lda
Linear discriminant analysis. LDA is based on the Bayes decision theory and assumes that the conditional probability density functions are normally distributed. LDA also makes the simplifying homoscedastic assumption (i.e. that the class covariances are identical) and that the covariances have full rank. With these assumptions, the discriminant function of an input being in a class is purely a function of this linear combination of independent variables.
LDA is closely related to ANOVA (analysis of variance) and linear regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements. In the other two methods, however, the dependent variable is a numerical quantity, while for LDA it is a categorical variable (i.e. the class label). Logistic regression and probit regression are more similar to LDA, as they also explain a categorical variable. These other methods are preferable in applications where it is not reasonable to assume that the independent variables are normally distributed, which is a fundamental assumption of the LDA method.
One complication in applying LDA (and Fisher's discriminant) 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
linear discriminant analysis model.
Parameters
training samples.
training labels in [0, k), where k is the number of classes.
the priori probability of each class. If null, it will be estimated from the training data.
a tolerance to decide if a covariance matrix is singular; it will reject variables whose variance is less than tol2.