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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2506.14952 |
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| _version_ | 1866916797642440704 |
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| author | Silva-Sánchez, David Lederman, Roy R. |
| author_facet | Silva-Sánchez, David Lederman, Roy R. |
| contents | Clustering and estimating cluster means are core problems in statistics and machine learning, with k-means and Expectation Maximization (EM) being two widely used algorithms. In this work, we provide a theoretical explanation for the failure of k-means in high-dimensional settings with high noise and limited sample sizes, using a simple Gaussian Mixture Model (GMM). We identify regimes where, with high probability, almost every partition of the data becomes a fixed point of the k-means algorithm. This study is motivated by challenges in the analysis of more complex cases, such as masked GMMs, and those arising from applications in Cryo-Electron Microscopy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Observation on Lloyd's k-Means Algorithm in High Dimensions Silva-Sánchez, David Lederman, Roy R. Machine Learning Clustering and estimating cluster means are core problems in statistics and machine learning, with k-means and Expectation Maximization (EM) being two widely used algorithms. In this work, we provide a theoretical explanation for the failure of k-means in high-dimensional settings with high noise and limited sample sizes, using a simple Gaussian Mixture Model (GMM). We identify regimes where, with high probability, almost every partition of the data becomes a fixed point of the k-means algorithm. This study is motivated by challenges in the analysis of more complex cases, such as masked GMMs, and those arising from applications in Cryo-Electron Microscopy. |
| title | An Observation on Lloyd's k-Means Algorithm in High Dimensions |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.14952 |