Tensor-based algorithms for image classification
This work addresses image classification for machine learning practitioners by offering tensor-based alternatives, though it is incremental as it adapts existing methods to a new application.
The authors tackled image classification by adapting tensor-based methods from dynamical systems to supervised learning, proposing two novel approaches that achieved competitive performance with state-of-the-art neural networks on MNIST and fashion MNIST datasets.
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.