Mendes Research Group

Ometer — Linear Multiple Discriminant Analysis (MDA)

MDA is a classic linear discriminant analysis for arbitrary number of classes. In the case of only two classes, this is also known as Fisher's discriminant analysis. The algorithm is based on rotating the data in such a way that maximizes the between-class variance while simultaneously minimizing the within-class variance. Then the data is projected on the first orthogonal axes (whose number is one less than the number of classes).

MDA is similar to PCA in the way that the data is projected onto orthogonal axes. In this case the rotation is determined by two criteria derived from a prior data classification (while in PCA the rotation is determined only by the maximal variance).

Usage

The data file must contain classification of samples. To see how to add class labels see Ometer file formats. Examples of usage:

ometer -m=mda -o result input.dat
will analyze the data in file input.dat and put results on the following files:

• result.html, a html report file with a summary of the classification success, including the confusion matrix
• result-mda-proj.dat, a tab-delimited text file with the data projected on the discriminant axes (this file could be used as input for further analyses).
• result-mda-loadings.dat, a tab-delimited text file with the loadings of each of the discriminant axes (DF).
• result-mda-scree.dat, a tab-delimited text file with the proportion of the between-groups variance explained by each discriminant axis.
• result-mda-scree.plt, a gnuplot input file for plotting the scree plot.

ometer -m=mda --proj-2dplots -o result input.dat
will carry out the same analysis as in the previous example, in addition it will create plots of the 2D plots of the data projection onto the discriminant axes (DF) *result-mda-2dplots.plt, a gnuplot input file that will display all of the 2D projection plots in a sequence

• result-mda-DF1_DF2.plt, a gnuplot file to display the projection onto the first two discriminant axes. Other files for DF3, DF4, etc., if they exist.

ometer -m=mda --proj-2dplots --plot-png -o result input.dat
will carry out the same as the previous two examples, but now the gnuplot files are already modified to produce PNG bitmaps (useful to display on web pages, import to word processors, etc.)

All tab-delimited text files can be easily loaded into spreadsheets. The html report file should be displayed with a web browser.

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