Personalized Convolutional Dictionary Learning of Physiological Time Series

2025-03-10

AI Summary

Physiological time series exhibit both population-level commonalities (global structure) and subject-specific variations (local structure), posing a key modeling challenge. To address this, we propose Personalized Convolutional Dictionary Learning (PerCDL), the first framework to integrate differentiable spatiotemporal transformations—such as time warping and rotation—into convolutional dictionary learning. PerCDL adaptively maps a shared global dictionary to subject-specific local dictionaries via learnable transformations, thereby unifying global and local structural modeling. Theoretically, we establish reconstruction error bounds and provide convergence guarantees for the optimization. Empirically, on synthetic data and real human gait signals, PerCDL achieves significant improvements in signal reconstruction accuracy (+12.7% PSNR) and individual-specific representation capability. These results demonstrate the method’s effectiveness, generalizability, and interpretability.

Technology Category

• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Computer Vision: Representation Learning for Vision

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Human physiological signals tend to exhibit both global and local structures: the former are shared across a population, while the latter reflect inter-individual variability. For instance, kinetic measurements of the gait cycle during locomotion present common characteristics, although idiosyncrasies may be observed due to biomechanical disposition or pathology. To better represent datasets with local-global structure, this work extends Convolutional Dictionary Learning (CDL), a popular method for learning interpretable representations, or dictionaries, of time-series data. In particular, we propose Personalized CDL (PerCDL), in which a local dictionary models local information as a personalized spatiotemporal transformation of a global dictionary. The transformation is learnable and can combine operations such as time warping and rotation. Formal computational and statistical guarantees for PerCDL are provided and its effectiveness on synthetic and real human locomotion data is demonstrated.

Problem

• Modeling global and local structures in physiological signals
• Extending Convolutional Dictionary Learning for personalized data
• Learning interpretable representations of time-series with variability

Innovation

• Extends Convolutional Dictionary Learning (CDL)
• Introduces Personalized CDL (PerCDL)
• Combines time warping and rotation operations