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.