Rank-constrained inherent clustering for supervised and unsupervised learning
Dr. Yiyuan She
Department of Statistics
Florida State University
ABSTRACT: Modern clustering applications are often faced with challenges from high dimensionality and nonconvex clusters. This paper gives a mathematical formulation of low-rank clustering and proposes an optimization based inherent clustering framework. The resulting method enjoys a nice kernel property to apply to similarity data and can be extended to supervised learning. By use of linearization and block coordinate descent, a simple-to-implement algorithm is developed, which performs subspace learning and clustering iteratively. Our non-asymptotic analyses show a tight error rate of the proposed rank constrained inherent clustering and its minimax optimality, along with a new information criterion for parameter tuning in jointly rank-deficient and equi-sparse models. Extensive simulations and real-data experiments in network community detection and machine learning demonstrate the excellent performance of the proposed approach.
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