Discriminative Feature Selection by Nonparametric Bayes Error Minimization

Feature selection is fundamental to knowledge discovery from massive amount of high-dimensional data. In an effort to establish theoretical justification for feature selection algorithms, this paper presents a theoretically optimal criterion, namely, the discriminative optimal criterion (DoC) for feature selection. Compared with the existing representative optimal criterion (RoC, [CHECK END OF SENTENCE]) which retains maximum information for modeling the relationship between input and output variables, DoC is pragmatically advantageous because it attempts to directly maximize the classification accuracy and naturally reflects the Bayes error in the objective. To make DoC computationally tractable for practical tasks, we propose an algorithmic framework, which selects a subset of features by minimizing the Bayes error rate estimated by a nonparametric estimator. A set of existing algorithms as well as new ones can be derived naturally from this framework. As an example, we show that the Relief algorithm [CHECK END OF SENTENCE] greedily attempts to minimize the Bayes error estimated by the k-Nearest-Neighbor (kNN) method. This new interpretation insightfully reveals the secret behind the family of margin-based feature selection algorithms [CHECK END OF SENTENCE], [CHECK END OF SENTENCE] and also offers a principled way to establish new alternatives for performance improvement. In particular, by exploiting the proposed framework, we establish the Parzen-Relief (P-Relief) algorithm based on Parzen window estimator, and the MAP-Relief (M-Relief) which integrates label distribution into the max-margin objective to effectively handle imbalanced and multiclass data. Experiments on various benchmark data sets demonstrate the effectiveness of the proposed algorithms.