Feature Selection via Independent Domination

Feature or variable selection is a fundamental problem in data analysis and statistical modeling. Classic methods resulting in dimensionality reduction are diverse and include things like statistical hypotheses testing for zero coefficients, ‘stepwise’ methods minimizing, e.g., AIC, the spectra of a data matrix or principal component analysis, regularization methods especially the Lasso, various heuristic and ‘shrinkage’ methods all of which result in a subset of the feature space used as a basis for statistical modeling. Combinatorial variable selection has also been used in a manner that aids in the selection of a good subset of the feature space. A graph, or the ‘data graph’, is based on the pairwise correlations of features and may be used to extract the most distinguishing features. Partly due to high computational cost, combinatorial variable selection methods have not been well studied. We consider a variable selection procedure via the Minimum Independent Dominating Set problem. We explore the use of some exact and heuristic methods that proved to be effective for feature extracting and ranking.