lda
Linear discriminant analysis
Contents
Syntax
- DS2 = lda(DS)
- DS2 = lda(DS, discrimVecNum)
- [DS2, discrimVec, eigValues] = lda(...)
Description
DS2 = lda(DS, discrimVecNum) returns the results of LDA (linear discriminant analysis) on DS
- DS: input dataset (Try "DS=prData('iris')" to get an example of DS.)
- discrimVecNum: No. of discriminant vectors
- DS2: output data set, with new feature vectors
[DS2, discrimVec, eigValues] = lda(DS, discrimVecNum) returns extra info:
- discrimVec: discriminant vectors identified by LDA
- eigValues: eigen values corresponding to the discriminant vectors
References
- [1] J. Duchene and S. Leclercq, "An Optimal Transformation for Discriminant and Principal Component Analysis," IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 10, No 6, November 1988
Example
Scatter plots of the LDA projection
dsName='wine'; ds=prData(dsName); ds.input=inputNormalize(ds.input); % Input normalization dsLda=lda(ds); ds12=dsLda; ds12.input=ds12.input(1:2, :); subplot(1,2,1); dsScatterPlot(ds12); xlabel('Input 1'); ylabel('Input 2'); title(sprintf('%s dataset projected on the first 2 LDA vectors', dsName)); ds34=dsLda; ds34.input=ds34.input(end-1:end, :); subplot(1,2,2); dsScatterPlot(ds34); xlabel('Input 3'); ylabel('Input 4'); title(sprintf('%s dataset projected on the last 2 LDA vectors', dsName));
Leave-one-out accuracy of the projected dataset using KNNC
fprintf('LOO accuracy of KNNC over the original %s dataset = %g%%\n', dsName, 100*perfLoo(ds, 'knnc')); fprintf('LOO accuracy of KNNC over the %s dataset projected onto the first two LDA vectors = %g%%\n', dsName, 100*perfLoo(ds12, 'knnc')); fprintf('LOO accuracy of KNNC over the %s dataset projected onto the last two LDA vectors = %g%%\n', dsName, 100*perfLoo(ds34, 'knnc'));
LOO accuracy of KNNC over the original wine dataset = 95.5056% LOO accuracy of KNNC over the wine dataset projected onto the first two LDA vectors = 98.8764% LOO accuracy of KNNC over the wine dataset projected onto the last two LDA vectors = 32.0225%