08-17-2017, 12:31 AM
number recognition hopfield with matlab
Introduction
The article describes the Hopfield model of neural network. The theory basics, algorithm and program code are provided. The ability of application of Hopfield neural network to pattern recognition problem is shown.
Opening
Here I will not talk about NNs in whole. The main goal of this article is to describe architecture and dynamics of Hopfield Neural network. The base concept of NN, like artificial neurons, synapses, weights, connection matrices and so on, are explained in countless books. If you want to know more about these things, I advise you to start with Simon Haykin Neural networks book. The Google search is also useful. And finally you can try out very good article of Anoop Madhusudanan s, here on CodeProject.
Hopfield neural network (a little bit of theory
In ANN theory, in most simple case (when threshold functions is equal to one) the Hopfield model is described as a one-dimensional system of N neurons spins (si = 1, i = 1,2, ,N) that can be oriented along or against the local field. The behavior of such spin system is described by Hamiltonian (also known as the energy of HNN):
Where si is the state of the ith spin and
is an interconnection matrix organized according to the Hebb rule on M randomized patterns, i.e., on N-dimensional binary vectors Sm=(sm1,sm2, smN) (m=1,2, M). The diagonal elements of interconnection matrix are assumed to be zero (Ti,i=0). The traditional approach to such a system is that all spins are assumed to be free and their dynamics are defined only by the action of a local field, along which they are oriented. The algorithm of functioning of HNN is described as follows. The initial spin directions (neuron states) are oriented according the components of input vector. The local field , which acts on the ith spin at time t (this field is produced by all the remaining spins of NN) is calculated as:
The spin energy in this field is . If the spin direction coincides with the direction of the local field (), its position is energetically stable and the spin state remains unchanged at the next time step. Otherwise (), the spin position is unstable, and the local field overturns it, passing spin into the state si(t+1)=-si(t) with the energy (). The energy of the NN is reduced reducing each time any spin flips; i.e., the NN achieves a stable state in a finite number of steps. At some precise conditions each stable states corresponds to one of patterns added to interconnection matrix.