支持向量机matlab实现源代码知识讲解

支持向量机m a t l a b 实现源代码edit svmtrain>>edit svmclassify>>edit svmpredictfunction [svm_struct, svIndex] = svmtrain(training, groupnames, varargin)%SVMTRAIN trains a support vector machine classifier%% SVMStruct = SVMTRAIN(TRAINING,GROUP) trains a support vector machine % classifier using data TRAINING taken from two groups given by GROUP.% SVMStruct contains information about the trained classifier that is% used by SVMCLASSIFY for classification. GROUP is a column vector of% values of the same length as TRAINING that defines two groups. Each% element of GROUP specifies the group the corresponding row of TRAINING % belongs to. GROUP can be a numeric vector, a string array, or a cell% array of strings. SVMTRAIN treats NaNs or empty strings in GROUP as% missing values and ignores the corresponding rows of TRAINING.%% SVMTRAIN(...,'KERNEL_FUNCTION',KFUN) allows you to specify the kernel % function KFUN used to map the training data into kernel space. The% default kernel function is the dot product. KFUN can be one of the% following strings or a function handle:%% 'linear' Linear kernel or dot product% 'quadratic' Quadratic kernel% 'polynomial' Polynomial kernel (default order 3)% 'rbf' Gaussian Radial Basis Function kernel% 'mlp' Multilayer Perceptron kernel (default scale 1)% function A kernel function specified using @,% for example @KFUN, or an anonymous function%% A kernel function must be of the form%% function K = KFUN(U, V)%% The returned value, K, is a matrix of size M-by-N, where U and V have M% and N rows respectively. If KFUN is parameterized, you can use% anonymous functions to capture the problem-dependent parameters. For% example, suppose that your kernel function is%% function k = kfun(u,v,p1,p2)% k = tanh(p1*(u*v')+p2);%% You can set values for p1 and p2 and then use an anonymous function:% @(u,v) kfun(u,v,p1,p2).%% SVMTRAIN(...,'POLYORDER',ORDER) allows you to specify the order of a% polynomial kernel. The default order is 3.%% SVMTRAIN(...,'MLP_PARAMS',[P1 P2]) allows you to specify the% parameters of the Multilayer Perceptron (mlp) kernel. The mlp kernel% requires two parameters, P1 and P2, where K = tanh(P1*U*V' + P2) and P1% > 0 and P2 < 0. Default values are P1 = 1 and P2 = -1.%% SVMTRAIN(...,'METHOD',METHOD) allows you to specify the method used% to find the separating hyperplane. Options are%% 'QP' Use quadratic programming (requires the Optimization Toolbox)% 'LS' Use least-squares method%% If you have the Optimization Toolbox, then the QP method is the default% method. If not, the only available method is LS.%% SVMTRAIN(...,'QUADPROG_OPTS',OPTIONS) allows you to pass an OPTIONS % structure created using OPTIMSET to the QUADPROG function when using% the 'QP' method. See help optimset for more details.%% SVMTRAIN(...,'SHOWPLOT',true), when used with two-dimensional data,% creates a plot of the grouped data and plots the separating line for% the classifier.%% Example:% % Load the data and select features for classification% load fisheriris% data = [meas(:,1), meas(:,2)];% % Extract the Setosa class% groups = ismember(species,'setosa');% % Randomly select training and test sets% [train, test] = crossvalind('holdOut',groups);% cp = classperf(groups);% % Use a linear support vector machine classifier% svmStruct = svmtrain(data(train,:),groups(train),'showplot',true);% classes = svmclassify(svmStruct,data(test,:),'showplot',true);% % See how well the classifier performed% classperf(cp,classes,test);% cp.CorrectRate%% See also CLASSIFY, KNNCLASSIFY, QUADPROG, SVMCLASSIFY.