[number recognition] recognize 0-9 numbers based on Hopfield neural network with matlab code

1 Content introduction

since １９４３ year  ＭｃＣｕｌｌｏｃｈ and  Ｐｉｔｔｓ Since the artificial neuron model was first proposed , New neuron models and their neural networks have been proposed constantly , It has become a major research direction of nonlinear science and computational intelligence . among , With the development of modern computer technology, neural network image recognition technology 、 The image processing 、 Artificial intelligence 、 Pattern recognition theory is developing rapidly , It is an image recognition method that combines the traditional image recognition method and neural network algorithm ［３－４］. Character recognition using neural network plays a more and more important role in the field of computer recognition , And it is widely used in traffic license plate recognition in fog or at night 、 Machine vision and other practical applications . In recent years , utilize  Ｈｏｐｆｉｅｌｄ Neural networks recognize noisy characters 、 Examples such as car license plate characters show that this method has a high recognition rate 、 Lu   Great   sex   good   And   have   Yes   very   good   Of   real   use   sex ： example   Such as   zhu   offer   writing ［５］ Research   了   The base   On   Legacy   Pass on   count   Law Ｈｏｐｆｉｅｌｄ Character recognition method based on neural network ; Wei Wu ［６］ Et al. Improved the neural network method of license plate character recognition template matching ; Qiu min ［７］ Et al. In the application of vehicle license plate character recognition  Ｈｏｐｆｉｅｌｄ and  ＢＰ The combination of network improves the recognition rate ;Ｔａｔｅｍ［８］ Others took advantage of  Ｈｏｐｆｉｅｌｄ Neural network recognizes land cover targets in remote sensing images . The above research on character recognition regards noise as a harmful factor , Focus on noise elimination , The beneficial effect of noise is ignored , In fact, noise can enhance the information processing ability of neurons , That is, the phenomenon of stochastic resonance in neuroscience ［９－１１］. lately ,Ｈｏｐｆｉｅｌｄ Great progress has been made in the study of stochastic resonance in Neural Networks , Such as  Ｋａｔａｄａ［９］ And so on  Ｈｏｐｆｉｅｌｄ Stochastic resonance in Networks , And extend to include １５６ In a network of neurons ;Ｐｉｎａｍｏｎｔｉ［１０］ Et al. Studied the important characteristics of multimodal stochastic resonance in Complex Networks ;Ｎｉｓｈｉｍｕｒａ［１１］ Et al. Studied by ３ Stochastic resonance feedback in a neural network composed of neurons , Take it as an effective double potential well model of chaotic dynamics . This paper mainly uses discrete  Ｈｏｐｆｉｅｌｄ Neural network recognizes handwritten digits , Turn the binary encoding of the recognized image into serial encoding , According to the law that the signal returns and reciprocates in the steady state, it is input to  Ｈｏｐｆｉｅｌｄ In Neural Networks , Not only the amplitude modulation of input signal is studied , The influence of inter symbol interval and the number of neuron coupling on network recognition image , The nonlinear characteristics of noise intensity and image recognition error rate during transmission are also studied Ｈｏｐｆｉｅｌｄ Neural network is composed of  Ｈｏｐｆｉｅｌｄ［１２－１３］ On １９８２ A single-layer 、 The output is a binary fully connected feedback nerve   The Internet . discrete  Ｈｏｐｆｉｅｌｄ Neural networks have only one neuron layer , The first ０ Layer is only used as the input of the network , No calculation function , And the first １ Layers are neurons   layer , It is used to calculate the cumulative sum of the product of input data and weight coefficient , And the output information is generated after being processed by the nonlinear activation function . The network simulates biological nerves   The memory mechanism of the network , It has the function of associative memory .３ A discrete of neurons  Ｈｏｐｆｉｅｌｄ Neural networks can be represented by weighted undirected graphs , Pictured  １ Shown .  chart １  discrete  Ｈｏｐｆｉｅｌｄ Neural network structure  Ｆｉｇ．１ Ａｒｃｈｉｔｅｃｔｕｒｅｏｆｄｉｓｃｒｅｔｅｎｅｕｒａｌｎｅｔｗｏｒｋｓ  From the picture １ It can be seen that neurons are interconnected , And the net   The output of each neuron in the collateral is fed back to other neurons , Every time   The weight on the edge indicates the connection strength between relevant neurons , Each section   A dot represents a neuron and is attached with a threshold , When a neuron receives   When the stimulus exceeds its threshold , Neurons are activated , otherwise   Neurons are at rest . We take the neuron activation function ［９］ by

