SAIL: A Voyage to Symbolic Approximation Solutions for Time-Series Analysis

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Abstract

Symbolic Approximation , a dimensionality reduction technique that transforms time series into discrete symbols, has gained increasing attention in various downstream applications. Despite decades of development, there is a noticeable absence of a comprehensive study in this domain, highlighting a need for more in-depth investigation and well-designed exploration tools. To address this gap, we propose SAIL , a modular web engine serving two purposes: (i) to provide the first comprehensive study on 7 state-of-the-art methods over 100+ time-series datasets, the largest study in this area; (ii) to evaluate the performance of a recently proposed solution, SPARTAN, that solves two core problems. First, SPARTAN exploits intrinsic dimensionality reduction to effectively model the underlying data distribution for approximation. Second, SPARTAN dynamically allocates alphabet sizes per segment, recognizing the non-uniform distribution of information in practice. Through its interactive interface, SAIL enables users to visualize and explore quantitative assessments across various methods, datasets, and analytical tasks. SAIL’s exploration reveals that (i) while SAX variants outperform SAX by sacrificing storage, none surpass SAX under the same budget, reinforcing it as a strong baseline; SFA is the only existing method that consistently outperforms SAX within the same budget; and (ii) across diverse scenarios, SPARTAN outperforms competing methods in all evaluated tasks significantly, including classification, clustering, indexing, and anomaly detection, without incurring additional storage or runtime overhead. Overall, SAIL not only facilitates the most comprehensive studies in this field but also provides new insights and concrete solutions for future research. We release the SAIL web engine at https://saildemo.streamlit.app/.