Training-Free Embeddings for Time Series with Applicability Criterion

This research presents D(τ), a novel training-free, fixed-length descriptor designed for multivariate time series analysis. This descriptor is constructed from a time-lagged correlation matrix, with signal-bearing eigenvalues extracted by truncating at the Marchenko-Pastur edge, and then classified using cosine similarity to class centroids without any learned parameters. The central innovation is not just the descriptor itself, but a clear, falsifiable criterion for its applicability. Derived from a stationary Gaussian VAR(1) model, this criterion posits that D(τ) will effectively distinguish between classes when the signals are approximately stationary and the class information resides in their cross-channel temporal coupling, rather than in marginal per-channel power. The criterion is operationalized through a two-part pre-flight test: an augmented Dickey-Fuller stationarity check and a power-baseline saturation check. This test accurately predicted the descriptor's performance across various datasets, showing competitive results on those satisfying the criterion (e.g., Sleep-EDF, BCI-IV-2a) and predictable failures on those violating it (e.g., non-stationary ERPs, power-discriminated financial data). This work provides a compact, efficient embedding method with a transparent domain of validity.