Abstract: This paper introduces the notion of moment deviation subspaces of dimension reduction for high-dimensional data with change structure. We propose a novel estimation method to identify subspaces by combining the Mahalanobis matrix and the pooled covariance matrix. The theoretical properties are investigated to show that the change point detection and clustering can be equivalently implemented in the dimension reduction subspaces, whether the data structure is dense or sparse, whenever the dimension divided by the sample size goes to zero. We propose an iterative algorithm based on dimension reduction subspaces that can be applied for data clustering of high-dimensional data. The numerical studies on synthetic and real datasets suggest that the dimension reduction versions of existing methods of change point detection and clustering methods significantly improve the performances of existing approaches in finite sample scenarios.

Key words and phrases: Clustering, dimension reduction, moment changes, moment deviation subspace.