MATLAB: Classify

classifydiscriminant analysis

dear all,

I have some doubt concerning the function "classify":

1) if I use the method 'linear', what does it mean that the covariance matrix is computed by a pooled estimate ?

2) if I use the method 'quadratic', what does it mean that the covariance matrix is computed by a estimate stratified by group?

3) if I do not use 'mahalanobis' method, how are the distances computed in 'linear' and 'quadratic' methods?

4) am I correct that these distances are computed between the fit obtained from the training and the data in sample?

many thanks, any code of support to eventual answers is more than welcome.

Michele

Best Answer

"Pooled" and "stratified" are conventional terms in the statistics literature. A pooled estimate is computed using all observations from all groups (classes). A stratified estimate is computed for each group (class) separately.

Every method in CLASSIFY computes the Mahalanobis distance from the center of each class (determined from the training data) and the data in sample. 'mahalanobis' method assigns an observation to the class with the minimal distance. All other methods estimate the posterior probabilities and assign an observation to the class with the largest posterior.

Related Solutions

MATLAB: Uniform class probabilities vs. Empirical class probabilities

If you are still looking for an answer, there is only one definition for error. In each case, you form a confusion matrix and then take a weighted sum of off-diagonal elements. This code snippet should explain it:

load ionosphere
prior = [1 3]'/4;
m = fitcsvm(X,Y,'prior',prior,'kfold',5,'stand',1);
Yhat = m.kfoldPredict;
C = confusionmat(Y,Yhat,'order',m.ClassNames)
Coff = C;
Coff(1:3:end) = 0
sum(sum(Coff,2).*prior./sum(C,2))
m.kfoldLoss

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

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.

Best Answer

Related Solutions

MATLAB: Uniform class probabilities vs. Empirical class probabilities

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

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