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==Discriminant analysis (classification)==

==Discriminant analysis (classification)==

''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 (Davis, 1986)<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:

# The determination of what makes each group different from the others. The answer may be that not all m predefined groups are significantly different from each other.

# The determination of what makes each group different from the others. The answer may be that not all m predefined groups are significantly different from each other.

# The definition of an allocation rule, usually taking the form of a "score" equal to a particular linear combination of the values of the P quantities.

# The definition of an allocation rule, usually taking the form of a "score" equal to a particular linear combination of the values of the P quantities.

Using this allocation rule, additional (new) samples can be classified into the predefined groups, and the corresponding probability of misclassification can be estimated (Figure 1).

Using this allocation rule, additional (new) samples can be classified into the predefined groups, and the corresponding probability of misclassification can be estimated ([[:Image:Charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg|Figure 1]]).

Discriminant analysis requires the definition of a "distance" between any two groups. A widely used measure is the Mahalanobis distance (see Davis, 1986, for further details)<ref name=Davis_1986 />.

Discriminant analysis requires the definition of a "distance" between any two groups. A widely used measure is the Mahalanobis distance.<ref name=Davis_1986 />

==Cluster analysis==

==Cluster analysis==