An Evolving Fuzzy Inference Algorithm With Multi-dimensional Temporal Association Rules
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摘要: 挖掘时态关联规则的目的是为了发现带有时态信息的项集之间有趣的关系.由于数据库经常动态更新，时态关联规则的挖掘也应该适应数据库的更新.然而，现有的大多数算法不仅需要重新挖掘更新的数据库，浪费了大量的时间和效率，而且不能利用已存在的规则定量地预测某些项的变化趋势.本文提出了一个基于多维时态关联规则的演化模糊推理预测建模算法（Evolving fuzzy inference model based on multidimensional temporal association rules，EFI-MTAR），主要优势是构建了一种基于多维时态关联规则的模糊推理建模算法（Fuzzy inference modeling algorithm based on multidimensional temporal association rules，FI-MTAR），实现了对时间序列的定量预测.此外，为了降低规则更新的代价和加快规则预测的速度，提出了概念漂移检测策略来处理时间序列数据以适应数据库的动态更新.实验结果表明了本文提出算法的有效性和准确性.Abstract: The purpose of mining temporal association rules is to find interesting relationships between item sets with temporal information. Due to the dynamic update of the database, the mining of temporal association rules should adapt to the updates. However, most of the existing algorithms not only need to remine the updated database but also are unable to quantitatively predict the tendency of certainitem. In this paper, an evolving fuzzy inference model based on multidimensional temporal association rules (EFI-MTAR) is proposed to predict the time series quantitatively, In addition, in order to reduce the cost and accelerate the efficiency for prediction, a concept drift detection method is put forward to deal with time series data to adapt to the updates dynamically. Experimental results show the effectiveness and accuracy of the proposed algorithm.
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Key words:
- Multi-dimensional temporal association rules /
- fuzzy inference /
- evolving /
- concept drift
1) 本文责任编委 张敏灵 -
图 5 数据集Synthetic Control Chart的拟合曲线
Fig. 5 The fitting curve of the data set Synthetic Control Chart
表 2 离散化项集的序列片段模式
Table 2 The segment patterns of the time series for the discrete item
时间序列变量 离散 斜率 斜率对 幅值变 归一化变化 化项 均值 应角度 化均值 幅值均值 PT08.S2(NMHC) 21 74.25 89.25 144.2 0.48 NOx(GT) 31 -31.6 -87.1 -92.4 -0.16 PT08.S5(O3) 61 80.8 89.3 911.1 0.45 
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表 3 序列片段模式的语义描述
Table 3 The semantic description of the segment patterns
斜率对应角度范围 语义描述 归一化变化幅值范围 语义描述 $[-90, -60]$ 剧烈下降 $[-1, -0.6]$ 大幅下降 $[-60, -30]$ 快速下降 $[-0.6, -0.3]$ 中幅下降 $[-30, 0 ]$ 平稳下降 $[-0.3, 0]$ 小幅下降 $[0, 30]$ 平稳上升 $[0, 0.3]$ 小幅上升 $[30, 60]$ 快速上升 $[0.3, 0.6]$ 中幅上升 $[60, 90]$ 剧烈上升 $[0.6, 1]$ 大幅上升
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表 4 最终预测输出上下界均方根误差
Table 4 The RMSE of upper bound and lower bound for the prediction output
$dx_{c3{j_3}}^L$ $dx_{c3{j_3}}^U$ 0.1656 0.1803
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表 5 不同滑动窗口的演化更新效果
Table 5 The evolution effect of different sliding window size
评价指标 演化次数 滑动窗口大小 本文方法 5 % 10 % 15 % 20 % 7 % Rules 0 16 17 19 19 17 1 20 19 22 24 18 2 20 21 24 26 20 3 21 21 25 29 21 4 24 27 29 33 21 5 25 24 30 34 24 6 25 29 31 33 23 CA 0 0.909 0.899 0.876 0.866 0.911 1 0.879 0.904 0.851 0.851 0.906 2 0.886 0.909 0.846 0.839 0.916 3 0.891 0.896 0.849 0.832 0.919 4 0.876 0.887 0.851 0.842 0.924 5 0.869 0.879 0.854 0.847 0.896 6 0.881 0.896 0.862 0.859 0.909 RMSE 0 0.144 0.152 0.187 0.197 0.137 1 0.179 0.145 0.221 0.224 0.145 2 0.168 0.139 0.234 0.264 0.121 3 0.159 0.157 0.227 0.279 0.112 4 0.187 0.165 0.224 0.241 0.104 5 0.194 0.183 0.209 0.236 0.154 6 0.175 0.156 0.201 0.214 0.146
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表 6 不同数据集的有效性和准确性对比
Table 6 Comparison of the validity and accuracy of different data sets
数据集 演化 方案1 方案2 次数 Rules CA Rules CA Air Quality 0 35 0.902 17 0.911 1 49 0.897 18 0.906 2 54 0.879 20 0.916 3 62 0.887 21 0.919 4 66 0.874 21 0.924 5 71 0.867 24 0.896 6 78 0.874 23 0.909 7 87 0.894 20 0.921 8 94 0.886 23 0.914 9 99 0.879 25 0.900 10 101 0.875 27 0.894 11 109 0.874 24 0.898 12 112 0.895 24 0.927 13 119 0.9004 26 0.932 Istanbul 0 32 0.806 19 0.855 1 36 0.814 17 0.881 2 39 0.743 21 0.805 3 51 0.807 21 0.801 4 57 0.764 21 0.805 5 67 0.794 25 0.801 6 74 0.7778 23 0.889 0 65 0.904 44 0.946 1 78 0.882 49 0.891 2 86 0.856 49 0.888 Synthetic 3 990.862 56 0.875 Control 4 108 0.843 48 0.851 Chart 5 110 0.856 53 0.956 6 114 0.854 59 0.896 7 124 0.889 48 0.926
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表 7 拟合误差
Table 7 Fitting error
数据集 演化次数 方案1 方案2 方案3 0 0.189 0.137 0.168 1 0.195 0.145 0.172 2 0.176 0.121 0.156 3 0.169 0.112 0.144 4 0.162 0.104 0.136 Air 5 0.201 0.154 0.159 Quality 6 0.194 0.146 0.174 7 0.156 0.108 0.144 8 0.186 0.133 0.176 9 0.197 0.148 0.185 10 0.211 0.158 0.195 11 0.197 0.155 0.186 12 0.154 0.099 0.129 13 0.146 0.091 0.132 Istanbul 0 0.144 0.094 0.129 1 0.184 0.139 0.165 2 0.226 0.172 0.208 3 0.198 0.149 0.184 4 0.188 0.139 0.171 5 0.209 0.168 0.196 6 0.148 0.103 0.139 0 0.132 0.072 0.095 1 0.154 0.094 0.124 2 0.169 0.113 0.146 Synthetic 3 0.187 0.132 0.167 Control 4 0.206 0.149 0.182 Chart 5 0.129 0.076 0.109 6 0.138 0.092 0.116 7 0.155 0.087 0.126
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