Support Measure Data Description

Jorge Guevara (1) , Stephane Canu (2) , Roberto Hirata Jr (1)

1 VISION - Computer vision research group
2 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

We address the problem of learning a data description model for datasets containing examples given by groups, clusters or sets of points. Specifically, we assume each example containing values drawing from some unknown local probability measure. We found such a description by empirically approximating a minimum volume set in the space of probability measures by means of a minimum enclosing ball in a Reproducing Kernel Hilbert Space of the representer functions of such measures. As a result, the data description model is a function that only depends on some probability measures called support measures. We formulated three data description models for such datasets. The optimization problem for the first one is a chance constrained program. The second and the third models are quadratic programs. We validate our method in the challenging setting of group anomaly detection task.

Keywords: Kernel on distributions; One-class classification; support vector data description; embedding of probability measures; mean map; group anomaly detection

Domains: Machine Learning [cs.LG]

Jorge Guevara, Stephane Canu, Roberto Hirata Jr. Support Measure Data Description. 2014. ⟨hal-01015718v1⟩