fisher
Fisher's linear discriminant. Fisher defined the separation between two distributions to be the ratio of the variance between the classes to the variance within the classes, which is, in some sense, a measure of the signal-to-noise ratio for the class labeling. FLD finds a linear combination of features which maximizes the separation after the projection. The resulting combination may be used for dimensionality reduction before later classification.
The terms Fisher's linear discriminant and LDA are often used interchangeably, although FLD actually describes a slightly different discriminant, which does not make some of the assumptions of LDA such as normally distributed classes or equal class covariances. When the assumptions of LDA are satisfied, FLD is equivalent to LDA.
FLD is also closely related to principal component analysis (PCA), which also looks for linear combinations of variables which best explain the data. As a supervised method, FLD explicitly attempts to model the difference between the classes of data. On the other hand, PCA is a unsupervised method and does not take into account any difference in class.
One complication in applying FLD (and LDA) to real data occurs when the number of variables/features does not exceed the number of samples. In this case, the covariance estimates do not have full rank, and so cannot be inverted. This is known as small sample size problem.
Return
fisher discriminant analysis model.
Parameters
training instances.
training labels in [0, k), where k is the number of classes.
the dimensionality of mapped space. The default value is the number of classes - 1.
a tolerance to decide if a covariance matrix is singular; it will reject variables whose variance is less than tol2.