The geometry of linear separability in data sets

We study the geometry of datasets, using an extension of the Fisher linear discriminant to the case of singular covariance, and a new regularization procedure. A dataset is called linearly separable if its different clusters can be reliably separated by a linear hyperplane. We propose a measure of linear separability, easily computed as an angle that arises naturally in our analysis. This angle of separability assumes values between 0 and π/2, with high [resp. low] values corresponding to datasets that are linearly separable, resp. inseparable.