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arXiv · 2503.04447

A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problems

Wei Liu·Xin Liu·Michael K. Ng·Zaikun Zhang
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Abstract

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.

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Wei Liu, Xin Liu, Michael K. Ng, Zaikun Zhang. 2025-03-06. A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problems. https://arxiv.org/abs/2503.04447

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