Incremental attribute reduction approaches for ordered data with time-evolving objects

Abstract

Dominance-based rough set approach (DRSA) is widely applied to multi-criteria decision analysis and sorting problems for data with preference-ordered relation, where attribute reduction is an important research field. At present, based on DRSA, many traditional attribute reduction approaches are extended to process a static ordered data. In real-world applications, ordered data with time-evolving objects widely exist, which is called a dynamic ordered data. However, for dynamic ordered data, employing these existing approaches to compute reducts is very time-consuming, since they need to recalculate knowledge from scratch when multiple objects vary. Incremental updating method can effectively complete the dynamic learning task, because it can acquire new knowledge based on previous knowledge. Inspired by this, this work studies incremental attribute reduction approaches for dynamic ordered data in DRSA framework. First, matrix-based method for calculating the dominance conditional entropy is investigated. Next, the updating principles of the dominance relation matrix and dominance diagonal matrix are studied when objects vary. Finally, two incremental algorithms of attribute reduction are proposed when multiple objects are added to or deleted from an ordered decision system, respectively. Experiments on different datasets provided by University of California at Irvine (UCI) are conducted to evaluate the proposed algorithms. Experimental results show that the proposed incremental algorithms can effectively and efficiently accomplish the task of attribute reduction in dynamic ordered data.