Robust modelling of binary decisions in Laplacian Eigenmaps-based Echo State Networks

This paper aims to present a framework for supervised binary classification of n-Boolean functions through Echo State Networks endowed with Laplacian Eigenmaps for dimensionality reduction. The proposed method is applied both to improve the classification performance when the learnt weights are quantised in view of a digital implementation and as a computational demonstration of the neural reuse theory when parallel outputs are allowed. Our analysis focuses on the effect of various forms of noise (i.e., normal noise, uniform noise and quantisation noise) when all the possible Boolean functions of n input bits are learnt. External disturbances are applied both over the learnt weights and the input features so that we can analyse how resilient the whole architecture is when various forms of parametric noise is injected into the system. Results presented here show that dimensionality reduction allowed by the Laplacian Eigenmaps-based approach improves robustness to these different sources of noise, leading to reduced memory storage requirements while maintaining high classification performance. Our results are compared to those derived from other more common classification techniques in terms of learning performance and computational complexity, also considering a realistic dataset describing a decision making task in a wall-following navigation session with mobile robots.