基于全局-局部散度的多元时间序列无监督降维方法

doi:10.11959/j.issn.1000-436x.2024008

通信学报 ›› 2024, Vol. 45 ›› Issue (1): 63-76.doi: 10.11959/j.issn.1000-436x.2024008

• 学术论文 • 上一篇

基于全局-局部散度的多元时间序列无监督降维方法

李正欣¹^,², 胡钢¹, 张凤鸣¹, 张晓丰¹, 赵永梅¹

¹ 空军工程大学装备管理与无人机工程学院，陕西西安 710051
² 西北工业大学光电与智能研究院，陕西西安 710072

修回日期:2023-07-04 出版日期:2024-01-01 发布日期:2024-01-01
作者简介:李正欣（1982- ），男，河南信阳人，博士，空军工程大学副教授、硕士生导师，主要研究方向为时间序列模式识别、数据挖掘与机器学习等
胡钢（1998- ），男，江西九江人，空军工程大学博士生，主要研究方向为时间序列降维、数据挖掘与机器学习等
张凤鸣（1963- ），男，重庆人，空军工程大学教授、博士生导师，主要研究方向为信息系统工程与智能决策
张晓丰（1978- ），男，天津人，博士，空军工程大学副教授、硕士生导师，主要研究方向为信息系统工程与智能决策
赵永梅（1982- ），女，陕西延安人，博士，空军工程大学副教授，主要研究方向为数据融合与补全、信息物理系统等
基金资助:
国家自然科学基金资助项目(62002381)

Unsupervised dimensionality reduction method for multivariate time series based on global and local scatter

Zhengxin LI¹^,², Gang HU¹, Fengming ZHANG¹, Xiaofeng ZHANG¹, Yongmei ZHAO¹

¹ Equipment Management and Unmanned Aerial Vehicle Engineering School, Air Force Engineering University, Xi’an 710051, China
² School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an 710072, China

Revised:2023-07-04 Online:2024-01-01 Published:2024-01-01
Supported by:
The National Natural Science Foundation of China(62002381)

摘要/Abstract

摘要：

针对传统降维方法不能直接应用于多元时间序列，现有的多元时间序列降维方法难以在保证降维有效性的同时大幅降低数据维度的问题，提出一种基于全局-局部散度的多元时间序列无监督降维方法。首先，提出一种特征序列提取方法，提取多元时间序列协方差矩阵的上三角元素，将其组合为特征序列。然后，以“局部散度最小、全局散度最大”为基本思想，提出一种无监督降维模型，在保持局部近邻关系的同时，尽可能保留全局信息。将特征序列作为输入，最小化所有样本点邻域方差之和，最大化邻域中心点方差。求解模型得到的投影矩阵能够实现多元时间序列的降维。最后，在 20 组公开数据集上，对所提方法进行了实验验证。结果表明，所提方法能够在保证降维有效性的同时，较大幅度地降低多元时间序列的维度。

关键词: 多元时间序列, 图结构, 特征提取, 无监督降维, 分类精度

Abstract:

To solve the problem that the traditional dimensionality reduction methods cannot be directly applied to multivariate time series, and for the existing approaches, it is difficult to ensure the effectiveness of dimensionality reduction while significantly reducing the dimension, an unsupervised dimensionality reduction method of multivariate time series based on global and local scatter was proposed.Firstly, a feature series extraction method was proposed to extract the upper triangular elements of the co-variance matrix of each multivariate time series and combine them into a feature sequence.Then, based on the idea of “minimum local scatter and maximum global scatter,” an unsupervised dimensionality reduction model was presented, which preserved the global information as much as possible while maintaining the local nearest neighbor relationship.Using the feature sequence as the input, the sum of the neighborhood variances of all sample points was minimized, and the variance of all the neighborhood centroids were maximized.The projection matrix obtained by solving the proposed model could be used to perform the dimensionality reduction.Finally, the proposed method was evaluated with experiments on 20 public data sets.The results show that the proposed method can significantly reduce the dimension of multivariate time series, while ensuring the effectiveness of dimensionality reduction.

Key words: multivariate time series, graph structure, feature extraction, unsupervised dimensionality reduction, classification accuracy

中图分类号:

TP311

李正欣, 胡钢, 张凤鸣, 张晓丰, 赵永梅. 基于全局-局部散度的多元时间序列无监督降维方法[J]. 通信学报, 2024, 45(1): 63-76.

Zhengxin LI, Gang HU, Fengming ZHANG, Xiaofeng ZHANG, Yongmei ZHAO. Unsupervised dimensionality reduction method for multivariate time series based on global and local scatter[J]. Journal on Communications, 2024, 45(1): 63-76.

图/表 10

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数据集编号	GLSUP	PCA	CPCA	PPCA	SVD_LPP	PBLDA	VPCA
1	0.81	0.76	0.83	0.85	0.64	0.60	0.90
2	0.64	0.66	0.66	0.60	0.55	0.51	0.66
3	0.70	0.68	0.68	0.62	0.53	0.53	0.68
4	0.91	0.89	0.85	0.84	0.86	0.78	0.91
5	0.62	0.63	0.65	0.60	0.58	0.51	0.63
6	0.99	0.48	0.99	0.50	0.99	0.82	0.78
7	0.54	0.46	0.50	0.56	0.53	0.52	0.50
8	0.30	0.30	0.29	0.30	0.32	0.29	0.28
9	0.78	0.73	0.78	0.73	0.57	0.21	0.83
10	0.98	0.67	0.78	0.67	0.87	1.00	0.96
11	0.79	0.55	0.76	0.56	0.57	0.60	0.81
12	0.88	0.44	0.59	0.47	0.78	0.42	0.59
13	1.00	0.69	0.70	0.69	0.64	0.51	0.73
14	0.44	0.35	0.41	0.34	0.45	0.33	0.36
15	0.91	0.58	0.95	0.55	0.60	0.11	0.96
16	0.79	0.75	0.79	0.50	0.75	0.50	—
17	0.98	0.98	0.98	0.97	0.98	0.93	—
18	0.96	0.89	0.98	0.73	0.75	0.93	—
19	0.85	0.69	0.80	0.62	0.62	0.65	—
20	0.93	0.31	0.49	0.57	0.73	0.50	—

