Abstract:
Machine learning’s multi-scale decision system (MDS) describes hierarchical data well. MDS knowledge discovery involves OSC selection and attribute reduction. Searching for all OSCs may cause a combinatorial explosion, and current methods are time-consuming. This study optimizes OSC search in scale space. By integrating three-way decision with the Hasse diagram, a sequential scale space three-way decision model reduces search space. First, a novel scale combination is proposed to perform scale selection and attribute reduction simultaneously, followed by an extended stepwise optimal scale selection (ESOSS) method to quickly search for a single local OSC on a subset of the scale space. Second, using the local OSCs, a sequential three-way decision model of the scale space divides the search space into three pair-wise disjoint regions: positive, negative, and boundary. The boundary region is a new search space, and a local OSC on it is a global OSC. Thus, searching for local OSCs on boundary regions step-by-step yields all OSCs of an MDS. To reduce space complexity, the Hasse diagram provides a formula for calculating the maximal elements of a boundary region. An efficient OSC selection algorithm reduces the search space to improve OSC search efficiency. Experimental results show that the proposed method significantly reduces computational time.
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