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==Discriminant analysis (classification)==

==Discriminant analysis (classification)==

[[File:Charles-l-vavra-john-g-kaldi-robert-m-sneider capillary-pressure 1.jpg|thumbnail|left|'''Figure 1.''']]

[[File:Charles-l-vavra-john-g-kaldi-robert-m-sneider capillary-pressure 1.jpg|thumbnail|left|'''Figure 1.''' Plot of two-bivariate distributions, showing overlap between groups a and b along both variables ''x''₁ and ''x''₂. Groups can be distinguished by projecting members of the two groups onto the discriminant function line.<ref name=Davis_1986 />.]]

''Discriminant analysis'' (DA) attempts to determine an allocation rule to classify multivariate data vectors into a set of predefined classes, with a minimum probability of misclassification.<ref name=Davis_1986>Davis, J. C., 1986, Statistics and data analysis in geology: New York, John Wiley, 646 p.</ref> Consider a set of n samples with P quantities being measured on each. Suppose that the n samples are divided into m classes or groups. Discriminant analysis consists of two steps:

''Discriminant analysis'' (DA) attempts to determine an allocation rule to classify multivariate data vectors into a set of predefined classes, with a minimum probability of misclassification.<ref name=Davis_1986>Davis, J. C., 1986, Statistics and data analysis in geology: New York, John Wiley, 646 p.</ref> Consider a set of n samples with P quantities being measured on each. Suppose that the n samples are divided into m classes or groups. Discriminant analysis consists of two steps: