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Is there a way to test linear separability of a two-class dataset in high dimensions? My feature vectors are 40-long.

I know I can always run logistic regression experiments and determine hitrate vs false alarm rate to conclude whether the two classes are linearly separable or not but it would be good to know if there already exists a standard procedure to do that.

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have a look here: –  user603 Jan 17 '13 at 10:11
    
It's useful to plot separabiity: x = misclassified points $\cdot$ normal-to-separating-plane, y = cumulative loss(x). (For a sample plot, try a new question with tags svm and data-visualization.) –  denis Feb 3 '13 at 11:13
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up vote 1 down vote accepted

Well, support vector machines (SVM) are probably, what you are looking for. For example, SVM with a linear RBF kernel, maps feature to a higher dimenional space and tries to separet the classes by a linear hyperplane. This is a nice short SVM video illustrating the idea.

You may wrap SVM with a search method for feature selection (wrapper model) and try to see if any of your features can linearly sparate the classes you have.

There are many interesting tools for using SVM including LIBSVM, MSVMPack and Scikit-learn SVM.

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+1. It's almost as if Nik were describing SVM's, not having heard of them. In R, you could use the (mysteriously-named) e1071 package's svm with kernel="linear" and look at the prediction versus actual. –  Wayne Jan 19 '13 at 15:13
    
I know about SVMs. Just that I didn't know I could use them for testing linear separability without actually classifying each sample. –  Nik Jan 24 '13 at 20:08
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