Digit Recognition by The Random Neural Network using Supervised Learning

Abstract

The Random Neural Network model with positive and negative neurons is studied as an autoassociative memory for pattem recognition. A neuron can excite its neighbours it emits positive signals or can inhibit them by emission of negative signals. There is accumulation of positive signals at positive neurons and negative signals at negative neurons. Let k(t) be the vector of neuron potentials at time t If all the steady state excitation probabilities qi are such that 0<qi<1, the stationary probability distribution of the network’s state is $${expressed by}:p(\underline{k})=\prod^{\Pi}{i}=1 (1-{q}_{{i}}^{{k}_{{i}}}) {where} {q}_{{i}}=\gamma^{+}({i})/[{r}({i})+\gamma ({i})] if {P}, {q}_{{i}}= \gamma({i})/[{r}({i})+\gamma ^{+}({i})] if i\in {N}$$ $$\gamma^{+}({i})=\Lambda ({i}) +\Sigma_{{j}\in}{P} {q}_{{j}}{r}({j}){p}^{+}({j,i})+\Sigma_{{j}\in}{N} {q}_{{j}} {r}({j}){p}^{-}({j,i})$$ $$\gamma^{-}({i})=\lambda ({i}) +\Sigma_{{j}\in}{P} {q}_{{j}}{r}({j}){p}^{-}({j,i})+\Sigma_{{j}\in}{N} {q}_{{j}} {r}({j}){p}^{+}({j,i})$$ with P (respectively N): set of positive (respectively negative) neurons Λ(i) (respectively λ(i)): external arrival rate of positive (respectively negative) signals to neuron i r(i): emission rate of signals by neuron i p+(i,j) (respectively p-(i,j)): probability that i emits a positive (respectively negative) signal to j, i ∈ P p+(i,j) (respectively p-(i,j)): probability that i emits a negative (respectively positive) signal to j, i ∈ N.