A gradient projection method for semi-supervised hypergraph clustering problems

Pub Date : 2023-06-20 DOI:10.61208/pjo-2023-025
Jingya Chang, Dongdong Liu, Min Xi
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Abstract

Semi-supervised clustering problems focus on clustering data with labels. In this paper,we consider the semi-supervised hypergraph problems. We use the hypergraph related tensor to construct an orthogonal constrained optimization model. The optimization problem is solved by a retraction method, which employs the polar decomposition to map the gradient direction in the tangent space to the Stefiel manifold. A nonmonotone curvilinear search is implemented to guarantee reduction in the objective function value. Convergence analysis demonstrates that the first order optimality condition is satisfied at the accumulation point. Experiments on synthetic hypergraph and hypergraph given by real data demonstrate the effectivity of our method.
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半监督超图聚类问题的梯度投影方法
半监督聚类问题主要关注带标签的数据聚类问题。本文研究一类半监督超图问题。利用超图相关张量构造了一个正交约束优化模型。利用极坐标分解将切空间中的梯度方向映射到stefield流形上,采用缩回法求解优化问题。采用非单调曲线搜索来保证目标函数值的减小。收敛性分析表明,该算法在累加点处满足一阶最优性条件。在合成超图和实际数据给出的超图上的实验证明了该方法的有效性。
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