Regularized k-POD: Sparse k-means clustering for high-dimensional missing data
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909690433110016 |
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| author | Guan, Xin Terada, Yoshikazu |
| author_facet | Guan, Xin Terada, Yoshikazu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11884 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularized k-POD: Sparse k-means clustering for high-dimensional missing data Guan, Xin Terada, Yoshikazu Methodology 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. |
| title | Regularized k-POD: Sparse k-means clustering for high-dimensional missing data |
| topic | Methodology |
| url | https://arxiv.org/abs/2507.11884 |