A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910861539409920 |
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| author | Liu, Wei Liu, Xin Ng, Michael K. Zhang, Zaikun |
| author_facet | Liu, Wei Liu, Xin Ng, Michael K. Zhang, Zaikun |
| contents | Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is another major challenge for these methods. In this work, we view the semi-supervised clustering task as a partitioning problem on a graph associated with the given dataset, where the similarity matrix includes a scaling parameter to reflect the must-link constraints. Utilizing a relaxation technique, we formulate the graph partitioning problem into a continuous optimization model that does not require the exact cluster number, but only an overestimate of it. We then propose a block coordinate descent algorithm to efficiently solve this model, and establish its convergence result. Based on the obtained solution, we can construct the clusters that theoretically meet the must-link constraints under mild assumptions. Furthermore, we verify the effectiveness and efficiency of our proposed method through comprehensive numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problems Liu, Wei Liu, Xin Ng, Michael K. Zhang, Zaikun Optimization and Control Machine Learning Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is another major challenge for these methods. In this work, we view the semi-supervised clustering task as a partitioning problem on a graph associated with the given dataset, where the similarity matrix includes a scaling parameter to reflect the must-link constraints. Utilizing a relaxation technique, we formulate the graph partitioning problem into a continuous optimization model that does not require the exact cluster number, but only an overestimate of it. We then propose a block coordinate descent algorithm to efficiently solve this model, and establish its convergence result. Based on the obtained solution, we can construct the clusters that theoretically meet the must-link constraints under mild assumptions. Furthermore, we verify the effectiveness and efficiency of our proposed method through comprehensive numerical experiments. |
| title | A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problems |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2503.04447 |