to the source code, dataset, or any other dependencies.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The paper presents a novel and well-motivated manifold-aware clustering framework that addresses an important limitation of existing deep clustering methods, namely off-manifold centroid estimation and cluster degeneracy. The integration of heat-kernel-based medoid selection, spectral regularization, and uncertainty estimation within a unified variational framework is technically sound and shows consistent empirical improvements across multiple datasets. The experimental results demonstrate better clustering performance and more coherent prototypes compared to strong generative baselines, with some evidence of clinical relevance. However, the evaluation is limited by a relatively narrow set of baselines and relies partly on controlled or low-complexity datasets, and the uncertainty estimates are not quantitatively validated. Overall, the strengths outweigh the weaknesses, placing the paper slightly above the acceptance threshold.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Review #4
- Please describe the contribution of the paper
The paper proposes a unsupervised clustering technique of imaging data using an approach that aims to keep cluster centroids (prototypes) on the data manifold. The idea is to integrate a heat-kernel prior into the EM algorithm (GMM-like clustering). Results are demonstrated on two clinical datasets (plus MNIST).
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
The approach is well motivated by highlighting the issue of current methods resulting in prototypes which can be off the manifold, and thus, are not representing high density areas with realistic fidelity. The proposed method is easy to implement, and the results suggest improved (unsupervised) clustering on two clinical datasets.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
The experimental evaluation could be improved. The paper does not yet make a strong case for the method to be useful for stratification of medical imaging data in large-scale, complex, heterogeneous data scenarios. The used datasets are either too simplistic (cardiac masks), or no quantitative evaluation is available (brain images). A major limitation is the setting where the number of clusters K always coincided with the true number of classes in each dataset. I understand that this was determined using the elbow method, but the fact that the optimal number coincides on all three cases with the true number classes is striking and may suggest that these datasets are too simplistic for assessing unsupervised clustering methods. In reality, we will most often not know the optimal number of clusters. It would have been good to assess the clustering performance under varying number of K.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission has provided an anonymized link to the source code, dataset, or any other dependencies.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
The proposed method could be very useful for the stratification of medical imaging data, in particular, in applications such as subgroup performance analysis, bias detection, and discovery of clinically meaningful subgroups. The current experiments, however, provide insufficient evidence that the proposed method could truly outperform existing methods in such applications.
It is recommended to employ the method on large-scale, heterogeneous datasets (e.g., CXR), to also demonstrate its scalability. It was unclear whether in the used settings, the EM algorithm was run using mini-batches, and it would interesting to know how this may affect convergence under the heat-kernel prior.
The paper could be improved by adding a sensitive analysis on the number of clusters.
Also, while the per-cluster uncertainty is intriguing, and potentially powerful to identify underperforming (or otherwise interesting) subgroups, this has not been demonstrated. Again, an application CXR disease detection could be a perfect setting for demonstrating this.
Lastly, a discussion or investigation about the role of the encoder/decoder model could be interesting. Different type of models (e.g., VQ-VAEs) could be interesting to use in combination with the proposed clustering method.
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(3) Weak Reject — marginally below the acceptance threshold, but would not mind if accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
An interesting approach with a well motivated method which lacks a strong evaluation to support the claims. Adding some of the recommended experiments and analyses would substantially strengthen the paper.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
I was happy with the rebuttal which clarified my concerns regarding the number of clusters, and most of my other points. I understand the authors’ point about the method focusing on data-constrained settings; it would still be interesting to see how it may perform on large-scale datasets, where subgroup discovery is an open challenge.
Author Feedback
We sincerely thank AC and all the reviewers for their constructive feedback.
Novelty & Contribution (R1). We present a unified generative framework integrating image clustering, prototype learning, and uncertainty quantification (UQ) within a manifold-aware objective. Our central theoretical contribution is the manifold-anchored EM algorithm. It offers a manifold-aware geometric extension to standard EM by constraining prototype inference to the data manifold via a heat-kernel graph. Unlike conventional EM, which often yields blurry Euclidean averages, our approach produces geometrically intrinsic prototypes. This establishes a generalizable theoretical tool for robust representation learning. Clinically, these learned atlases serve as faithful templates for disease subtyping, while the derived uncertainty maps provide spatially coherent confidence estimates that may assist interpretation of anatomically variable regions.
