Tensor Train Neighborhood Preserving Embedding

Abstract

In this paper, we propose a tensor train neighborhood preserving embedding (TTNPE) to embed multidimensional tensor data into low-dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate a novel tradeoff gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior tradeoff in classification, computation, and dimensionality reduction in MNIST handwritten digits, Weizmann face datasets, and financial market datasets.