基于导向随机狼群算法的多元时间序列变量选择研究

How to select variable for multivariate time series is a difficult yet fundamental problem in many fields. However, this scientific problem exists a lot of difficulties, including multiple learning mode, complex optimization model, high dimensional variables and complex relationship between them. In this project, the evaluation criteria of variable subsets are researched and the key breakthrough is the search problem of optimal variable subset, which has the highly nonlinear and NP-Hard characteristics. For the former, according to the matrix form characteristics of multivariate time series and following the main line of supervised/unsupervised learning, multivariate time series similarity matching model and cluster integration model are respectively established based on similarity measurement of multivariate time series. For the latter, firstly, the study on the high dimensional combinatorial optimization is conducted from the view of the relationship between heuristic information guiding and stochastic strategies, and a ‘guided-stochastic’ optimization mechanism which has the universal theoretical guidance significance is tentatively proposed; Secondly, study on the improvement and theoretical analysis about the guided-stochastic wolf pack algorithm, to further improve;the performance of the algorithm and enrich the theoretical basis, and then establish the variable selection model based on wolf pack algorithm. Finally, the performance verification and application research among theory, algorithm and the model is studied based on a large number of benchmarks and actual multivariate time series data. Expected results will provide new ideas and methods for swarm intelligence optimization and multivariate time series data mining, and have good research significance and broad application prospect.

多元时间序列变量选择是多个领域的基础难题。针对该科学问题中存在的学习模式多样、优化模型复杂、变量维度高、关系复杂等问题，研究多元时间序列变量子集的评价准则，并重点突破具有高度非线性和NP-Hard特性的最优变量子集搜索问题。对于前者，针对多元时间序列的矩阵形式特点，以监督/无监督学习为主线，基于多元时间序列相似性度量分别建立多元时间序列相似性匹配模型和聚类集成模型，进行多元时间序列变量子集评价准则的研究；对于后者，从启发式信息导向与随机策略间关系的角度研究高维组合优化，力图提出一种具有普适性理论指导意义的“导向随机”优化机制，并进行导向随机狼群算法的改进和理论分析研究，进而建立基于狼群算法的多元时间序列变量选择模型；最后，结合大量标准算例和实际多元时间序列数据，开展性能验证与应用研究。预期成果将为多元时间序列数据挖掘和群体智能优化提供新思路和新方法，具有非常好的研究意义和广泛的应用前景。

数据时代，多元时间序列类型的数据随处可见，多元时间序列变量选择可在降维的同时保留数据的时序信息和实际物理意义，降低模型过拟合/过学习的风险，节约建模、存储和计算成本，被广泛应用于诸多领域。课题构建了基于导向随机狼群算法的多元时间序列变量选择模型，并重点就其中变量子集的评价问题、最优子集搜索的高维离散空间优化问题等关键科学问题做了如下3个方面的研究工作：.1）多元时间序列变量子集的评价问题。结合实际将该问题分为无监督和有监督两种情况。对于前者，设计了一种无需进行相空间重构的多元时间序列分形维数计算方法，利用属性子集的分形维数及其变量数目的变化作为子集优劣的评价标准；对于后者，在分析欧式距离、主成分分析、基于点分布特征等各相似匹配方法的优劣后设计了基于二维奇异值分解的相似匹配方法，采用变量子集的相似性匹配的准确率期望作为子集优劣的评价标准。而后利用导向随机狼群算法对两种情况下最优变量子集进行寻优搜索。.2）狼群算法改进研究。为提升搜索效率，进行了算法改进。通过量子旋转门控制人工狼概率位置向全局最好位置逼近，然后以量子塌缩实现了概率位置向准确位置的映射，提出量子狼群算法。从“导向随机”思想角度研究反向学习机制，后又引入混沌优化，提出了反向混沌狼群算法。仿真实验结果表明所提算法具有较好的全局寻优能力，特别是在求解高维复杂函数和背包问题时具有优势。.3）导向随机优化机制及应用研究。在狼群算法改进和对比研究中，针对普遍存在的广域开拓与深度开采，计算代价与求解质量的权衡问题，总结探索了一种“导向随机”优化机制，即群智启发信息导向+随机策略，并启发该机制构建了一种自下而上的具有多状态、自适应响应阈值、多个体响应等特点的动态蚁群劳动分工模型用于解决呈现高度非线性、对抗性、多模态等复杂特点的动态任务分配问题，实验表明该模型具有较好的任务分配柔性和较好的结果实时输出性。