Homogeneity and Sub-homogeneity Pursuit: Iterative Complement Clustering PCA

TL;DR

This paper introduces an iterative clustering PCA method that effectively captures both group-wide and group-specific patterns in high-dimensional data, addressing limitations of traditional PCA.

Contribution

It proposes a novel iterative complement-clustering PCA technique and a principal component regression clustering method, enhancing group-specific pattern detection.

Findings

Successfully identifies cluster memberships under certain conditions

Demonstrates superior performance in simulations

Validates effectiveness on stock return data

Abstract

Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as much information as possible from the original data. However, in the presence of a group structure of the data, PCA often fails to identify the group-specific pattern, which is known as sub-homogeneity in this study. Group-specific information that is missed can result in an unsatisfactory representation of the data from a particular group. It is important to capture both homogeneity and sub-homogeneity in high-dimensional data analysis, but this poses a great challenge. In this study, we propose a novel iterative complement-clustering principal component analysis (CPCA) to iteratively estimate the homogeneity and sub-homogeneity. A principal component regression based clustering method is also introduced to provide reliable information about clusters. Theoretically, this study shows that our proposed clustering approach can correctly identify the cluster membership under certain conditions. The simulation study and real analysis of the stock return data confirm the superior performance of our proposed methods.