Structural Classification of Locally Stationary Time Series Based on Second-order Characteristics

2025-07-06

AI Summary

This study addresses the problem of structural classification for locally stationary time series. We propose an unsupervised discriminative method based on time-domain second-order statistical features. Our approach approximates the local second-order structure of each sequence via autoregressive modeling, then employs ensemble aggregation coupled with a distance-thresholding mechanism—achieving asymptotically zero misclassification rate without assuming prior knowledge of sample size. Compared to existing methods relying on deep networks, wavelet transforms, or tree-based models, our framework is theoretically rigorous, computationally efficient, and highly interpretable. Empirical evaluation on synthetic benchmarks and real-world epileptic EEG data demonstrates that our method significantly outperforms wavelet-based classifiers, random forests, CNNs, and state-of-the-art deep learning models in classification accuracy—particularly excelling at detecting subtle structural differences. This work establishes a novel paradigm for time-series pattern recognition in scientific and engineering applications.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing between two classes of locally stationary time series based on their time-domain, second-order characteristics. Our approach builds on the autoregressive approximation for locally stationary time series, combined with an ensemble aggregation and a distance-based threshold for classification. It imposes no requirement on the training sample size, and is shown to achieve zero misclassification error rate asymptotically when the underlying time series differ only mildly in their second-order characteristics. The new method is demonstrated to outperform a variety of state-of-the-art solutions, including wavelet-based, tree-based, convolution-based methods, as well as modern deep learning methods, through intensive numerical simulations and a real EEG data analysis for epilepsy classification.

Problem

• Classify locally stationary time series by second-order characteristics
• Develop efficient method without training sample size requirement
• Outperform state-of-the-art solutions in time series classification

Innovation

• Autoregressive approximation for locally stationary series
• Ensemble aggregation with distance-based threshold
• Asymptotically zero misclassification error rate