粒计算的不确定性度量及其特征选择算法研究

Granular computing is a vivid research direction in the domain of intelligent information processing. Many theories and methods about uncertainty measures and knowledge acquisition in granular computing have been studied. However, there still exist some problems related to the absence of fusion of the different measure methods, high computational complexity in big data, and low processing ability in hybrid data, etc. In this project, we focus on proposing novel theories and methods of uncertainty measures in approximation spaces with different knowledge granularity levels, analyzing reasonableness and monotonicity of these new measures, and constructing fusion methods with other correlated measures. Next, heuristic algorithms of attributes reduction based on information theory in multi-granular space and incremental algorithms of attributes reduction based on algebraic methods are investigated by using radix sort and Hash table, which aim to improve the efficiency of the computation. Then, relative neighborhood relation and general neighborhood relation are further studied. Extended neighborhood rough set models are constructed according to these neighborhood relations, and their feature selection algorithms are proposed. Feature selection algorithms for hybrid data are studied by integrating strategies of Filter algorithms and Wrapper algorithms. Finally, gene expression data sets are employed to verify the effectiveness of algorithms proposed in this project for hybrid data. The results in this project will give important support for the processing of uncertain problems and knowledge acquisition of big complex data both in theory and technology.

粒计算是当前智能信息处理领域非常活跃的研究方向。粒计算中的不确定性度量与知识获取的研究已取得许多成果，但仍存在度量方法融合研究较少、大规模数据计算复杂度较高、混合数据处理能力较弱等问题。本项目拟在不同知识粒度的近似空间下，提出新的不确定性度量理论及方法，分析论证这些度量的合理性和单调性，构建其与现有相关度量方法的融合形式。在此基础上，应用基数排序、Hash表等技术，建立多粒度空间的启发式信息论约简算法，构建粒空间的增量式代数约简算法，以提高计算效率。针对混合型数据，研究相对邻域关系和广义邻域关系，构建相应的邻域粗糙集扩展模型，提出其特征选择算法；融合Filter和Wrapper策略，构建混合型的特征选择算法。最后，利用基因表达数据进行仿真实验，测试和验证上述算法对混合数据处理的有效性。该研究成果可为不确定性问题的处理和大规模复杂数据的知识获取提供重要的理论基础和技术支撑。

针对复杂数据的处理，粒计算是当前人工智能研究领域中模拟人类思维和解决复杂问题的新理论与新方法，是研究大规模复杂问题求解、大数据分析与挖掘、不确定性智能信息处理的有力工具。按照项目计划书的要求，项目组围绕粒计算的不确定性度量及其特征选择算法进行了系统而深入的研究工作，提出了不完备条件熵、条件信息粒度等不确定性度量方法，构建了粗糙粒空间下的增量式约简和分布约简算法，给出了相对邻域关系和广义邻域关系，建立了相应的邻域粗糙集扩展模型，进而设计了一些混合型特征选择算法，并将其应用于基因表达谱数据集分析，在理论和应用方面取得了有价值的研究成果。该课题对传统的粒计算方法进行了扩展和丰富，提升了其处理大规模复杂数据的能力，并且对粒计算在模式识别、不确定性人工智能以及数据挖掘与知识发现等相关领域的应用做了积极的研究探索，对于智能信息处理的研究具有重要的理论和应用价值。