Feature Selection for Interval-Valued Data Based on D-S Evidence Theory

Abstract

Feature selection is one basic and critical technology for data mining, especially in current "big data era". Rough set theory (RST) is sensitive to noise in feature selection due to the strict condition of equivalence relation. However, D-S evidence theory is flexible to measure uncertainty of information. This paper introduces robust feature evaluation metrics "belief function" and "plausibility function" into feature selection algorithm to avoid the defect that classification effect is affected by noise. First of all, similarity between information values in an interval-valued information system (IVIS) is given and a variable parameter to control the similarity of samples is introduced. Then, θ-lower approximation and θ-upper approximation in IVIS are put forward. Next, belief function and plausibility function based on θlower approximation and θ-upper approximation are put forward. Finally, four feature selection algorithms in an IVIS based on D-S evidence theory are proposed. The experimental results on four real interval-valued datasets show that the proposed metrics are robust to noise, and the proposed algorithms are more effective than the existing algorithms.

Belief functions and rough sets: Survey and new insights

“…Furthermore, several theoretical problems related to this approach remain open. These include finding theoretical conditions for equivalence between the two reduct definitions, the study of rule induction algorithms, as well as studying the properties of these definitions of reducts in the other generalized relation-based models that have been more recently considered in the literature [17,36,68,87,88,91].…”

“…First, the same authors [110] considered the application of belief and plausibility reducts to random information systems, showing that Theorems 4.3 and 4.4 hold also in this setting. Furthermore, the extension to the case of continuous and interval-valued data has been widely studied [17,68,88], and it has been shown that the equivalence between belief and classical reducts holds also in these settings.…”