Automatic Time-Series Labeling via Grammatical Inference With Error-Bounded Variable-Length Motifs

Data labeling is a crucial step in machine learning, providing semantic annotations that give raw data context, meaning, and structure. In time series, point-level automatic labeling is particularly challenging because it must transform continuous, high-dimensional signals into discrete and interpretable representations. Most existing approaches, mainly based on discretization and motif discovery, often rely on sensitive design choices (e.g., window length, alphabet size, or exact pattern matching), which can limit robustness on noisy or heterogeneous datasets. This article proposes GI4EVM (grammatical inference (GI) with error-bounded variable-length motif discovery), a two-stage framework for automatic time-series labeling. Phase 1 performs an adaptive, error-bounded discretization controlled by a single user-facing relative error budget $\epsilon $ , producing a compact symbolic sequence while preserving local variability. Phase 2 applies noise-tolerant GI to discover recurring variable-length patterns and to group structurally similar motifs using a tolerance $\tau $ derived deterministically from $\epsilon $ . Experiments on 50datasets show that GI4EVM yields favorable fidelity/compression tradeoffs and competitive performance compared to state-of-the-art discretization and grammar-based baselines, while producing structured and interpretable symbolic representations.