【数字识别】基于Hopfield神经网络识别0-9数字附Matlab代码

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); end end 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 % ==========================================================