区间值时序数据挖掘中聚类与预测的研究

As two kinds of mining tasks, clustering and forecasting of interval-valued time series are studied. For the clustering of a group of unequal-length interval-valued time series, the existing research literatures are very few. By means of ‘breaking up the whole into parts’, knowledge guidance is introduced to supervised clustering, and the project proposes a clustering algorithm with knowledge-based guidance. In addition, the project proposes a new distance measure of interval-valued time series combined with trend filtering and dynamic time warping, and provides a new hierarchical clustering algorithm based on this distance measure. Existing interval-valued time-series forecasting methods are mainly divided into linear and non-linear methods. The linear forecasting methods are used in the case of the stationary series, and the scope of application is limited. Nonlinear forecasting methods rely on the artificial neural network which presents highly nonlinear and adaptive learning ability. However, the artificial neural network has the following disadvantages: poor global search ability, slow convergence, easily to fall into local minimum value and the number of hidden layer neuron network is difficult to determine. To solve these problems, the project intends to construct fuzzy logic relationship group based on the original data, and establish a reasonable forecasting model for interval-valued time series under the quantization of fuzzy inference. Finally, we can obtain a more reasonable and more accurate forecasting result.

围绕区间值时间序列的聚类以及预测两类挖掘任务来研究。针对不等长区间值时间序列族的聚类，已有成果较少。本项目一是采用 “化整为零”的手段，将知识指导的思想引入进行有监督的聚类，并提出一种基于知识指导的聚类方法；二是结合趋势滤波、动态时间规整给出区间值时间序列新的距离度量，并在此基础上提出新的层次聚类算法。此外，针对区间值时间序列的预测问题，现有的方法主要分为线性的和非线性的。线性的预测方法主要应用于原始序列是平稳的情况，应用范围受到一定限制；非线性的预测方法主要依赖具有高度非线性和很强的自适应学习能力的人工神经网络，然而人工神经网络存在全局搜索能力差、收敛速度慢，结果易陷入局部极值以及网络隐含层神经元的个数难确定等缺点。针对这些不足，本项目拟从原始数据出发，构造模糊逻辑关系群，并在模糊推理量化下建立合理的预测模型，最终产生更合理更准确的预测结果。

本项目针对区间值时间序列的聚类以及预测开展研究，主要研究成果包括：(1)对于不等长的区间值时间序列，给出基于重心和半径的距离度量算法，大大提高计算效率和准确性。同时结合层次聚类，提出不等长区间值时间序列族一种新的聚类算法；(2)当遇到大规模区间值时间序列时，需要先对原始序列进行粒化处理，本项目将信息粒看作是不确定集合，提出不确定集的距离度量，为进一步聚类打下基础；(3)考虑区间值时间序列的退化形式——单变量时间序列，结合基于形状的距离度量以及层次聚类算法，提出不等长时间序列族的聚类算法；(4)结合不确定理论，提出新的非线性回归模型；(5)基于模糊逻辑关系建立预测模型，提出基于长关联关系的时间序列预测方法；(6)提出模糊可见性图，基于模糊可见性图给出时间序列的新的距离度量，从而建立新的时间序列的预测模型。本项目的研究进展与成果丰富了区间值时间序列聚类和预测方法，具有重要的学术价值与应用价值。目前已在国内外重要期刊及国际会议发表论文15篇，其中SCI论文11篇。