集值系统基于特定类的广义决策最短约简

The Minimal Attribute Reduction Algorithm of General Decision Based on Class-Specific in Set-Value Decision Systems

摘要: 近年来，信息技术不断完善并飞速发展，数据呈现出指数型增长趋势，这使得数据挖掘技术效率降低且性能变差。属性约简能去除信息系统中的冗余属性保留重要属性，是一种有效的数据降维方法，而最短约简能最大限度地删除不相关的属性，从而提高系统数据处理和分析的效率。现有在集值系统下的属性约简方法需要所有决策类的参与，算法的效率较低，而一些实际应用中，针对所有决策类的约简可能是非必要的。针对上述问题，本文以集值决策系统为数据背景，给出了特定类广义决策约简的定义，构造了特定类广义决策约简的差别矩阵及差别函数，引入最短约简算法，提出了特定类广义决策最短约简算法，最后使用8组UCI数据集从约简结果、差别矩阵非空项占比以及约简效率三个方法验证了算法的有效性。

Abstract: In recent years, information technology has been improved and developed rapidly, and data has shown an exponential growth trend, which makes data mining techniques less efficient and less performant. Attribute reduction, which can remove redundant attributes and retain important attributes in information systems, is an effective method for data dimensionality reductionand the shortest reduction can delete irrelevant attributes, thereby improving the efficiency of data processing and analysis of the systems. The existing attribute reduction methods under set-valued systems require the participation of all decision classes, and the efficiency of the algorithm is low, while the reduction for all decision classes may be non-essential in some practi-cal applications. To address the above problems, this paper takes the set-valued decision system as the data background, proposes the definition of class-specific generalized decision simplifica-tion, constructs the discernibility matrix and discernibility function for class-specific generalized decision simplification, introduces the shortest simplification algorithm, proposes the shortest reduction algorithm for class-specific generalized decision, and finally verifies the algorithm using eight sets of UCI data sets from the length of reduction results, the percentage of non-empty terms in the discernibility matrix and the reduction efficiency.