Some notes on the $k$-means clustering for missing data
Abstract
The classical -means clustering requires a complete data matrix without missing entries. As a natural extension of the -means clustering for missing data, the -POD clustering has been proposed, which ignores the missing entries in the -means clustering. This paper shows the inconsistency of the -POD clustering even under the missing completely at random mechanism. More specifically, the expected loss of the -POD clustering can be represented as the weighted sum of the expected -means losses with parts of variables. Thus, the -POD clustering converges to the different clustering from the -means clustering as the sample size goes to infinity. This result indicates that although the -means clustering works well, the -POD clustering may fail to capture the hidden cluster structure. On the other hand, for high-dimensional data, the -POD clustering could be a suitable choice when the missing rate in each variable is low.
Keywords
Cite
@article{arxiv.2410.00546,
title = {Some notes on the $k$-means clustering for missing data},
author = {Yoshikazu Terada and Xin Guan},
journal= {arXiv preprint arXiv:2410.00546},
year = {2024}
}
Comments
16 pages, 4 figures