Peter M. Groen / openbr

Commit b860556d56a97ba0c8d330e77cfcc603b9efd673

Authored by Brendan K 2015-07-07 12:01:18 -0400

Merge pull request #394 from biometrics/matlabLDA

Matlab lda

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Showing 3 changed files with 263 additions and 0 deletions

scripts/matlab/LDA.m 0 → 100644

View file @b860556

	1	+function [subspaceData]=LDA(X,classNo,varargin)
	2	+% [subspaceData]=LDA(X,classNo)
	3	+%
	4	+% LDA method for learning a subspace that seeks to maximize the Fisher
	5	+% seperability measure. 'X' is d x n matrix, where d is the feature
	6	+% vector size, and n is the number of instaces. 'classNo' is a n x 1
	7	+% vector that indicates which class/subject each instance belongs to.
	8	+%
	9	+% Optional parameters:
	10	+
	11	+% 'EnergyRetain' - percentage of variance (0.0 to 1.0) to retain in the initial
	12	+% PCA step. (default = 0.98)
	13	+%
	14	+% 'do_direct' - Whether or not to perform Direct LDA (default = false)
	15	+%
	16	+% 'FixedRetain' - Keep a fixed number of eigenvectors in the initial PCA.
	17	+% If used, then specify number to keep (e.g. 100)
	18	+%
	19	+%
	20	+% 'DominantEig' - whether or not to use the dominant eigenvector method. If
	21	+% the d >> n, then this should be set to true.
	22	+% (default = true)
	23	+%
	24	+% 'SkipPCA' - whether of not to skip the PCA step. If Sw is believed to
	25	+% be non-singular then PCA step can be safely skipped.
	26	+% (default = false)
	27	+%
	28	+% 'ScaleW' - the factor by which to scale the within-class scatter matrix.
	29	+% This controls the importance of the between and within
	30	+% class scatter to each other in the fisher criterion
	31	+%
	32	+% The output 'subspaceData' is a struct that contains the following important fields:
	33	+% subspaceData.mean - d x 1 vector containing the mean of the training data
	34	+% subspaceData.W - d x k LDA projection matrix, where k is the number of
	35	+% subspace dimensions
	36	+%
	37	+%
	38	+% Algorithm based on Fukanaga's LDA method. This code was orginally written by Zhifeng Li,
	39	+% and has since been modified and improved by Brendan Klare.
	40	+%
	41	+%
	42	+
	43	+ useFixedEnergy = false;
	44	+ doDominantEig = true;
	45	+ doPCA = true;
	46	+ useFixedEig = false;
	47	+ energyPercentage = .98;
	48	+ ScaleW = 1;
	49	+ doDLDA = false;
	50	+ do_null = false;
	51	+
	52	+ cnt = 1;
	53	+ while cnt < length(varargin)
	54	+ switch varargin{cnt}
	55	+ case 'EnergyRetain'
	56	+ useFixedEnergy = true;
	57	+ energyPercentage = varargin{cnt+1};
	58	+ case 'FixedRetain'
	59	+ useFixedEig = true;
	60	+ fixedEig = varargin{cnt+1};
	61	+ case 'DominantEig'
	62	+ doDominantEig = varargin{cnt+1};
	63	+ case 'SkipPCA'
	64	+ doPCA = ~varargin{cnt+1};
	65	+ case 'ScaleW'
	66	+ ScaleW = varargin{cnt+1};
	67	+ case 'do_direct'
	68	+ do_null = varargin{cnt+1};
	69	+ otherwise
	70	+ fprintf('Error, unknown argument %s\n',varargin{cnt});
