Discriminant analysis, Advanced Statistics

A term which covers the large number of techniques for the analysis of the multivariate data which have in common the aim to assess whether or not the set of variables distinguish or discriminate between the two or more groups of the individuals. In medicine, for instance, this type of methods are generally applied to the problem of using optimally the results from the various tests or the observations of various symptoms to make the diagnosis which can only be confirmed perhaps by the post-mortem examination. In the two group case the mainly used method is Fisher's linear discriminant function, in which a linear function of variables giving the maximal separation between the groups is then determined. This results in the classification rule which may be used to assign the new patient to one of the two groups. The derivation of the linear function supposes that the variance-covariance matrices of the two groups are the same. If they are not then a quadratic discriminant function might be essential to distinguish between the groups. Such a function comprises of powers and cross-products of variables. The sample of the observations from which the discriminant function is derived is commonly known as the training set. When more than two groups are involved then it is possible to determine the several linear functions of the variables for separating them. In common the number of such functions which can be derived is the smaller of q and g-1 where q is the number of variables and g is the number of groups. The collection of the linear functions for discrimination is called as canonical discriminant functions or simply as canonical variates.

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