# Fisher Discriminant Analysis

A Fisher Discriminant Analysis is a feature selection algorithm that finds a linear combination of features which characterizes or separates two or more classes of objects or events.

**See:**Fisher Score, Fisher Kernel, Linear Discriminant Analysis, Linear Combination, Features (Pattern Recognition), Linear Classifier, Dimensionality Reduction, Statistical Classification, ANOVA.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Linear_discriminant_analysis Retrieved:2014-9-29.
**Linear discriminant analysis (LDA)**and the related Fisher's linear discriminant are methods used in statistics, pattern recognition and machine learning to find a linear combination of features which characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.LDA is closely related to ANOVA (analysis of variance) and regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements.

^{[1]}^{[2]}However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant analysis has continuous independent variables and a categorical dependent variable (*i.e.*the class label).^{[3]}Logistic regression and probit regression are more similar to LDA, as they also explain a categorical variable by the values of continuous independent variables. These other methods are preferable in applications where it is not reasonable to assume that the independent variables are normally distributed, which is a fundamental assumption of the LDA method. LDA is also closely related to principal component analysis (PCA) and factor analysis in that they both look for linear combinations of variables which best explain the data.^{[4]}LDA explicitly attempts to model the difference between the classes of data. PCA on the other hand does not take into account any difference in class, and factor analysis builds the feature combinations based on differences rather than similarities. Discriminant analysis is also different from factor analysis in that it is not an interdependence technique: a distinction between independent variables and dependent variables (also called criterion variables) must be made. LDA works when the measurements made on independent variables for each observation are continuous quantities. When dealing with categorical independent variables, the equivalent technique is discriminant correspondence analysis.^{[5]}^{[6]}

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- ↑ Analyzing Quantitative Data: An Introduction for Social Researchers, Debra Wetcher-Hendricks, p.288
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- ↑ Abdi, H. (2007) "Discriminant correspondence analysis." In: N.J. Salkind (Ed.):
*Encyclopedia of Measurement and Statistic*. Thousand Oaks (CA): Sage. pp. 270–275. - ↑ Perriere, G.; & Thioulouse, J. (2003). “Use of Correspondence Discriminant Analysis to predict the subcellular location of bacterial proteins",
*Computer Methods and Programs in Biomedicine*, 70, 99–105.