Adaptive law-based feature representation for time series classification.

Area of Science:

• Machine Learning
• Data Science
• Signal Processing

Background:

• Time series classification (TSC) is crucial for finance, healthcare, and environmental monitoring.
• Real-world time series data often exhibit noise, local misalignment, and multiscale patterns, challenging traditional TSC methods.

Purpose of the Study:

• Introduce Adaptive Law-based Transformation (ALT), a novel multiscale approach for robust TSC.
• To develop a method that generates compact, transparent features enhancing linear separability for TSC.

Main Methods:

• ALT generalizes Linear Law-based Transformation (LLT) by scanning series with variable-length, shifted windows.
• Constructs symmetric delay embeddings and extracts eigenvectors ('shapelet laws') capturing stable local patterns.
• Assembles class-specific dictionaries and projects new series for feature extraction compatible with standard classifiers.

Main Results:

• ALT improved test accuracy by 15-20 pp over raw inputs and 5-10 pp over LLT on noisy synthetic data.
• Across ten UCR datasets, ALT boosted median test accuracy by +7.6 pp (KNN) and +4.8 pp (SVM), with significant gains on industrial series.
• ALT reduced SVM training time on FordA/B datasets while maintaining or improving accuracy.

Conclusions:

• ALT provides a lightweight, transparent, and effective TSC alternative to complex pipelines.
• The method generates stable, discriminative features suitable for challenging real-world data.
• ALT demonstrates competitive or superior accuracy, especially under noisy and complex conditions.