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# Regularized Discriminant Analysis (RapidMiner Studio Core)

## Synopsis

This operator performs a regularized discriminant analysis (RDA). for nominal labels and numerical attributes. Discriminant analysis is used to determine which variables discriminate between two or more naturally occurring groups, it may have a descriptive or a predictive objective.

## Description

The regularized discriminant analysis (RDA) is a generalization of the linear discriminant analysis (LDA) and the quadratic discreminant analysis (QDA). Both algorithms are special cases of this algorithm. If the alpha parameter is set to 1, this operator performs LDA. Similarly if the alpha parameter is set to 0, this operator performs QDA. For more information about LDA and QDA please study the documentation of the corresponding operators.

Discriminant analysis is used to determine which variables discriminate between two or more naturally occurring groups. For example, an educational researcher may want to investigate which variables discriminate between high school graduates who decide (1) to go to college, (2) NOT to go to college. For that purpose the researcher could collect data on numerous variables prior to students' graduation. After graduation, most students will naturally fall into one of the two categories. Discriminant Analysis could then be used to determine which variable(s) are the best predictors of students' subsequent educational choice. Computationally, discriminant function analysis is very similar to analysis of variance (ANOVA). For example, suppose the same student graduation scenario. We could have measured students' stated intention to continue on to college one year prior to graduation. If the means for the two groups (those who actually went to college and those who did not) are different, then we can say that intention to attend college as stated one year prior to graduation allows us to discriminate between those who are and are not college bound (and this information may be used by career counselors to provide the appropriate guidance to the respective students). The basic idea underlying discriminant analysis is to determine whether groups differ with regard to the mean of a variable, and then to use that variable to predict group membership (e.g., of new cases).

Discriminant Analysis may be used for two objectives: either we want to assess the adequacy of classification, given the group memberships of the objects under study; or we wish to assign objects to one of a number of (known) groups of objects. Discriminant Analysis may thus have a descriptive or a predictive objective. In both cases, some group assignments must be known before carrying out the Discriminant Analysis. Such group assignments, or labeling, may be arrived at in any way. Hence Discriminant Analysis can be employed as a useful complement to Cluster Analysis (in order to judge the results of the latter) or Principal Components Analysis.

## Differentiation

### Linear Discriminant Analysis

The RDA operator performs regularized discriminant analysis (RDA) which is a generalization of the LDA which is special cases of this algorithm. If the alpha parameter is set to 1, the RDA operator performs LDA.

The RDA operator performs regularized discriminant analysis (RDA) which is a generalization of the QDA which is special cases of this algorithm. If the alpha parameter is set to 0, the RDA operator performs QDA.

## Input

• training set (Data Table)

This input port expects an ExampleSet. It is the output of the Retrieve operator in the attached Example Process. The output of other operators can also be used as input.

## Output

• model (Model)

The Discriminant Analysis is performed and the resultant model is delivered from this output port

• example set (Data Table)

The ExampleSet that was given as input is passed without changing to the output through this port. This is usually used to reuse the same ExampleSet in further operators or to view the ExampleSet in the Results Workspace.

## Parameters

• alphaThis parameter specifies the strength of regularization. If set to 1, only global covariance is used. If set to 0, only per class covariance is used. Range: real
• approximate_covariance_inverseThis parameter indicates whether the inverse of the covariance matrices should be approximated if the actual inverse does not exist. This is activated by default. Range: boolean

## Tutorial Processes

### Introduction to the RDA operator

The 'Sonar' data set is loaded using the Retrieve operator. A breakpoint is inserted here so that you can have a look at this ExampleSet. The Regularized Discriminant Analysis operator is applied on this ExampleSet. The Regularized Discriminant Analysis operator performs the discriminant analysis and the resultant model can be seen in the Results Workspace.