	71	+ return
	72	+ end
	73	+ cnt = cnt + 2;
	74	+ end
	75	+
	76	+
	77	+ [FeatureLength SampleNumber]=size(X);
	78	+ % ClassNum=round(SampleNumber/2);
	79	+
	80	+ [a1 a2 classNo] = unique(classNo);
	81	+ ClassNum = max(classNo);
	82	+
	83	+ %Calculate eigenspace from X
	84	+ if doPCA
	85	+ if ~doDominantEig
	86	+ [eigenvalues, eigenvectors, Mean_Vector]=PCA2(X);
	87	+ else
	88	+ [eigenvalues, eigenvectors, Mean_Vector, V1]=PCA(X);
	89	+ end
	90	+
	91	+ if useFixedEnergy
	92	+ d1 = cumsum(eigenvalues)./sum(eigenvalues);
	93	+ [a nEigs] = max(d1 > energyPercentage);
	94	+ elseif useFixedEig
	95	+ nEigs = fixedEig;
	96	+ else
	97	+ nEigs = min(FeatureLength,SampleNumber - 1);
	98	+ end
	99	+
	100	+ %Select eigenvectors
	101	+ Select_eigenvectors=eigenvectors(:,1:nEigs);
	102	+ eigenvalues = eigenvalues(1:nEigs);
	103	+
	104	+ %Project the sample data on to the eigenvectors
	105	+ W=Select_eigenvectors'*(X-repmat(Mean_Vector,1,SampleNumber));
	106	+ else
	107	+ W = X;
	108	+ Mean_Vector = zeros(size(X,1),1);
	109	+ nEigs = size(X,1);
	110	+ Select_eigenvectors = eye(size(X,1));
	111	+ eigenvalues = ones(size(X,1),1);
	112	+ end
	113	+
	114	+ %Caculate the centers for each class
	115	+ ClassCenters = zeros(nEigs,ClassNum);
	116	+ for i = 1:ClassNum
	117	+ ClassCenters(:,i) = mean(W(:,classNo == i),2);
	118	+ end
	119	+
	120	+ for i = 1:ClassNum,
	121	+ W(:,classNo == i) = W(:,classNo == i) - repmat(ClassCenters(:,i),1,sum(classNo == i));
	122	+ end
	123	+
	124	+ if ScaleW ~= 1
	125	+ W = ScaleW .* W;
	126	+ end
	127	+
	128	+ [W_val, W_vec, W_m]=PCA2(W);
	129	+
	130	+ if ~do_null
	131	+ nDim2 = min(nEigs,SampleNumber - ClassNum);
	132	+ SW_val=W_val(1:nDim2);
	133	+ SW_vec=W_vec(:,1:nDim2);
	134	+ SW_vec=SW_vec./(repmat(SW_val',[size(SW_vec,1) 1]).^0.5);
	135	+ else
	136	+ nDim2 = nEigs;
	137	+ SW_val = W_val;
	138	+ SW_vec = W_vec;
	139	+ if nEigs > SampleNumber - ClassNum
	140	+ SW_val(SampleNumber-ClassNum+1:end) = SW_val(SampleNumber-ClassNum)/2;
	141	+ end
	142	+
	143	+ d1 = cumsum(W_val)/sum(W_val);
	144	+ [d1 start_idx] = max(d1 > .1);
	145	+
	146	+ SW_vec = SW_vec(:,start_idx:end);
	147	+ SW_val = SW_val(start_idx:end);
	148	+ nDim2 = size(SW_vec,2);
	149	+ SW_vec=SW_vec./(repmat(SW_val',[size(SW_vec,1) 1]).^0.15);
	150	+ end
	151	+
	152	+
	153	+ m = mean(W,2);
	154	+ M=repmat(m(:),1,ClassNum);
	155	+ mean2 = m;
	156	+ B=SW_vec'*(ClassCenters-M);
	157	+ % Between_Class_Matrix=B*B';
	158	+
	159	+
	160	+ [B_val,B_vec,B_m]=PCA2(B);
	161	+
	162	+ nDim3 = min(ClassNum-1,nDim2);
	163	+ SB_vec=B_vec(:,1:nDim3);
	164	+
	165	+ subspaceData.mean = Mean_Vector(:);
	166	+ subspaceData.mean2 = mean2(:);
	167	+ subspaceData.W1 = Select_eigenvectors;
	168	+ subspaceData.D1 = eigenvalues;
	169	+ subspaceData.W2 = SW_vec;
	170	+ subspaceData.W3 = SB_vec;
	171	+ subspaceData.W = (subspaceData.W3' * subspaceData.W2' * subspaceData.W1')';
...	...

