AH3: An adaptive hierarchical feature representation model for three-way decision boundary processing

Abstract

Three-way decision theory is an effective method to deal with uncertain data in classification problems. For binary classification, it divides samples into positive, negative and boundary regions (POS, NEG, and BND). The BND region is regarded as a feasible selection of decision-making when the useful information is too limited to make a correct decision, which needs further processing to improve the binary classification. Many existing boundary processing methods are oriented only toward the data and not to the problem. How to obtain effective decision rules from the problem itself to guide boundary division is a challenge. In this article, we propose an adaptive hierarchical feature representation model based on three-way decision theory (named AH3) with a problem oriented for boundary processing. We firstly divide all samples into two certain regions (POS and NEG) and an uncertain region (BND) using a three-way decision model based on a minimum covering algorithm. Secondly, we obtain the hierarchical feature representation of POS and NEG regions on the basis of fuzzy quotient space theory, and select the optimal layer with a problem-oriented validating BND region of the training set. Finally, we adaptively decompose the optimal layer between the upper layer and the lower layer to find the adaptive granular space for boundary processing. The experimental results obtained with five University of California, Irivine datasets show that our algorithm effectively increases binary classification accuracy.