Infinite Feature Selection: a Graph-based Feature Filtering Approach

Giorgio Roffo, Simone Melzi, Marco Cristani, Alessandro Vinciarelli, Umberto Castellani

Abstract:

We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is
a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles.
By two different interpretations (exploiting properties of power series of matrices and relying on Markov chains fundamentals) we can
evaluate the values of paths (i.e., feature subsets) of arbitrary lengths, eventually go to infinite, from which we dub our framework
Infinite Feature Selection (Inf-FS). Going to infinite allows to constrain the computational complexity of the selection process, and to
rank the features in an elegant way, that is, considering the value of any path (subset) containing a particular feature. We also propose
a simple unsupervised strategy to cut the ranking, so providing the subset of features to keep. In the experiments, we analyze diverse
settings with heterogeneous features, for a total of 11 benchmarks, comparing against 18 widely-know comparative approaches. The
results show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori, or when
the decision of the subset cardinality is part of the process