Keywords: clustering; dimension reduction
Modern clustering applications are often faced with challenges from high dimensionality and/or nonconvex clusters. The purpose of the work is to give a mathematical formulation of clustering with concurrent dimension reduction and proposes an optimization-based inherent clustering framework. Inherent clustering enjoys a kernel property to work on similarity matrices and can be extended to supervised learning. A simple-to-implement iterative algorithm is developed by use of linearization and block coordinate descent. Nonasymptotic analysis shows the tight error rate of inherent clustering in the supervised setting. Extensive simulations, as well as real-data experiments in network community detection and bioinformatics, demonstrate the excellent performance of the proposed approach.