FISHERM

Optimal discrimination linear mapping (Fisher mapping, LDA)

   W = FISHERM(A,N,ALF)

Input
A	Dataset
N	Number of dimensions to map to, N < C, where C is the number of classes  (default: min(C,K)-1, where K is the number of features in A)
ALF	Preserved variance in the pre-whitening step

Output
W	Fisher mapping

Description

Finds a mapping of the labeled dataset A onto an N-dimensional linear  subspace such that it maximizes the the between scatter over the within  scatter (also called the Fisher mapping [1 or LDA]). Note that N should be  less than the number of classes in A. If supplied, ALF determines the  preserved variance in the prewhitening step (i.e. removal of insignificant  eigenvectors in the within-scatter, the EFLD procedure [2]), see KLMS.

The resulting mapping is not orthogonal. It may be orthogonalised by ORTH.

Reference(s)

[1] K. Fukunaga, Introduction to statistical pattern recognition, 2nd ed., Academic Press, New York, 1990. [2] C. Liu and H. Wechsler, Robust Coding Schemes for Indexing and Retrieval from Large Face Databases, IEEE Transactions on Image Processing, vol. 9, no. 1, 2000, 132-136.

See also

mappings, datasets, nlfisherm, klm, pca, klms, orth,