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Linear discriminant analysis (lineardiscriminantanalysis) and quadratic discriminant analysis (quadraticdiscriminantanalysis) are two classic classifiers, with, as their names suggest, a linear and a quadratic decision surface, respectively.   quadratic discriminant analysis (qda) is a variant of lda that allows for non-linear separation of data. Finally, regularized discriminant analysis (rda) is a compromise between lda and qda. This post focuses mostly on lda and explores its use as a classification and visualization technique, both in theory and in practice.   in this blog post we will be looking at the differences between linear discriminant analysis (lda) and quadratic discriminant analysis (qda). Both statistical learning methods are used for classifying observations to a class or category. This quadratic discriminant function is very much like the linear discriminant function except that because k, the covariance matrix, is not identical, you cannot throw away the quadratic terms. This discriminant function is a quadratic function and will contain second order terms. The assumption of groups with matrices having equal covariance is not present in quadratic discriminant analysis. Similar to the linear discriminant analysis, an observation is classified into the group having the least squared distance. But, the squared distance does not reduce to a linear function as evident. Quadratic discriminant analysis (qda) more flexible than lda. Here, there is no assumption that the covariance matrix of classes is the same. Mixture discriminant analysis (mda) each class is assumed to be a gaussian mixture of subclasses. Flexible discriminant analysis (fda) non-linear combinations of predictors is used such as splines. Discriminant analysis is a vital statistical tool that is used by researchers worldwide. Machine learning, pattern recognition, and statistics are some of the spheres where this practice is widely employed.

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