# Rich Component Analysis

arXiv: https://arxiv.org/abs/1507.03867 · HTML: https://mlsanity.com/paper/1507.03867/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2015.

## Built on by (most cited first, 6 of 6)

- [Interactive Dimensionality Reduction for Comparative Analysis](https://mlsanity.com/paper/2106.15481/) (2021)
- [SepVAE: a contrastive VAE to separate pathological patterns from healthy ones](https://mlsanity.com/paper/2307.06206/) (2023)
- [Separating common from salient patterns with Contrastive Representation Learning](https://mlsanity.com/paper/2402.11928/) (2024)
- [Visual Analytics Using Tensor Unified Linear Comparative Analysis](https://mlsanity.com/paper/2507.19988/) (2025)
- [Clustering-friendly Representation Learning for Enhancing Salient Features](https://mlsanity.com/paper/2408.04891/) (2024)
- [CASL-VAE: Learning Structured Latent Variables from Unpaired Data for Semi-supervised Clustering and Paired Sample Generation](https://mlsanity.com/paper/2607.08254/) (2026)

## Abstract (arXiv)

In many settings, we have multiple data sets (also called views) that capture different and overlapping aspects of the same phenomenon. We are often interested in finding patterns that are unique to one or to a subset of the views. For example, we might have one set of molecular observations and one set of physiological observations on the same group of individuals, and we want to quantify molecular patterns that are uncorrelated with physiology. Despite being a common problem, this is highly challenging when the correlations come from complex distributions. In this paper, we develop the general framework of Rich Component Analysis (RCA) to model settings where the observations from different views are driven by different sets of latent components, and each component can be a complex, high-dimensional distribution. We introduce algorithms based on cumulant extraction that provably learn each of the components without having to model the other components. We show how to integrate RCA with stochastic gradient descent into a meta-algorithm for learning general models, and demonstrate substantial improvement in accuracy on several synthetic and real datasets in both supervised and unsupervised tasks. Our method makes it possible to learn latent variable models when we don't have samples from the true model but only samples after complex perturbations.