Tensor-based projection depth

TL;DR

This paper introduces a tensor-based projection depth (TPD) method that extends traditional vector-based depth functions to tensors, improving data classification performance for tensor-structured data.

Contribution

The paper proposes a novel tensor projection depth (TPD) that directly operates on tensors, enhancing depth analysis for tensor data and extending the applicability of depth functions.

Findings

TPD outperforms traditional PD on tensor-structured data

TPD performs comparably to PD on vector data

The method effectively handles sparse samples and higher order tensors

Abstract

The conventional definition of a depth function is vector-based. In this paper, a novel projection depth (PD) technique directly based on tensors, such as matrices, is instead proposed. Tensor projection depth (TPD) is still an ideal depth function and its computation can be achieved through the iteration of PD. Furthermore, we also discuss the cases for sparse samples and higher order tensors. Experimental results in data classification with the two projection depths show that TPD performs much better than PD for data with a natural tensor form, and even when the data have a natural vector form, TPD appears to perform no worse than PD.