Subspace clustering of high-dimensional data: a predictive approach
This addresses the challenge of identifying natural clusters in high-dimensional data, such as gene expression, for researchers in bioinformatics and data analysis, though it appears incremental as it builds on subspace clustering methods.
The paper tackles the problem of clustering high-dimensional data by assuming each cluster lies in a linear subspace, proposing the Predictive Subspace Clustering (PSC) algorithm that partitions data and estimates PCA parameters simultaneously, with results showing state-of-the-art performance on six real gene expression datasets.
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.