Unsupervised neighborhood component analysis for clustering

In this paper, we propose a novel unsupervised distance metric learning algorithm. The proposed algorithm aims to maximize a stochastic variant of the leave-one-out K-nearest neighbor (KNN) score on unlabeled data, which performs distance metric learning and clustering simultaneously. We show that the joint distance metric learning and clustering problem is formulated as a trace optimization problem, and can be solved efficiently by an iterative algorithm. Moreover, the proposed approach can also learn a low dimensional projection of high dimensional data, thus it can serve as an unsupervised dimensionality reduction tool, which is capable of performing joint dimensionality reduction and clustering. We validate our method on a number of benchmark datasets, and the results demonstrate the effectiveness of the proposed algorithm.