Optimal Scale Combination Selection Based on Relatively Relevant Attribute Subsets

Knowledge acquisition of multi-scale hybrid data is an important research direction in data modeling under a multi-granularity environment, and the selection of an optimal scale is a key step in the knowledge acquisition of multi-scale data. However, in the calculation of an optimal scale, most of multi-scale granular computing analysis models are only based on all attributes without considering the influence of the order of the selected attributes on the performance of the obtained optimal scale, which affects the robustness and effectiveness of the models. Based on this observation, a new method to search an optimal scale combination based on relatively relevant attribute subsets is proposed to deal with the optimal scale selection in multi-scale hybrid data. Based on conditional entropies, quantitative measures of relatively relevance of conditional attributes with respect to the decision are first introduced in a generalized multi-scale hybrid decision system (GMHDS). The concept of positive region optimal scale combinations based on relatively relevant subsets of attributes is then defined to ensure that the optimal scale combinations are selected in highly relevant subsets of attributes. Furthermore, a new stepwise search algorithm for positive region optimal scale combinations with a directed order is designed in a GMHDS, which is used to select the scales corresponding to conditional attributes with high relevance to the decision during the search process. Finally, the experimental results demonstrate that, in most cases, the results of this model have better classification performances than those of other comparative models.