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.

本文旨在提出一个框架的监督二进制分类 $ñ$-通过具有Laplacian特征图的Echo State Networks进行布尔运算以减少维数。所提出的方法既可用于提高学习权重（根据数字实现进行量化）时的分类性能，又可在允许并行输出时作为神经重用理论的计算演示。当所有可能的布尔函数为时，我们的分析集中于各种形式的噪声（即正常噪声，均匀噪声和量化噪声）的影响。$ñ$学习输入位。在学习的权重和输入特征上都施加了外部干扰，因此我们可以分析当各种形式的参数噪声注入系统时整个体系结构的弹性。此处显示的结果表明，基于Laplacian Eigenmaps的方法允许的降维效果提高了对这些不同噪声源的鲁棒性，从而在保持较高分类性能的同时降低了内存存储需求。在学习性能和计算复杂性方面，我们的结果与从其他更常见的分类技术中得出的结果进行了比较，同时考虑了描述在移动机器人跟随墙壁的导航会话中的决策任务的实际数据集。