# Disentangling Interpretable Factors with Supervised Independent Subspace Principal Component Analysis

arXiv: https://arxiv.org/abs/2410.23595 · HTML: https://mlsanity.com/paper/2410.23595/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 31 Oct 2024.

## Builds on (most cited first, 7 of 7)

- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis](https://mlsanity.com/paper/1704.00708/) (2017)
- [Guaranteed Matrix Completion via Non-convex Factorization](https://mlsanity.com/paper/1411.8003/) (2014)
- [The HSIC Bottleneck: Deep Learning without Back-Propagation](https://mlsanity.com/paper/1908.01580/) (2019)
- [Self-Supervised Learning with Kernel Dependence Maximization](https://mlsanity.com/paper/2106.08320/) (2021)
- [Information Constraints on Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1805.08672/) (2018)
- [Contrastive Variational Autoencoder Enhances Salient Features](https://mlsanity.com/paper/1902.04601/) (2019)

## Built on by (most cited first, 1 of 1)

- [Supervised Stochastic Gradient Algorithms for Multi-Trial Source Separation](https://mlsanity.com/paper/2508.20618/) (2025)

## Abstract (arXiv)

The success of machine learning models relies heavily on effectively representing high-dimensional data. However, ensuring data representations capture human-understandable concepts remains difficult, often requiring the incorporation of prior knowledge and decomposition of data into multiple subspaces. Traditional linear methods fall short in modeling more than one space, while more expressive deep learning approaches lack interpretability. Here, we introduce Supervised Independent Subspace Principal Component Analysis (textttsisPCA), a PCA extension designed for multi-subspace learning. Leveraging the Hilbert-Schmidt Independence Criterion (HSIC), textttsisPCA incorporates supervision and simultaneously ensures subspace disentanglement. We demonstrate textttsisPCA's connections with autoencoders and regularized linear regression and showcase its ability to identify and separate hidden data structures through extensive applications, including breast cancer diagnosis from image features, learning aging-associated DNA methylation changes, and single-cell analysis of malaria infection. Our results reveal distinct functional pathways associated with malaria colonization, underscoring the essentiality of explainable representation in high-dimensional data analysis.