scripts/matlab/PCA.m 0 → 100644

View file @b860556

	1	+function [eigenvalues, eigenvectors, meanVector, V]=PCA(X,varargin)
	2	+%function [eigenvalues, eigenvectors, meanVector, V]=PCA(X)
	3	+ cnt = 1;
	4	+ doVar = false;
	5	+ doEigs = false;
	6	+
	7	+ if nargin < 2,
	8	+ end
	9	+ while cnt < length(varargin)
	10	+ switch varargin{cnt}
	11	+ case 'VarEnergy'
	12	+ doVar = true;
	13	+ varPercent = varargin{cnt+1};
	14	+ case 'nEigs'
	15	+ doEigs = true;
	16	+ eigKeep = varargin{cnt+1};
	17	+ otherwise
	18	+ fprintf('Error, unknown argument %s\n',varargin{cnt});
	19	+ return
	20	+ end
	21	+ cnt = cnt + 2;
	22	+ end
	23	+
	24	+
	25	+ [Row Column]=size(X);
	26	+
	27	+ %Mean center X
	28	+ meanVector = mean(X,2); meanVector = meanVector(:);
	29	+ M=repmat(meanVector,1,Column);
	30	+ X=X-M;
	31	+
	32	+ C=X'*X./Column;
	33	+ [V,D]=eig(C);
	34	+ eigenvalues=diag(D);
	35	+
	36	+ %Ordered by eigenvalues%
	37	+ [eigenvalues,Index]=sort(eigenvalues,'descend');
	38	+
	39	+ V=V(:,Index) ; %V1 is the the eigenvectors got from X'X;
	40	+ eigenvectors=X*V;%eigenvectors is the eigenvectors for XX';
	41	+
	42	+ %normalize%
	43	+ NV=sum(eigenvectors.^2);
	44	+ NV=NV.^(1/2);
	45	+
	46	+ %normalize eigenvectors
	47	+ NM=repmat(NV,Row,1);
	48	+ eigenvectors=eigenvectors./NM;
	49	+
	50	+ if doVar
	51	+ d = cumsum(eigenvalues)/ sum(eigenvalues);
	52	+ [a1 a2] = max(d > varPercent);
	53	+ eigenvalues = eigenvalues(1:a2);
	54	+ eigenvectors = eigenvectors(:,1:a2);
	55	+ end
	56	+
	57	+ if doEigs
	58	+ eigenvalues = eigenvalues(1:eigKeep);
	59	+ eigenvectors = eigenvectors(:,1:eigKeep);
	60	+ end
	61	+
	62	+ %normalize V1;
	63	+ NN=repmat(NV,[Column,1]);
	64	+ V=V./NN;
	65	+
	66	+
	67	+
	68	+end
...	...

scripts/matlab/PCA2.m 0 → 100644

View file @b860556

	1	+function [eigenvalues, eigenvectors, Mean_Vector]=PCA2(X,varRetain)
	2	+% [eigenvalues, eigenvectors, Mean_Vector]=PCA2(X)
	3	+%
	4	+%Compute the eienvectors of X when the sample number is larger than the feature lenght
	5	+
	6	+[Row Column]=size(X);
	7	+Mean_Vector=mean(X,2);
	8	+m=repmat(Mean_Vector(:),1,Column);
	9	+X=X-m;
	10	+C=X*X'./Column;
	11	+[V,D]=eig(C);
	12	+eigenvalues=diag(D);
	13	+%Ordered by eigenvalues%
	14	+[eigenvalues,Index]=sort(eigenvalues);
	15	+eigenvalues=eigenvalues(end:-1:1);
	16	+Index=Index(end:-1:1);
	17	+eigenvectors=V(:,Index);
	18	+
	19	+if nargin == 2,
	20	+ d = cumsum(eigenvalues)/ sum(eigenvalues);
	21	+ [a1 a2] = max(d > varRetain);
	22	+ eigenvalues = eigenvalues(1:a2);
	23	+ eigenvectors = eigenvectors(:,1:a2);
	24	+end
...	...