2 Simulation code

function out1 = newhop(varargin)%NEWHOP Design a Hopfield recurrent network.%%  Hopfield networks perform a kind of pattern recall.  They are included%  primarily for historical purposes.  For more robust pattern recognition%  use <a href="matlab:doc patternnet">patternnet</a>.%%  <a href="matlab:doc newhop">newhop</a>(T) takes  an RxQ matrix of Q target vectors T with element%  values of +1 or -1, and returns a new Hopfield recurrent neural%  network with stable points at the vectors in T.%%  Here a Hopfield network with two three-element stable points is%  designed and simulated.%%    T = [-1 -1 1; 1 -1 1]';%    net = <a href="matlab:doc newhop">newhop</a>(T);%    Ai = T;%    [Y,Pf,Af] = net(2,[],Ai)%    %  To see if the network can correct a corrupted vector, run%  the following code which simulates the Hopfield network for%  five timesteps.  (Since Hopfield networks have no inputs,%  the second argument to SIM is {Q TS} = [1 5] when using cell%  array notation.)%%    Ai = {[-0.9; -0.8; 0.7]};%    [Y,Pf,Af] = net({1 5},{},Ai);%    Y{1}%%  If you run the above code Y{1} will equal T(:,1) if the%  network has managed to convert the corrupted vector Ai to%  the nearest target vector.%%  See also SIM, SATLINS.% Mark Beale, 11-31-97% Copyright 1992-2011 The MathWorks, Inc.%% =======================================================%  BOILERPLATE_START%  This code is the same for all Network Functions.​  persistent INFO;  if isempty(INFO), INFO = get_info; end  if (nargin > 0) && ischar(varargin{1}) ...      && ~strcmpi(varargin{1},'hardlim') && ~strcmpi(varargin{1},'hardlims')    code = varargin{1};    switch code      case 'info',        out1 = INFO;      case 'check_param'        err = check_param(varargin{2});        if ~isempty(err), nnerr.throw('Args',err); end        out1 = err;      case 'create'        if nargin < 2, error(message('nnet:Args:NotEnough')); end        param = varargin{2};        err = nntest.param(INFO.parameters,param);        if ~isempty(err), nnerr.throw('Args',err); end        out1 = create_network(param);        out1.name = INFO.name;      otherwise,        % Quick info field access        try          out1 = eval(['INFO.' code]);        catch %#ok<CTCH>          nnerr.throw(['Unrecognized argument: ''' code ''''])        end    end  else    [args,param] = nnparam.extract_param(varargin,INFO.defaultParam);    [param,err] = INFO.overrideStructure(param,args);    if ~isempty(err), nnerr.throw('Args',err,'Parameters'); end    net = create_network(param);    net.name = INFO.name;    out1 = init(net);  endend​function v = fcnversion  v = 7;end%  BOILERPLATE_END%% =======================================================​function info = get_info  info = nnfcnNetwork(mfilename,'Hopfield Network',fcnversion, ...    [ ...    nnetParamInfo('targets','Target Data','nntype.data',{1},...    'Target output data.'), ...    ]);end​function err = check_param(param)  err = '';end​function net = create_network(param)  % Format  t = param.targets;  if iscell(t), t = cell2mat(t); end    % CHECKING  if (~isa(t,'double')) || ~isreal(t) || isempty(t)    error(message('nnet:NNData:TargetsNotRealNonEmpty'));  end  % DIMENSIONS  [S,Q] = size(t);  % NETWORK PARAMETERS  [w,b] = solvehop2(t);  % NETWORK ARCHITECTURE  net = network(0,1,[1],[],[1],[1]);  % RECURRENT LAYER  net.layers{1}.size = S;  net.layers{1}.transferFcn = 'satlins';  net.b{1} = b;  net.lw{1,1} = w;  net.layerWeights{1,1}.delays = 1;end%==========================================================function [w,b] = solvehop2(t)​  [S,Q] = size(t);  Y = t(:,1:Q-1)-t(:,Q)*ones(1,Q-1);  [U,SS,V] = svd(Y);  K = rank(SS);​  TP = zeros(S,S);  for k=1:K    TP = TP + U(:,k)*U(:,k)';  end​  TM = zeros(S,S);  for k=K+1:S    TM = TM + U(:,k)*U(:,k)';    end​  tau = 10;  Ttau = TP - tau*TM;  Itau = t(:,Q) - Ttau*t(:,Q);​  h = 0.15;  C1 = exp(h)-1;  C2 = -(exp(-tau*h)-1)/tau;​  w = expm(h*Ttau);  b = U * [  C1*eye(K)         zeros(K,S-K);           zeros(S-K,K)  C2*eye(S-K)] * U' * Itau;end%==========================================================​

3 Running results

4 reference

[1] Wang Xiaofeng . Based on discrete Hopfield Research on number recognition of neural network [J]. Journal of Xinzhou Normal University , 2012, 028(002):21-24.

[2] Ren Donghong , Lin Peng , and Yuan Qingping . " Based on discrete Hopfield Digital pattern recognition based on Neural Network ." Modern vocational education 14(2018):1.

About bloggers ： Good at intelligent optimization algorithms 、 Neural networks predict 、 signal processing 、 Cellular automata 、 The image processing 、 Path planning 、 UAV and other fields Matlab Simulation , relevant matlab Code problems can be exchanged by private letter .

Some theories cite network literature , If there is infringement, contact the blogger to delete .