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Bibliographic Details
Main Authors: Yamamoto, Michio, Terada, Yoshikazu
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2411.08256
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author Yamamoto, Michio
Terada, Yoshikazu
author_facet Yamamoto, Michio
Terada, Yoshikazu
contents In longitudinal data analysis, observation points of repeated measurements over time often vary among subjects except in well-designed experimental studies. Additionally, measurements for each subject are typically obtained at only a few time points. From such sparsely observed data, identifying underlying cluster structures can be challenging. This paper proposes a fast and simple clustering method that generalizes the classical $k$-means method to identify cluster centers in sparsely observed data. The proposed method employs the basis function expansion to model the cluster centers, providing an effective way to estimate cluster centers from fragmented data. We establish the statistical consistency of the proposed method, as with the classical $k$-means method. Through numerical experiments, we demonstrate that the proposed method performs competitively with, or even outperforms, existing clustering methods. Moreover, the proposed method offers significant gains in computational efficiency due to its simplicity. Applying the proposed method to real-world data illustrates its effectiveness in identifying cluster structures in sparsely observed data.
format Preprint
id arxiv_https___arxiv_org_abs_2411_08256
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle $K$-means clustering for sparsely observed longitudinal data
Yamamoto, Michio
Terada, Yoshikazu
Methodology
62H30
In longitudinal data analysis, observation points of repeated measurements over time often vary among subjects except in well-designed experimental studies. Additionally, measurements for each subject are typically obtained at only a few time points. From such sparsely observed data, identifying underlying cluster structures can be challenging. This paper proposes a fast and simple clustering method that generalizes the classical $k$-means method to identify cluster centers in sparsely observed data. The proposed method employs the basis function expansion to model the cluster centers, providing an effective way to estimate cluster centers from fragmented data. We establish the statistical consistency of the proposed method, as with the classical $k$-means method. Through numerical experiments, we demonstrate that the proposed method performs competitively with, or even outperforms, existing clustering methods. Moreover, the proposed method offers significant gains in computational efficiency due to its simplicity. Applying the proposed method to real-world data illustrates its effectiveness in identifying cluster structures in sparsely observed data.
title $K$-means clustering for sparsely observed longitudinal data
topic Methodology
62H30
url https://arxiv.org/abs/2411.08256