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

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.