Infinite Feature Selection

Filter-based feature selection has become crucial in many classification settings, especially object recognition, recently faced with feature learning strategies that originate thousands of cues. In this paper, we propose a feature selection method exploiting the convergence properties of power series of matrices, and introducing the concept of infinite feature selection (Inf-FS). Considering a selection of features as a path among feature distributions and letting these paths tend to an infinite number permits the investigation of the importance (relevance and redundancy) of a feature when injected into an arbitrary set of cues. Ranking the importance individuates candidate features, which turn out to be effective from a classification point of view, as proved by a thoroughly experimental section. The Inf-FS has been tested on thirteen diverse benchmarks, comparing against filters, embedded methods, and wrappers, in all the cases we achieve top performances, notably on the classification tasks of PASCAL VOC 2007-2012.