Mahalanobis-Based One-Class Classification

Patric Nader (1) , Paul Honeine (1) , Pierre Beauseroy (1)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes

Machine learning techniques have become very popular in the past decade for detecting nonlinear relations in large volumes of data. In particular, one-class classification algorithms have gained the interest of the researchers when the available samples in the training set refer to a unique/single class. In this paper, we propose a simple one-class classification approach based on the Mahalanobis distance. We make use of the advantages of kernel whitening and KPCA in order to compute the Mahalanobis distance in the feature space, by projecting the data into the subspace spanned by the most relevant eigenvectors of the covariance matrix. We also propose a sparse formulation of this approach. The tests are conducted on simulated data as well as on real data.

Mots clés: machine learning; one-class; cybersecurity; learning (artificial intelligence); pattern classification; Mahalanobis-based one-class classification; machine learning techniques; nonlinear relation detection; Mahalanobis distance; kernel whitening; KPCA; feature space; covariance matrix eigenvectors; Kernel; Training; Covariance matrices; Support vector machines; Pipelines; Matrix decomposition; Eigenvalues and eigenfunctions; Kernel methods; one-class classification

Domaines: Apprentissage [cs.LG]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Patric Nader, Paul Honeine, Pierre Beauseroy. Mahalanobis-Based One-Class Classification. Proc. 24th IEEE workshop on Machine Learning for Signal Processing (MLSP), 2014, Reims, France. pp.1 - 6, ⟨10.1109/MLSP.2014.6958934⟩. ⟨hal-01965995⟩