Preprint | arXiv:2504.04079v2
A fully variational co-clustering framework that learns row clusters, column clusters, and cell-level interaction structure in one noise-robust training pipeline.
Noisy input
Co-clustered blocks
Problem
Co-clustering identifies homogeneous groups of both instances and features in a matrix. Traditional methods often depend on shallow factorizations, linear transformations, or assumptions that struggle with sparse, high-dimensional, corrupted, or missing data.
Approach
SRVCC uses row-side and column-side VAEs with Gaussian mixture priors, adds a joint cell-level latent variable, and optimizes a compositional objective with mutual information coupling and doubly reparameterized gradients.
Core contributions
Learns row and column clusters directly in latent space, replacing separate post-hoc clustering with a generative, end-to-end objective.
Combines row-side, column-side, and joint cell-level variational objectives so each part of the matrix contributes structured evidence.
Regularized reconstruction, KL structure, and noise learning are designed to keep cluster assignments stable under corrupted or sparse data.
A mutual-information cross-loss encourages row and column assignments to preserve dependence in the original matrix.
Method
The framework turns a raw matrix into soft row clusters, soft column clusters, and joint block labels while retaining uncertainty throughout the training objective.
Rows are instances; columns are features.
Separate encoders learn probabilistic latent spaces for each axis.
Mixture components provide soft cluster anchors in both latent spaces.
A third latent variable models row-column interaction and local deviations.
Soft row and column partitions are coupled through mutual information.
Rows and columns reorder into interpretable blocks.
Reported results
Selected values from the paper tables. ACC is clustering accuracy; NMI is normalized mutual information.
| Dataset | SRVCC ACC | SRVCC NMI | Note |
|---|---|---|---|
| Fashion-MNIST-test | 68.2 +/- 1.8 | 65.0 +/- 1.6 | Strong image benchmark gain over DeepCC |
| WebKB4 | 83.2 +/- 1.6 | 42.3 +/- 1.2 | Large accuracy gain on sparse text/web data |
| Yale | 58.1 +/- 1.7 | 61.0 +/- 1.5 | Improved facial-image latent separation |
| WebKB wisconsin | 81.6 +/- 2.2 | 51.5 +/- 1.6 | Best reported result in both ACC and NMI table columns |
| IMDb movies actors | 26.2 +/- 2.4 | 19.4 +/- 1.8 | Modest gain on a harder sparse movie-feature split |
Ablation
The paper compares feature-only clustering, a simple cascade, and the two-stage compositional ELBO design. The two-stage version with DREG reports the strongest accuracy and NMI on the shown ablations.
DREG helps, but without the joint stage it remains weaker.
Better than feature-only, still below two-stage ELBO.
Best reported ACC and NMI for this ablation.
Best reported ACC and NMI under DREG.
Biomedical appendix
The paper appendix applies the co-clustering approach to PPMI clinical and imaging variables. This section is exploratory and should be read as biomarker-discovery analysis, not diagnostic deployment.
One near-singleton group shows low motor burden, high MoCA, early Hoehn and Yahr stage, and mild or near-normal imaging values.
An older cluster displays wider motor severity and comparatively preserved DaTSCAN signals, suggesting non-linear relationships among age, imaging, and symptoms.
Several broader groups share moderate severity but differ by cognition, imaging spread, age at diagnosis, and ventricular or striatal measures.
Putamen and caudate DaTSCAN ratios, ventricular and striatal MRI volumes, UPDRS-III, Hoehn and Yahr stage, and MoCA emerge as separating variables.
Resources
@article{vinod2025scalable,
title={Scalable Robust Bayesian Co-Clustering with Compositional ELBOs},
author={Vinod, Ashwin and Bajaj, Chandrajit},
journal={arXiv preprint arXiv:2504.04079},
year={2025}
}