有噪声的非线性时间序列的分类

数学物理学报 ›› 2025, Vol. 45 ›› Issue (5): 1632-1651.

有噪声的非线性时间序列的分类

张梦瑶(),杨双全^*()

冶金工业过程系统科学湖北省重点实验室武汉 430065; 武汉科技大学理学院武汉 430065

收稿日期:2025-01-18 修回日期:2025-05-24 出版日期:2025-10-26 发布日期:2025-10-14
通讯作者: * 杨双全,E-mail:yangsq@wust.edu.cn
作者简介:张梦瑶, E-mail:myzhang@wust.edu.cn
基金资助:
国家重点研发计划项目(2020YFA0714200)

Classification of Noisy Nonlinear Time Series

Mengyao Zhang(),Shuangquan Yang^*()

Hubei Key Laboratory of Metallurgical Process System Science, Wuhan 430065; School of Science, Wuhan University of Science and Technology, Wuhan 430065

Received:2025-01-18 Revised:2025-05-24 Online:2025-10-26 Published:2025-10-14
Supported by:
National Key Research and Development Program of China(2020YFA0714200)

摘要/Abstract

摘要：

时间序列分类问题广泛应用于各个领域, 现有分类指标对复杂度较高且有噪声的非线性时间序列的分类仍存在不足. 该文引入一种复杂度不变距离结合基于复杂度不变距离的多维尺度 (CID-CIDMDS) 的方法. 该方法具有较强的准确性和稳健性, 且不依赖时间序列的长度. 通过分段线性 Lorenz 映射、Logistic 映射、帐篷映射和二次映射模型生成的时间序列验证该方法的有效性和序列长度的影响, 并以网络的形式直观展示其分类效果. 通过添加白噪声、高斯噪声、脉冲噪声系统验证其具有较强的稳健性, 并将其应用于股票市场的分类.

关键词: 时间序列, 分类, CID, CIDMDS, 网络

Abstract:

The classification of time series problems is widely applied across various fields. Existing classification metrics still face challenges when dealing with complex, noisy, and nonlinear time series. This paper introduces a method that combines complexity-invariant distance with complexity-invariant distance-based multidimensional scaling (CID-CIDMDS). This method demonstrates strong accuracy and robustness, and it does not depend on the length of the time series. The effectiveness of the method and the impact of sequence length are validated using time series generated from piecewise linear Lorenz maps, logistic maps, tent maps, and quadratic mapping models. The classification results are visually presented in a network format. The method's robustness is further confirmed through tests involving the addition of white noise, Gaussian noise, and impulse noise systems. Additionally, it is applied to the classification of stock market data.

Key words: time series, classification, CID, CIDMDS, network

中图分类号:

TN911.7

张梦瑶, 杨双全. 有噪声的非线性时间序列的分类[J]. 数学物理学报, 2025, 45(5): 1632-1651.

Mengyao Zhang, Shuangquan Yang. Classification of Noisy Nonlinear Time Series[J]. Acta mathematica scientia,Series A, 2025, 45(5): 1632-1651.

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