Feature Selection by Nonparametric Bayes Error Minimization

This paper presents an algorithmic framework for feature selection, which selects a subset of features by minimizing the nonparametric Bayes error. A set of existing algorithms as well as new ones can be derived naturally from this framework. For example, we show that the Relief algorithm greedily attempts to minimize the Bayes error estimated by k-Nearest-Neighbor method. This new interpretation not only reveals the secret behind Relief but also offers various opportunities to improve it or to establish new alternatives. In particular, we develop a new feature weighting algorithm, named Parzen-Relief, which minimizes the Bayes error estimated by Parzen method. Additionally, to enhance its ability to handle imbalanced and multiclass data, we integrate the class distribution with the max-margin objective function, leading to a new algorithm, named MAP-Relief. Comparison on benchmark data sets confirms the effectiveness of the proposed algorithms.