基于DTW的长期直觉模糊时间序列预测模型

doi:10.11959/j.issn.1000-436x.2016160

摘要/Abstract

摘要：

针对现有直觉模糊时间序列模型中直觉模糊关系组和确定性转换规则过度依赖训练数据规模的问题，提出一种基于动态时间弯曲（DTW,dynamic time warping）距离的长期直觉模糊时间序列预测模型。通过直觉模糊C均值（IFCM,intuitionistic fuzzy C mean）聚类构建直觉模糊时间序列片段库，动态更新和维护规则库，减少系统复杂度。提出基于DTW距离的直觉模糊时间序列片段相似度计算方法，有效解决不等长时间序列片段匹配问题。通过对合成数据以及包含不同时间序列模式的气温数据的实验，与其他相关模型比较，说明该模型对于不同时间序列趋势变化模式中均具有较高的预测能力，克服传统模型提高模型只能满足单一模式时间序列预测，提高模型的泛化性能。

关键词: DTW, 直觉模糊集合, IFCM聚类, 时间序列, 预测

Abstract:

In existing fuzzy time series forecasting models,the intuitionistic fuzzy relationship groups and deterministic transition rules excessively relied on scale of the training data.A long-term intuitionistic fuzzy time series (IFTS) fore-casting model based on DTW was proposed.The IFTS segment base was constructed by IFCM.The complexity of sys-tem was reduced by dynamic update and maintaining of the rule base.The computing method of IFTS segments similar-ity based on the distance of DTW was proposed,which was valid for matching unequal length time series segments.The proposed model implements on the synthetic and the temperature dataset,which including different time series patterns,respectively.The experiments illustrate that the forecasting accuracy of the proposed model is higher than the others on the different tendency patterns of time series.The proposed model overcomes the limitation of single time series pattern and improves the generalization ability.

Key words: DTW, intuitionistic fuzzy sets, IFCM clustering, time series, forecasting

范晓诗,雷英杰,路艳丽,王亚男. 基于DTW的长期直觉模糊时间序列预测模型[J]. 通信学报, 2016, 37(8): 95-104.

Xiao-shi FAN,Ying-jie LEI,Yan-li LU,Ya-nan WANG. Long-term intuitionistic fuzzy time series forecasting model based on DTW[J]. Journal on Communications, 2016, 37(8): 95-104.

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序号	Base
1	＜0.38,0.61＞,＜0.66,0.33＞,＜0.56,0.43＞,＜0.47,0.52＞,＜0.72,0.27＞
2	＜0.61,0.37＞,＜0.54,0.45＞,＜0.43,0.56＞,＜0.69,0.30＞,＜0.48,0.50＞
3	＜0.51,0.48＞,＜0.40,0.59＞,＜0.68,0.31＞,＜0.55,0.44＞,＜0.47,0.53＞
4	＜0.50,0.48＞,＜0.67,0.32＞,＜0.53,0.45＞,＜0.48,0.51＞,＜0.35,0.64＞
5	＜0.70,0.28＞,＜0.50,0.49＞,＜0.46,0.53＞,＜0.37,0.62＞,＜0.62,0.37＞
6	＜0.41,0.58＞,＜0.70,0.29＞,＜0.44,0.55＞,＜0.39,0.6＞,＜0.78,0.21＞,＜0.62,0.37＞
7	＜0.75,0.24＞,＜0.44,0.55＞,＜0.72,0.27＞,＜0.44,0.55＞,＜0.31,0.68＞,＜0.58,0.40＞
8	＜0.31,0.67＞,＜0.50,0.48＞,＜0.64,0.35＞,＜0.61,0.38＞,＜0.49,0.50＞,＜0.88,0.11＞
9	＜0.17,0.81＞,＜0.66,0.33＞,＜0.75,0.24＞,＜0.44,0.55＞,＜0.72,0.27＞,＜0.61,0.38＞
10	＜0.28,0.71＞,＜0.66,0.33＞,＜0.29,0.70＞,＜0.56,0.43＞,＜0.24,0.75＞,＜0.42,0.58＞
11	＜0.41,0.58＞,＜0.78,0.21＞,＜0.31,0.68＞,＜0.450.55＞,＜0.17,0.82＞,＜0.38,0.60＞,＜0.44,0.55＞,
12	＜0.70,0.29＞,＜0.40,0.60＞,＜0.52,0.47＞,＜0.34,0.65＞,＜0.66,0.63＞,＜0.51,0.48＞,＜0.72,0.28＞
13	＜0.88,0.11＞,＜0.50,0.49＞,＜0.66,0.33＞,＜0.75,0.25＞,＜0.78,0.21＞,＜0.66,0.33＞,＜0.61,0.38＞
14	＜0.61,0.38＞,＜0.82,0.17＞,＜0.29,0.61＞,＜0.66,0.33＞,＜0.62,0.37＞,＜0.66,0.33＞,＜0.44,0.55＞
15	＜0.28,0.71＞,＜0.61,0.38＞,＜0.40,0.59＞,＜0.28,0.71＞,＜0.58,0.41＞,＜0.61,0.38＞,＜0.31.0.68＞

序列	测试数据	预测值 1	预测值 2
1	51.5	—	—
2	31.8	—	—
3	30.6	—	—
4	40.5	41.50	39.25
5	50.6	—	—
6	46.6	43.72	57.05
7	51.4	—	—
8	33.2	29.32	38.34
9	44.7	—	—
10	35.0	31.23	48.54
11	50.3	—	—
12	38.0	47.75	34.12
13	31.5	—	—
14	50.6	52.31	59.78
15	56.1	—	—
16	45.3	43.74	40.12
17	36.2	—	—
18	54.0	52.12	56.32
19	52.0	—	—
20	48.8	42.12	45.23

模型	MSE	AFER
文献[16](w=5,d=2,c=5)	73.443 6	15.57%
文献[13] (w=5,d=2,c=5)	30.64	11.35%
本文(w=5,6,7,d=2,c=5)	26.227 4	9.76%

模型		MSE			AFER
模型	3月	8月	全年	3月	8月	全年
文献[2]模型，i=8	5.462 2	4.499 8	5.284 7	22.75%	7.28%	52.20%
文献[12]模型，i=8	1.938 3	4.633 4	3.060 1	13.08%	7.66%	39.67%
文献[16]模型，w=6,d=1,c=7	6.673 6	4.676 5	6.131 7	24.38%	6.82%	32.92%
文献[18]模型，i=8	3.076 0	2.115 2	3.022 9	16.91%	4.53%	42.76%
本文模型，w=6,d=1,c=5	1.579 8	2.096 9	2.074 4	13.04%	4.64%	30.74%