Rank-R FNN: A Tensor-Based Learning Model for High-Order Data Classification

TL;DR

The paper introduces Rank-R FNN, a tensor-based neural network that efficiently handles high-order structured data, reducing parameters and improving performance on multidimensional datasets.

Contribution

It proposes a novel tensor-based neural network model with canonical decomposition, enabling structural data exploitation and parameter reduction.

Findings

Achieves state-of-the-art results on hyperspectral datasets.

Reduces model parameters significantly compared to traditional FNN.

Demonstrates universal approximation and learnability for tensor data.

Abstract

An increasing number of emerging applications in data science and engineering are based on multidimensional and structurally rich data. The irregularities, however, of high-dimensional data often compromise the effectiveness of standard machine learning algorithms. We hereby propose the Rank-R Feedforward Neural Network (FNN), a tensor-based nonlinear learning model that imposes Canonical/Polyadic decomposition on its parameters, thereby offering two core advantages compared to typical machine learning methods. First, it handles inputs as multilinear arrays, bypassing the need for vectorization, and can thus fully exploit the structural information along every data dimension. Moreover, the number of the model's trainable parameters is substantially reduced, making it very efficient for small sample setting problems. We establish the universal approximation and learnability properties of Rank-R FNN, and we validate its performance on real-world hyperspectral datasets. Experimental evaluations show that Rank-R FNN is a computationally inexpensive alternative of ordinary FNN that achieves state-of-the-art performance on higher-order tensor data.