数据集编号	GLSUP	PCA	CPCA	PPCA	SVD_LPP	PBLDA	VPCA
1	0.96	0.50	0.83	0.50	0.97	0.83	0.80
2	0.90	0.50	0.67	0.50	0.94	0.67	0.93
3	0.93	0.50	0.67	0.50	0.94	0.17	0.93
4	0.91	0.50	0.83	0.50	0.94	0.83	0.80
5	0.94	0.50	0.83	0.50	0.94	0.67	0.80
6	0.96	0.51	0.84	0.51	1.00	0.89	0.99
7	0.75	0.71	0.71	0.61	1.00	0.14	0.98
8	0.99	0.70	0.80	0.70	1.00	0.20	0.94
9	0.95	0.92	0.92	0.88	0.99	0.92	0.96
10	1.00	0.33	0.67	0.33	1.00	0.83	1.00
11	0.93	0.33	0.33	0.33	0.97	0.00	0.77
12	1.00	0.00	0.33	0.00	1.00	0.67	0.87
13	1.00	0.33	0.50	0.33	0.99	0.00	0.86
14	0.91	0.33	0.67	0.33	0.97	0.33	0.97
15	0.98	0.56	0.44	0.56	0.99	0.11	0.99
16	0.99	0.64	0.86	0.64	1.00	0.64	—
17	0.98	0.67	0.67	0.67	0.99	0.00	—
18	1.00	0.92	0.92	0.94	1.00	0.90	—
19	1.00	0.94	0.94	0.95	1.00	0.87	—
20	0.88	0.86	0.86	0.86	0.98	0.00	—
注：降维幅度1.00为保留两位小数的四舍五入结果

数据集		GLSUP			PCA			CPCA			PPCA
数据集	降维时间代价/s	分类时间代价/s	总时间代价/s	降维时间代价/s	分类时间代价/s	总时间代价/s	降维时间代价/s	分类时间代价/s	总时间代价/s	降维时间代价/s	分类时间代价/s	总时间代价/s
DSA	17.47	2.68	20.15	1.35	386.24	387.59	0.16	82.85	83.01	417.77	414.56	832.32
LSST	0.25	7.55	7.80	0.09	108.52	108.61	0.03	54.41	54.43	0.15	130.87	131.03
HMD	0.04	0.03	0.07	0.02	1.93	1.95	0.01	1.51	1.52	0.02	1.42	1.44
Cricket	0.04	0.01	0.05	0.02	1.92	1.93	0.01	1.91	1.92	0.02	1.62	1.64
FM	0.77	0.21	0.98	0.05	1.83	1.87	0.01	1.81	1.82	0.06	2.73	2.79
NATOPS	0.24	0.05	0.29	0.03	0.33	0.36	0.00	0.33	0.34	0.04	0.58	0.62

数据集		SVD_LPP			PBLDA			VPCA
数据集	降维时间代价/s	分类时间代价/s	总时间代价/s	降维时间代价/s	分类时间代价/s	总时间代价/s	降维时间代价/s	分类时间代价/s	总时间代价/s
DSA	1.84	2.60	4.44	26.41	48.08	74.49	4.31	1.96	6.27
LSST	0.26	10.90	11.16	5.72	98.83	104.55	0.67	7.19	7.86
HMD	0.37	0.03	0.39	4.50	2.39	6.89	0.15	0.64	0.79
Cricket	1.23	0.02	1.25	5.75	0.09	5.84	0.73	0.10	0.82
FM	0.07	0.08	0.15	0.46	6.10	6.55	0.08	0.06	0.14
NATOPS	0.05	0.07	0.11	0.11	0.33	0.45	0.06	0.24	0.30

基于全局-局部散度的多元时间序列无监督降维方法

Unsupervised dimensionality reduction method for multivariate time series based on global and local scatter

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摘要/Abstract

引用本文

使用本文

图/表 10

参考文献 36

相关文章 15

Metrics

推荐阅读 0

编号	数据集	类别	特征维度	序列长度	序列均长	样本数
1	LP1	4	6	15	15	88
2	LP2	5	6	15	15	47
3	LP3	4	6	15	15	47
4	LP4	5	6	15	15	47
5	LP5	4	6	15	15	47
6	DSA	19	45	125	125	2 400
7	FM	2	28	50	50	416
8	HMD	4	10	400	400	234
9	NATOPS	6	24	51	51	360
10	Cricket	12	6	1197	1197	180
11	RS	4	6	30	30	303
12	Epilepsy	4	3	206	206	275
13	BM	4	6	100	100	80
14	LSST	14	6	36	36	4 925
15	AWR	25	9	144	144	575
16	EEGeye	2	14	20～2 401	624	24
17	Wafer	2	6	104～198	137	1 194
18	WR	2	62	128～1 918	368	44
19	KP	2	62	274～841	427	26
20	ASL	95	22	45～136	57	2 565

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