Partition First, Embed Later: Laplacian-Based Feature Partitioning for Refined Embedding and Visualization of High-Dimensional Data

Erez Peterfreund, Ofir Lindenbaum, Yuval Kluger, Boris Landa

International Conference on Machine Learning 2025 · Oral

In this compelling talk from ICML 2025, Erez Peterfreund, a postdoc at Yale University, presented novel research on **Laplacian-based feature partitioning** for enhancing the embedding and visualization of complex high-dimensional data. Titled "Partition First, Embed Later," the work addresses a critical challenge in unsupervised data analysis: how to generate interpretable embeddings when the observed data is influenced by multiple, distinct latent variables. This is particularly prevalent in fields like genomics and medical imaging, where samples (e.g., cells, images) are characterized by a vast number of features (e.g., genes, pixels), yet these features ultimately reflect a much smaller set of underlying biological or physical processes.

AI review

A competent and honest contribution that proposes a principled feature-partitioning framework for disentangled manifold learning. The alternating minimization approach is well-motivated and the genomic validation is genuinely satisfying, with gene-level biological recovery being a strong sanity check. However, the theoretical guarantees are narrow (K=2, asymptotic, modified objective with entropy regularization), the core optimization is susceptible to local minima in ways that are not carefully analyzed, and the relationship to prior work on multi-view learning, independent subspace…