% Copyright 2004 The MathWorks, Inc.% $Revision: 1.1.12.1 $ $Date: 2004/12/24 20:43:35 $% References:% [1] Kecman, V, Learning and Soft Computing,% MIT Press, Cambridge, MA. 2001.% [2] Suykens, J.A.K., Van Gestel, T., De Brabanter, J., De Moor, B.,% Vandewalle, J., Least Squares Support Vector Machines,% World Scientific, Singapore, 2002.% [3] Scholkopf, B., Smola, A.J., Learning with Kernels,% MIT Press, Cambridge, MA. 2002.%% SVMTRAIN(...,'KFUNARGS',ARGS) allows you to pass additional% arguments to kernel functions.% set defaultsplotflag = false;qp_opts = [];kfunargs = {};setPoly = false; usePoly = false;setMLP = false; useMLP = false;if ~isempty(which('quadprog'))useQuadprog = true;elseuseQuadprog = false;end% set default kernel functionkfun = @linear_kernel;% check inputsif nargin < 2error(nargchk(2,Inf,nargin))endnumoptargs = nargin -2;optargs = varargin;% grp2idx sorts a numeric grouping var ascending, and a string grouping % var by order of first occurrence[g,groupString] = grp2idx(groupnames);% check group is a vector -- though char input is special...if ~isvector(groupnames) && ~ischar(groupnames)error('Bioinfo:svmtrain:GroupNotVector',...'Group must be a vector.');end% make sure that the data is correctly oriented.if size(groupnames,1) == 1groupnames = groupnames';end% make sure data is the right sizen = length(groupnames);if size(training,1) ~= nif size(training,2) == ntraining = training';elseerror('Bioinfo:svmtrain:DataGroupSizeMismatch',...'GROUP and TRAINING must have the same number of rows.')endend% NaNs are treated as unknown classes and are removed from the training% datanans = find(isnan(g));if length(nans) > 0training(nans,:) = [];g(nans) = [];endngroups = length(groupString);if ngroups > 2error('Bioinfo:svmtrain:TooManyGroups',...'SVMTRAIN only supports classification into two groups.\nGROUP contains %d different groups.',ngroups) end% convert to 1, -1.g = 1 - (2* (g-1));% handle optional argumentsif numoptargs >= 1if rem(numoptargs,2)== 1error('Bioinfo:svmtrain:IncorrectNumberOfArguments',...'Incorrect number of arguments to %s.',mfilename);okargs = {'kernel_function','method','showplot','kfunargs','quadprog_opts','polyorder','mlp_params'}; for j=1:2:numoptargspname = optargs{j};pval = optargs{j+1};k = strmatch(lower(pname), okargs);%#okif isempty(k)error('Bioinfo:svmtrain:UnknownParameterName',...'Unknown parameter name: %s.',pname);elseif length(k)>1error('Bioinfo:svmtrain:AmbiguousParameterName',...'Ambiguous parameter name: %s.',pname);elseswitch(k)case 1 % kernel_functionif ischar(pval)okfuns = {'linear','quadratic',...'radial','rbf','polynomial','mlp'};funNum = strmatch(lower(pval), okfuns);%#okif isempty(funNum)funNum = 0;endswitch funNum %maybe make this less strict in the futurecase 1kfun = @linear_kernel;case 2kfun = @quadratic_kernel;case {3,4}kfun = @rbf_kernel;case 5kfun = @poly_kernel;usePoly = true;case 6kfun = @mlp_kernel;useMLP = true;otherwiseerror('Bioinfo:svmtrain:UnknownKernelFunction',...'Unknown Kernel Function %s.',kfun);endelseif isa (pval, 'function_handle')kfun = pval;elseerror('Bioinfo:svmtrain:BadKernelFunction',...'The kernel function input does not appear to be a function handle\nor valid function name.')case 2 % methodif strncmpi(pval,'qp',2)useQuadprog = true;if isempty(which('quadprog'))warning('Bioinfo:svmtrain:NoOptim',...'The Optimization Toolbox is required to use the quadratic programming method.') useQuadprog = false;endelseif strncmpi(pval,'ls',2)useQuadprog = false;elseerror('Bioinfo:svmtrain:UnknownMethod',...'Unknown