Tensor-based algorithms for image classification

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.

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• Feature space approximation for kernel-based supervised learning
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• A quantum inspired approach to learning dynamical laws from data -- block-sparsity and gauge-mediated weight sharing
• WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-Like Systems Based on Tensor Trains
• Quantum tensor network algorithms for evaluation of spectral functions on quantum computers
• Personalized Tucker Decomposition: Modeling Commonality and Peculiarity on Tensor Data
• Fast Tucker Rank Reduction for Non-Negative Tensors Using Mean-Field Approximation
• Patch-based Medical Image Segmentation using Matrix Product State Tensor Networks
• Solving the time-independent Schrödinger equation for chains of coupled excitons and phonons using tensor trains