Local homeomorphism regularized non-negative Tucker decomposition of tensor data

Abstract

Non-negative Tucker decomposition of tensor data has a wide range of applications in machine learning. With the non-negative constraints, tensor data can be decomposed into the mode product of a core tensor and a series of projection matrices. The core tensor usually is be regarded as the low-dimensional representation of the original tensor. The process of dimensionality reduction preserves the global properties of tensor data. But many applications in machine learning expect the continuous dependencies of data local feature to remain unchanged during dimensionality reduction. To this end, this paper proposes a local homeomorphism regularized non-negative Tucker decomposition algorithm for tensor data. The proposed method introduce a local homeomorphism regularized term to tensor non-negative Tucker decomposition constrain for effectively preserving the global and local characters of tensor. Experiments on four commonly used real data sets and six compared algorithms have demonstrate the well performance of the proposed algorithms.