Warp Quantification Analysis: A Framework For Path-based Signal Alignment Metrics

2025-09-18

AI Summary

Dynamic Time Warping (DTW) is commonly reduced to a scalar distance, discarding rich geometric and structural information embedded in the alignment path. Method: We propose Warp Quantification Analysis (WQA), the first multidimensional, structured metric framework grounded in DTW paths, which extracts interpretable geometric descriptors—such as path curvature, compression ratio, and local lag—that orthogonally capture distinct nonlinear temporal alignment characteristics. Contribution/Results: Through controlled simulations, we validate descriptor specificity; applied to large-scale fMRI data, WQA identifies schizophrenia-negative-symptom-specific alterations in brain network coupling—significantly correlated with clinical severity—undetectable by conventional DTW distance. WQA preserves computational compatibility with standard DTW implementations while substantially enhancing sensitivity, interpretability, and clinical traceability of time-series alignment analysis.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content

Abstract

Dynamic time warping (DTW) is widely used to align time series evolving on mismatched timescales, yet most applications reduce alignment to a scalar distance. We introduce warp quantification analysis (WQA), a framework that derives interpretable geometric and structural descriptors from DTW paths. Controlled simulations showed that each metric selectively tracked its intended driver with minimal crosstalk. Applied to large-scale fMRI, WQA revealed distinct network signatures and complementary associations with schizophrenia negative symptom severity, capturing clinically meaningful variability beyond DTW distance. WQA transforms DTW from a single-score method into a family of alignment descriptors, offering a principled and generalizable extension for richer characterization of temporal coupling across domains where nonlinear normalization is essential.

Problem

• Develops interpretable geometric descriptors from DTW alignment paths
• Provides metrics for tracking temporal coupling with minimal crosstalk
• Enables clinical characterization beyond scalar distance in fMRI analysis

Innovation

• Framework deriving geometric descriptors from DTW
• Metrics tracking intended drivers with minimal crosstalk
• Transforming DTW into alignment descriptor family