Dynamical system autoencoders using piecewise linear transformation

Dynamical system autoencoders (DSAEs) are a novel class of autoencoders (AEs) capable of addressing both unsupervised and supervised learning tasks, similar to classical AEs. DSAEs employ iterative maps, which offer greater flexibility in function form. In this work, we propose a new deep learning layer architecture, called piecewise linear transformation (PLT), that evince some advantageous mathematical properties. We further propose to use this transformation as an iterative map, apply it to DSAEs, and investigate its performance on dimensionality reduction tasks. Experiments conducted on the MNIST and Fashion MNIST datasets demonstrate that DSAEs equipped with PLT can outperform classic multilayer perceptron AEs in dimensionality reduction tasks in scenarios with limited training samples and low-dimensional encoded representation.