Regularized k-POD: Sparse k-means clustering for high-dimensional missing data

TL;DR

This paper introduces a regularized k-POD method that enhances high-dimensional missing data clustering by reducing bias through feature-wise regularization, maintaining efficiency and flexibility.

Contribution

It proposes the first bias-mitigating regularized k-POD approach for high-dimensional missing data clustering, improving accuracy over existing methods.

Findings

Effectively reduces bias in high-dimensional missing data clustering.

Improves clustering accuracy in simulations and real-world data.

Maintains computational efficiency and flexibility.

Abstract

The classical k-means clustering, based on distances computed from all data features, cannot be directly applied to incomplete data with missing values. A natural extension of k-means to missing data, namely k-POD, uses only the observed entries for clustering and is both computationally efficient and flexible. However, for high-dimensional missing data including features irrelevant to the underlying cluster structure, the presence of such irrelevant features leads to the bias of k-POD in estimating cluster centers, thereby damaging its clustering effect. Nevertheless, the existing k-POD method performs well in low-dimensional cases, highlighting the importance of addressing the bias issue. To this end, in this paper, we propose a regularized k-POD clustering method that applies feature-wise regularization on cluster centers into the existing k-POD clustering. Such a penalty on cluster centers enables us to effectively reduce the bias of k-POD for high-dimensional missing data. To the best of our knowledge, our method is the first to mitigate bias in k-means-type clustering for high-dimensional missing data, while retaining the computational efficiency and flexibility. Simulation results verify that the proposed method effectively reduces bias and improves clustering performance. Applications to real-world single-cell RNA sequencing data further show the utility of the proposed method.