Tensor-based Nonlinear Classifier for High-Order Data Analysis

TL;DR

This paper introduces a tensor-based nonlinear classifier called Rank-1 FNN for high-order data, which reduces parameters, preserves spatial structure, and outperforms existing methods especially with limited training data.

Contribution

It proposes a novel tensor-based neural network model with rank-1 decomposition and a new training algorithm for improved high-order data classification.

Findings

Outperforms state-of-the-art classification methods.

Requires fewer training samples due to reduced parameters.

Effective on third-order hyperspectral data.

Abstract

In this paper we propose a tensor-based nonlinear model for high-order data classification. The advantages of the proposed scheme are that (i) it significantly reduces the number of weight parameters, and hence of required training samples, and (ii) it retains the spatial structure of the input samples. The proposed model, called \textit{Rank}-1 FNN, is based on a modification of a feedforward neural network (FNN), such that its weights satisfy the {\it rank}-1 canonical decomposition. We also introduce a new learning algorithm to train the model, and we evaluate the \textit{Rank}-1 FNN on third-order hyperspectral data. Experimental results and comparisons indicate that the proposed model outperforms state of the art classification methods, including deep learning based ones, especially in cases with small numbers of available training samples.