Learning From Hidden Traits: Joint Factor Analysis and Latent Clustering

TL;DR

This paper introduces a joint factor analysis and latent clustering framework that learns low-dimensional, cluster-aware representations of matrix and tensor data, improving data analysis tasks like clustering and classification.

Contribution

It proposes a novel joint factorization and clustering method that leverages unique latent representations to uncover hidden cluster structures while enhancing factorization performance.

Findings

Effective in revealing hidden cluster structures in data

Improves clustering and classification accuracy

Validated on real-world datasets like Reuters and MNIST

Abstract

Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis, such as clustering or classification. Finding reduced-dimension representations that are well-suited for the intended task is more appealing. This paper proposes a joint factor analysis and latent clustering framework, which aims at learning cluster-aware low-dimensional representations of matrix and tensor data. The proposed approach leverages matrix and tensor factorization models that produce essentially unique latent representations of the data to unravel latent cluster structure -- which is otherwise obscured because of the freedom to apply an oblique transformation in latent space. At the same time, latent cluster structure is used as prior information to enhance the performance of factorization. Specific contributions include several custom-built problem formulations, corresponding algorithms, and discussion of associated convergence properties. Besides extensive simulations, real-world datasets such as Reuters document data and MNIST image data are also employed to showcase the effectiveness of the proposed approaches.