What is the difference between quadratic and mahalanobis distance with stratified covaraiance estimates when using classify

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Barry Troniqes 2014-10-28

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回答： Siddharth Sundar 2014-10-29

Sorry for what may be a silly question but I'm very new to pattern recognition and am having trouble understanding matlabs classify function.

I have a training set for which I have performed bartlett's test for equality of covariance matrices with equal numbers of cases for each class. This returns a p of 0 which I understand to mean I should use stratified covariance estimates for each group.

classify offers two options with stratified covariance

mahalanobis — Uses Mahalanobis distances with stratified covariance estimates

Quadratic — Fits multivariate normal densities with covariance estimates stratified by group

http://www.mathworks.co.uk/help/stats/classify.html

Assuming equal priors what is the difference between performing a discriminant analysis using the mahalanobis and quadratic options? for my data the quadratic seems to perform better but I would like to understand why.

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Answer 1

Siddharth Sundar 2014-10-29

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The first place I would look at when trying to get some details about the Math behind the implementation would be the references mentioned in the documentation for the classify function.

Wikipedia also provides some basic information about Quadratic Discriminant Analysis(the method that is chosen when the 'type' input to the classify function is 'quadratic') as seen here.

The Mahalanobis distance and its application in discriminant analysis is also talked about in this Wikipedia page. However, I would rely on the references mentioned in the documentation page for the details.

With respect to one of the options working better than the other, from experience, that depends completely on the data that you use.