Tensor Train Neighborhood Preserving Embedding

TL;DR

This paper introduces TTNPE, a tensor embedding method that effectively reduces dimensionality while preserving neighborhood structure, leading to improved classification performance with efficient computation and storage.

Contribution

The paper presents a novel Tensor Train Neighborhood Preserving Embedding (TTNPE) method with new optimization approaches for tensor data embedding.

Findings

TTNPE outperforms existing tensor embedding methods in classification accuracy.

TTNPE achieves better trade-offs among classification, computation, and storage.

Experimental results on MNIST and Weizmann datasets validate TTNPE's effectiveness.

Abstract

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off 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 trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.