Subspace clustering of high-dimensional data: a predictive approach

TL;DR

This paper introduces Predictive Subspace Clustering (PSC), a novel method for high-dimensional data that simultaneously clusters data and estimates PCA-based subspaces, demonstrating superior performance on gene expression datasets.

Contribution

The paper presents PSC, a new algorithm for high-dimensional subspace clustering that integrates PCA estimation with clustering and introduces a measure of influence for PCA models.

Findings

PSC often outperforms competing methods in gene expression data clustering.

The algorithm effectively estimates cluster-specific PCA models.

Extensive simulations validate the convergence and robustness of PSC.

Abstract

In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a new approach for partitioning such high-dimensional data. Our assumption is that, within each cluster, the data can be approximated well by a linear subspace estimated by means of a principal component analysis (PCA). The proposed algorithm, Predictive Subspace Clustering (PSC) partitions the data into clusters while simultaneously estimating cluster-wise PCA parameters. The algorithm minimises an objective function that depends upon a new measure of influence for PCA models. A penalised version of the algorithm is also described for carrying our simultaneous subspace clustering and variable selection. The convergence of PSC is discussed in detail, and extensive simulation results and comparisons to competing methods are presented. The comparative performance of PSC has been assessed on six real gene expression data sets for which PSC often provides state-of-art results.