Baseline Choice (R3, R4). We thank reviewers for suggesting more baselines. Our baselines (VAE-GMM and Diffusion-GMM) were selected to match our multi-task objective: simultaneous clustering, prototype generation, and UQ. Non-generative methods like DEC or spectral clustering are useful for clustering metrics, but lack the native capacity to generate anatomical atlases or spatial uncertainty maps. We will clarify this evaluative scope and consider broader comparisons in future work.
Evaluation & Dataset Complexity (R1–R4). We thank R1 for emphasizing statistical reliability. We ensure this through consistent performance across multiple random seeds, confirming that gains are not stochastic. Regarding R4’s query on subject count, OASIS is a validated benchmark for neuroanatomical discovery, where the main challenge is high-dimensional morphological variance rather than sample size alone. Our framework is optimized for such data-constrained clinical settings, demonstrating superior data-efficiency by leveraging geometric priors to capture subtle structural transitions. For R3, improved sharpness reflects better preservation of cortical structure, which we will highlight with zoomed ROIs. For R2, uncertainty maps exhibit anatomically localized structure (e.g., scar-borders in cardiac MRI, ventricular/cortical variability in brain MRI), rather than diffuse uncertainty observed in baseline methods. We agree that future work should include quantitative validation of uncertainty quality, such as calibration or correlation with reconstruction error.
Choice of K and OASIS (R4). We thank R4 for the opportunity to clarify K selection. Known category numbers were used for MNIST and cardiac benchmarks only to facilitate objective quantitative evaluation. For OASIS, K=8 was determined purely by the unsupervised elbow criterion, independent of clinical metadata. Since OASIS clinical scores are functional assessments rather than direct image-morphology labels, they were not used for model selection. Our framework discovers distinct anatomical prototypes that remain stable across K values, confirming findings are not artifacts of hyperparameter choice.
Complexity & Scalability (R1, R3, R4). While our focus is performance, the computational cost is bounded. During training, the heat-kernel graph is computed within mini-batches, adding O(B^2d) time and O(B^2) memory, avoiding O(N^2) global complexity. At inference, parameters are fixed, so prediction requires no graph reconstruction. Our approach is more efficient than diffusion-based baselines requiring expensive iterative denoising.
Manifold Assumptions (R2, R4). We appreciate R2’s technical inquiry regarding manifold recovery. We use mini-batch graphs as local, bounded approximations of geometry rather than claiming global manifold recovery. We assume local neighborhoods in the learned latent space are biologically meaningful, while GMM/KL terms regularize embeddings toward a structured mixture distribution.
All minor issues will be addressed in the final version.
Meta-Review
Meta-review #1
- Your recommendation
Invite for Rebuttal
- Please justify your decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.
Even if some reviewers suggested rejection due to a lack of important experiments (larger-scale datasets, robustness/sensitivity analysis on the number of clusters, different encoder/decoder models, more baselines), I believe that many concerns raised by the reviewers could be addressed in the rebuttal. Authors are invited to discuss in particular the choice of baseline methods, some unclear implementation details (e.g., EM setup, mini-batch behavior, model choices about the encoder/decoder), and why the used datasets are enough to validate the proposed method.
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
The authors managed to consistently and accurately address most of the concerns raised by the reviewers. All reviewers lean toward acceptance, and I agree with this assessment.
Meta-review #2
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
This paper proposes a manifold-aware deep clustering framework for label-free stratification of medical images, selecting cluster prototypes as heat-kernel medoids on the latent manifold to avoid off-manifold drift, with Dirichlet-energy spectral regularization and per-cluster uncertainty estimates within a variational framework. The reviewers agree that the off-manifold drift problem is well motivated, the geometric formulation is elegant and integrated end-to-end, and the approach is practically relevant for low-annotation settings. The rebuttal clarified that the cluster number for OASIS was set by an unsupervised elbow criterion independent of clinical metadata, the rationale for restricting baselines to generative methods matching the multi-task objective, and the mini-batch construction and bounded complexity of the heat-kernel graph, and the reviewer who had placed the paper below the threshold confirmed these resolved their concerns. The main remaining reservation is the reliance on relatively controlled datasets and a narrow set of baselines, and the authors are encouraged to qualify the stratification claims accordingly and to add the quantitative uncertainty validation noted as future work.
Meta-review #3
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
Reviewers in agreement, rebuttal answered questions.