# Discriminant Analysis

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## Discriminant Analysis

Discriminant analysis is a statistical classifying technique often used in Market Research. The function of discriminant analysis is to identify distinctive sets of characteristics and allocate new ones to those pre-defined groups. This is known as constructing a classifier, in which the set of characteristics and observations from the target population is distinguished. With this classifier, unclassified characteristics can then be sorted into the distinct, labelled groupings.

In order to carry out discriminant analysis, the smallest grouping must have a sample size that is larger than the number of variables. The norm is for there to be over twenty in the sample for every variable. Furthermore, there can be no repeats within the various groups, so each characteristic must be unique and independent from each other.

There are several different types of discriminant analysis; for example linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA). Bayes’ Theorem can even be applied to discriminant analysis, in the form of Bayesian quadratic discrimination analysis. As the nomenclature suggests, LDA has a linear decision surface, while QDA has a quadratic decision surface. Because QDA makes it possible to learn quadratic boundaries, it is the more flexible of the two forms of discriminant analysis. One key difference between LDA and QDA, is that with QDA there is no assumption that the designated groups have equal covariance matrices. The data used in QDA is varying covariance.

As mentioned, a key use for discriminant analysis is in Marketing, and Market Research. However, other techniques such as logistic regression are now used to a greater extent. The main marketing purpose is to distinguish which factors differentiate customers or products into certain profiles, based on the responses gathered during surveys or other forms of data collection.

In addition to Market Research, this statistical classification technique is often used in biomedical studies, facial recognition technologies, and in the insurance industry with the aim of determining risk.

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