@article{86faa7eeb5c047d3b12ca852f3b36eee,
title = "Tensor-based algorithms for image classification",
abstract = "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 = "Image classification, Kernel-based methods, Quantum machine learning, Ridge regression, Tensor train format",
author = "Stefan Klus and Patrick Gel{\ss}",
note = "Funding Information: Funding: This research has been funded by Deutsche Forschungsgemeinschaft (DFG) through grant CRC 1114 “Scaling Cascades in Complex Systems”. Part of this research was performed while S.K. was visiting the Institute for Pure and Applied Mathematics (IPAM), which is supported by the National Science Foundation (Grant No. DMS-1440415). Funding Information: Acknowledgments: We would like to thank Michael G{\"o}tte and Alex Goe{\ss}mann from the TU Berlin for interesting discussions related to tensor decompositions and system identification. The publication of this article was funded by Freie Universit{\"a}t Berlin. Funding Information: This research has been funded by Deutsche Forschungsgemeinschaft (DFG) through grant CRC 1114 {"}Scaling Cascades in Complex Systems{"}. Part of this research was performed while S.K. was visiting the Institute for Pure and Applied Mathematics (IPAM), which is supported by the National Science Foundation (Grant No. DMS-1440415). Publisher Copyright: {\textcopyright} 2019 by the authors.",
year = "2019",
month = nov,
doi = "10.3390/a12110240",
language = "English",
volume = "12",
journal = "Algorithms",
issn = "1999-4893",
publisher = "MDPI",
number = "11",
}