Semi-supervised partially labeled heterogeneous feature selection based on information-theoretic three-way decision model

Feature selection plays an increasingly vital role in addressing large-scale partially labeled heterogeneous data. Three-way decision (TWD) theory is an important extension of classical two-way decision, which provides an approach to acquire a ternary classification of the universe as acceptance region, rejection region and boundary region, respectively, while the boundary region can capture the uncertain information. In this paper, taking consideration of heterogeneous data possessing tremendous unlabeled samples, we present two kinds of feature representation metric based on unlabeled sample selection mechanism to construct more effective feature selection models. Specifically, a generalized variable-precision neighborhood rough set model is first proposed based on a TWD model developed by optimal threshold pair, which describes the relationships between features and labels from a more fine-grained level. Second, a unlabeled sample selection framework is proposed to comprehensively measure the importance of unlabeled samples based on their uncertainty, graph density and label transfer ability. We then define six TWD-based measures which reveal nonlinear correlation and inconsistency between features and labels by extended information entropy and complementary entropy, respectively. Furthermore, the unified feature measures are established to boost global feature selection in partially labeled heterogeneous datasets. Finally, the corresponding feature selection algorithm is designed, and the comparative experiments demonstrate the effectiveness and efficiency.