Python Programming for Biology: Bioinformatics and Beyond

Linear discriminant analysis

While PCA finds the directions of maximum variance within a data set, LDA attempts  to

determine  the  line  of  separation  between  different  data  sets.  What  we  show  here  is

sometimes referred to as Fisher’s linear discriminant.

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This particular approach assumes

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a normal distribution within the data.

The basic idea is that we wish to determine a discrimination matrix that represents how

to  transform  the  data  sets  into  an  orientation  that  best  separates  them.  This  can  be

imagined as rotating the data sets so that they maximally align with an axis of separation,

equivalent to a line between the two sets. If the data sets had the same scatter (variance)

then this line is simply the line between the averages (means) of the two data sets.