Recurrent Spectral Network (RSN): shaping the basin of attraction of a discrete map to reach automated classification

TL;DR

The paper introduces Recurrent Spectral Network (RSN), a new classification method using a trained dynamical system with spectral decomposition to steer data toward distinct attractors, improving classification accuracy.

Contribution

It presents RSN, a novel spectral decomposition-based dynamical system for classification that can handle sequential data and shape attractor boundaries.

Findings

Successfully tested on illustrative and image datasets

Demonstrates effective data separation via attractor shaping

Handles sequential datasets with multiple memory kernels

Abstract

A novel strategy to automated classification is introduced which exploits a fully trained dynamical system to steer items belonging to different categories toward distinct asymptotic attractors. These latter are incorporated into the model by taking advantage of the spectral decomposition of the operator that rules the linear evolution across the processing network. Non-linear terms act for a transient and allow to disentangle the data supplied as initial condition to the discrete dynamical system, shaping the boundaries of different attractors. The network can be equipped with several memory kernels which can be sequentially activated for serial datasets handling. Our novel approach to classification, that we here term Recurrent Spectral Network (RSN), is successfully challenged against a simple test-bed model, created for illustrative purposes, as well as a standard dataset for image processing training.