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{1416}  
Learning data manifolds with a Cutting Plane method
 
{760} 
ref: 0
tags: LDA myopen linear discriminant analysis classification
date: 01032012 02:36 gmt
revision:2
[1] [0] [head]


How does LDA (Linear discriminant analysis) work? It works by projecting data points onto a series of planes, one per class of output, and then deciding based which projection plane is the largest. Below, to the left is a topview of this projection with 9 different classes of 2D data each in a different color. Right is a size 3D view of the projection  note the surfaces seem to form a parabola. Here is the matlab code that computes the LDA (from myopen's ceven % TrainData and TrainClass are inputs, column major here. % (observations on columns) N = size(TrainData,1); Ptrain = size(TrainData,2); Ptest = size(TestData,2); % add a bit of interpolating noise to the data. sc = std(TrainData(:)); TrainData = TrainData + sc./1000.*randn(size(TrainData)); K = max(TrainClass); % number of classes. %% Compute the means and the pooled covariance matrix %% C = zeros(N,N); for l = 1:K; idx = find(TrainClass==l); % measure the mean per class Mi(:,l) = mean(TrainData(:,idx)')'; % sum all covariance matrices per class C = C + cov((TrainData(:,idx)Mi(:,l)*ones(1,length(idx)))'); end C = C./K; % turn sum into average covariance matrix Pphi = 1/K; Cinv = inv(C); %% Compute the LDA weights %% for i = 1:K Wg(:,i) = Cinv*Mi(:,i); % this is the slope of the plane Cg(:,i) = 1/2*Mi(:,i)'*Cinv*Mi(:,i) + log(Pphi)'; % and this, the originintersect. end %% Compute the decision functions %% Atr = TrainData'*Wg + ones(Ptrain,1)*Cg; % see  just a simple linear function! Ate = TestData'*Wg + ones(Ptest,1)*Cg; errtr = 0; AAtr = compet(Atr'); % this compet function returns a sparse matrix with a 1 % in the position of the largest element per row. % convert to indices with vec2ind, below. TrainPredict = vec2ind(AAtr); errtr = errtr + sum(sum(abs(AAtrind2vec(TrainClass))))/2; netr = errtr/Ptrain; PeTrain = 1netr;  
{724}  
 
{147}  
PMID12899253 Boosting bit rates and error detection for the classification of fastpaced motor commands based on singletrial EEG analysis
 
{66} 
ref: bookmark0
tags: machine_learning classification entropy information
date: 002006 0:0
revision:0
[head]


http://iridia.ulb.ac.be/~lazy/  Lazy Learning. 