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{1433} 
ref: 2008
tags: representational similarity analysis fMRI
date: 02152019 02:27 gmt
revision:1
[0] [head]


PMID19104670 Representational Similarity Analysis â€“ Connecting the Branches of Systems Neuroscience
 
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IEEE4120642 (pdf) Mechanical Factors in the Design of Chronic Recording Intracortical Microelectrodes ____References____ Goldstein, Seth R. and Salcman, Michael Mechanical Factors in the Design of Chronic Recording Intracortical Microelectrodes Biomedical Engineering, IEEE Transactions on BME20 4 260 269 (1973)  
{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;  
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follow up paper: http://spikelab.jbpierce.org/Publications/LaubachEMBS2003.pdf
____References____ Laubach, M. and Arieh, Y. and Luczak, A. and Oh, J. and Xu, Y. Bioengineering Conference, 2003 IEEE 29th Annual, Proceedings of 17  18 (2003.03)  
{827} 
ref: OSuilleabhain1998.11
tags: analysis tremor parkinsons disease
date: 07192010 19:22 gmt
revision:2
[1] [0] [head]


PMID9827772[0] Timefrequency analysis of tremor
____References____
 
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Studies in astronomical time series analysis. II  Statistical aspects of spectral analysis of unevenly spaced data Scargle, J. D.
 
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images/588_1.pdf  Good lecture on LDA. Below, simple LDA implementation in matlab based on the same: % data matrix in this case is 36 x 16, % with 4 examples of each of 9 classes along the rows, % and the axes of the measurement (here the AR coef) % along the columns. Sw = zeros(16, 16); % withinclass scatter covariance matrix. means = zeros(9,16); for k = 0:8 m = data(1+k*4:4+k*4, :); % change for different counts / class Sw = Sw + cov( m ); % sum the means(k+1, :) = mean( m ); %means of the individual classes end % compute the classindependent transform, % e.g. one transform applied to all points % to project them into one plane. Sw = Sw ./ 9; % 9 classes criterion = inv(Sw) * cov(means); [eigvec2, eigval2] = eig(criterion); See {587} for results on EMG data.  
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