The granulation attribute reduction of multi-label data

In multi-label learning, the classification obtained by attribute set is usually inconsistent with that based on label set. This makes multi-label learning to possess fuzziness and uncertainty, which leads to the poor performance of learning algorithms. To address this fuzziness and uncertainty, this paper first combines multiple labels into a granulation multi-label decision function by using the classification obtained by attribute set. Then we give three kinds of formulations to construct the granulation multi-label decision functions, which are divided three levels, that is, macroscopic level, mesoscopic level and microscopic level. Moreover, by using the granulation multi-label decision function, this paper provides the method that transforms a multi-label decision table into a granulation multi-label decision table. Then three-level granulation attribute reductions of a multi-label decision table are defined and investigated. Furthermore, this paper shows that the existing multi-label attribute reduction, complementary decision reduction, can be viewed as the coarsest granularity reduction proposed by this paper, that is, a macroscopic-level granulation attribute reduction. In summary, this paper establishes a relatively systematic theoretical framework for attribute reduction of multi-label data based on rough set theory. Finally, by several comparative analysis, the reasonability, feasibility and effectiveness of these granulation attribute reductions are demonstrated.