91直播

91直播：孔令臣 教授（北京交通大学）

时间：2025年04月20日 09:30-

地点：数统91直播 LD718

摘要：Traditional subspace clustering methods face dual challenges when handling large-scale high-dimensional data: exponentially increasing computational complexity and superlinearly growing storage demands. These challenges are particularly pronounced in parallel frameworks, where balancing the sparsity of the coefficient matrix and global consistency is difficult. To address these issues, this paper proposes a parallel row-sparse constrained subspace clustering model, which incorporates a Frobenius norm regularization to ensure data reconstruction accuracy while introducing an $\ell_{2,0}$ sparsity constraint to achieve row sparsity of the coefficient matrix. Theoretically, we explore the relationships between local optimal solutions, KKT points, and $\alpha$-stable points. Algorithmically, we design a Newton-augmented Lagrangian algorithm and rigorously prove its global convergence. Furthermore, to leverage the advantages of parallel computing, we introduce a support point-based dictionary initialization strategy, which significantly improves computational efficiency while maintaining data representation quality and boosting clustering performance. Finally, extensive experiments validate the superiority of the proposed method in terms of clustering performance, robustness, and computational efficiency.

邀请人: 蒋杰

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