Some Clustering-based Change-point Detection Methods Applicable to High Dimension, Low Sample Size Data

TL;DR

This paper introduces clustering-based change-point detection methods tailored for high-dimensional, low-sample-size data, addressing the challenges of change detection in such complex scenarios.

Contribution

The paper proposes novel clustering-based methods for detecting single and multiple change-points in high-dimensional, low sample size data, with theoretical analysis and extensive numerical comparisons.

Findings

Methods effectively detect change-points in high-dimensional data.

Proposed methods outperform some existing techniques in simulations.

High-dimensional behavior of methods is theoretically analyzed.

Abstract

Detection of change-points in a sequence of high-dimensional observations is a very challenging problem, and this becomes even more challenging when the sample size (i.e., the sequence length) is small. In this article, we propose some change-point detection methods based on clustering, which can be conveniently used in such high dimension, low sample size situations. First, we consider the single change-point problem. Using k-means clustering based on some suitable dissimilarity measures, we propose some methods for testing the existence of a change-point and estimating its location. High-dimensional behavior of these proposed methods are investigated under appropriate regularity conditions. Next, we extend our methods for detection of multiple change-points. We carry out extensive numerical studies to compare the performance of our proposed methods with some state-of-the-art methods.