Tensor-based algorithms for image classification

TL;DR

This paper introduces two tensor-based methods for image classification, demonstrating their competitiveness with neural networks on MNIST datasets, and expanding tensor applications into supervised learning.

Contribution

It presents two novel tensor-based algorithms for image classification, adapting methods from dynamical systems to supervised learning tasks.

Findings

Both methods perform competitively with neural networks on MNIST.

Tensor-based approaches offer a promising alternative to traditional deep learning.

The methods are applicable to large-scale image datasets.

Abstract

The interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used for supervised learning problems and propose two novel approaches for image classification. One is a kernel-based reformulation of the previously introduced MANDy (multidimensional approximation of nonlinear dynamics), the other an alternating ridge regression in the tensor-train format. We apply both methods to the MNIST and fashion MNIST data set and show that the approaches are competitive with state-of-the-art neural network-based classifiers.