An Efficient Mixed-Signal Neural Cell Based on Simplicial Preprocessing and its Applications for Nonlinear Image Processing and Signal Classification

Motivated by recent research in the area of cellular neural networks (CNN) this paper introduces a novel neural architecture, called a simplicial neural cell, and its corresponding circuit. The novel cell has several attractive properties which makes it well suited for intelligent signal processing in portable multimedia devices: (i) There are no multiplicative synapses; (ii) The cell admits a very simple, compact and efficient mixed-signal implementation in common VLSI technologies but also in nanotechnologies; (iii) The functional performances for either regression and classification problems are similar to those of more complicated neural networks; (iv) The central device around which the entire cell is built is a digital RAM which stores cell the parameters (the gene) and which can be easily reprogrammed; (v) The learning process consists in a simple LMS algorithm which tunes the gene and has a guaranteed convergence. The simplicial cell is defined as a linear perceptron operating in an extended feature space. The extended feature space with a dimension of 2n is obtained by computing only n+1 fuzzy-membership functions of the n-dimensional input vector. Therefore the computational complexity is only O(n) for both learning and retrieval. The novelty of our approach consists in exploiting the theory of simplicial subdivision (previously used in PWL approximations of nonlinear circuits) for defining the above fuzzy-memebership functions.