method option %s. Valid methods are ''QP'' and ''LS''',pval);endcase 3 % displayif pval ~= 0if size(training,2) == 2plotflag = true;elsewarning('Bioinfo:svmtrain:OnlyPlot2D',...'The display option can only plot 2D training data.')endendcase 4 % kfunargsif iscell(pval)kfunargs = pval;elsekfunargs = {pval};endcase 5 % quadprog_optsif isstruct(pval)qp_opts = pval;elseif iscell(pval)qp_opts = optimset(pval{:});elseerror('Bioinfo:svmtrain:BadQuadprogOpts',...'QUADPROG_OPTS must be an opts structure.');endcase 6 % polyorderif ~isscalar(pval) || ~isnumeric(pval)error('Bioinfo:svmtrain:BadPolyOrder',...'POLYORDER must be a scalar value.');endif pval ~=floor(pval) || pval < 1error('Bioinfo:svmtrain:PolyOrderNotInt',...'The order of the polynomial kernel must be a positive integer.')endkfunargs = {pval};setPoly = true;case 7 % mlpparamsif numel(pval)~=2error('Bioinfo:svmtrain:BadMLPParams',...'MLP_PARAMS must be a two element array.');endif ~isscalar(pval(1)) || ~isscalar(pval(2))error('Bioinfo:svmtrain:MLPParamsNotScalar',...'The parameters of the multi-layer perceptron kernel must be scalar.'); endkfunargs = {pval(1),pval(2)};setMLP = true;endendendendif setPoly && ~usePolywarning('Bioinfo:svmtrain:PolyOrderNotPolyKernel',...'You specified a polynomial order but not a polynomial kernel');endif setMLP && ~useMLPwarning('Bioinfo:svmtrain:MLPParamNotMLPKernel',...'You specified MLP parameters but not an MLP kernel');end% plot the data if requestedif plotflag[hAxis,hLines] = svmplotdata(training,g);legend(hLines,cellstr(groupString));end% calculate kernel functiontrykx = feval(kfun,training,training,kfunargs{:});% ensure function is symmetrickx = (kx+kx')/2;catcherror('Bioinfo:svmtrain:UnknownKernelFunction',...'Error calculating the kernel function:\n%s\n', lasterr);end% create Hessian% add small constant eye to force stabilityH =((g*g').*kx) + sqrt(eps(class(training)))*eye(n);if useQuadprog% The large scale solver cannot handle this type of problem, so turn it% off.qp_opts = optimset(qp_opts,'LargeScale','Off');% X=QUADPROG(H,f,A,b,Aeq,beq,LB,UB,X0,opts)alpha = quadprog(H,-ones(n,1),[],[],...g',0,zeros(n,1),inf *ones(n,1),zeros(n,1),qp_opts);% The support vectors are the non-zeros of alphasvIndex = find(alpha > sqrt(eps));sv = training(svIndex,:);% calculate the parameters of the separating line from the support% vectors.alphaHat = g(svIndex).*alpha(svIndex);% Calculate the bias by applying the indicator function to the support% vector with largest alpha.[maxAlpha,maxPos] = max(alpha); %#okbias = g(maxPos) - sum(alphaHat.*kx(svIndex,maxPos));% an alternative method is to average the values over all support vectors % bias = mean(g(sv)' - sum(alphaHat(:,ones(1,numSVs)).*kx(sv,sv)));% An alternative way to calculate support vectors is to look for zeros of % the Lagrangians (fifth output from QUADPROG).%% [alpha,fval,output,exitflag,t] = quadprog(H,-ones(n,1),[],[],...% g',0,zeros(n,1),inf *ones(n,1),zeros(n,1),opts);%% sv = t.lower < sqrt(eps) & t.upper < sqrt(eps);else % Least-Squares% now build up compound matrix for solverA = [0 g';g,H];b = [0;ones(size(g))];x = A\b;% calculate the parameters of the separating line from the support % vectors.sv = training;bias = x(1);alphaHat = g.*x(2:end);endsvm_struct.SupportVectors = sv;svm_struct.Alpha = alphaHat;svm_struct.Bias = bias;svm_struct.KernelFunction = kfun;svm_struct.KernelFunctionArgs = kfunargs;svm_struct.GroupNames = groupnames;svm_struct.FigureHandles = [];if plotflaghSV = svmplotsvs(hAxis,svm_struct);svm_struct.FigureHandles = {hAxis,hLines,hSV};end。