Adaptive Law-Based Transformation (ALT): A Lightweight Feature Representation for Time Series Classification

TL;DR

ALT extends the linear law-based transformation (LLT) for time series classification by introducing variable-length shifted windows, enabling multi-scale pattern capture while preserving interpretability and low computational cost. The method maps features into a linearly separable space through a sequence of steps that involve time-delay embedding, spectral analysis, and shapelet-based transformations governed by triplets $(r,l,k)$, producing class-specific features for fast classifiers. Extensive evaluation on eleven UCR datasets shows ALT achieving high accuracy, often surpassing neural baselines, with simpler hyperparameter tuning and transparent transformations. The approach offers a practical, scalable alternative for time series tasks in domains demanding efficiency and interpretability, with future work targeting automatic tuning of $(r,l,k)$, shapelet pruning, and domain-specific visualizations.

Abstract

Time series classification (TSC) is fundamental in numerous domains, including finance, healthcare, and environmental monitoring. However, traditional TSC methods often struggle with the inherent complexity and variability of time series data. Building on our previous work with the linear law-based transformation (LLT) - which improved classification accuracy by transforming the feature space based on key data patterns - we introduce adaptive law-based transformation (ALT). ALT enhances LLT by incorporating variable-length shifted time windows, enabling it to capture distinguishing patterns of various lengths and thereby handle complex time series more effectively. By mapping features into a linearly separable space, ALT provides a fast, robust, and transparent solution that achieves state-of-the-art performance with only a few hyperparameters.

Figures (1)

• Figure 1: Applied ML framework