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Tensor-Based Algorithms for Image Classification

by Stefan Klus *,† and Patrick Gelß *,†
Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Algorithms 2019, 12(11), 240; https://doi.org/10.3390/a12110240
Received: 20 October 2019 / Revised: 5 November 2019 / Accepted: 7 November 2019 / Published: 9 November 2019
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 multidimensional approximation of nonlinear dynamics (MANDy), 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.
Keywords: quantum machine learning; image classification; tensor train format; kernel-based methods; ridge regression quantum machine learning; image classification; tensor train format; kernel-based methods; ridge regression
MDPI and ACS Style

Klus, S.; Gelß, P. Tensor-Based Algorithms for Image Classification. Algorithms 2019, 12, 240.

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