Convolutional Sparse Coding for Time Series Via a ℓ0 Penalty: An Efficient Algorithm With Statistical Guarantees

ABSTRACT Identifying characteristic patterns in time series, such as heartbeats or brain responses to a stimulus, is critical to understanding the physical or physiological phenomena monitored with sensors. Convolutional sparse coding (CSC) methods, which aim to approximate signals by a sparse combi...

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Bibliographic Details
Published in:Statistical analysis and data mining Vol. 17; no. 6
Main Authors: Truong, Charles, Moreau, Thomas
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.12.2024
Wiley Subscription Services, Inc
Wiley
Subjects:
Algorithms
Atomic properties
Coding
compressive statistical learning
Computer Science
convolutional sparse coding
Error analysis
Error correction
Error detection
L0 penalty
Mathematics
Noise measurement
Optimization
Physiology
signal processing
Statistics
Time series
convolutional sparse coding
statistical learning
L0 penalty
compressive statistical learning
signal processing
ISSN:1932-1864, 1932-1872
Online Access:Get full text
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Summary:ABSTRACT Identifying characteristic patterns in time series, such as heartbeats or brain responses to a stimulus, is critical to understanding the physical or physiological phenomena monitored with sensors. Convolutional sparse coding (CSC) methods, which aim to approximate signals by a sparse combination of short signal templates (also called atoms), are well‐suited for this task. However, enforcing sparsity leads to non‐convex and untractable optimization problems. This article proposes finding the optimal solution to the original and non‐convex CSC problem when the atoms do not overlap. Specifically, we show that the reconstruction error satisfies a simple recursive relationship in this setting, which leads to an efficient detection algorithm. We prove that our method correctly estimates the number of patterns and their localization, up to a detection margin that depends on a certain measure of the signal‐to‐noise ratio. In a thorough empirical study, with simulated and real‐world physiological data sets, our method is shown to be more accurate than existing algorithms at detecting the patterns' onsets.
Bibliography:This work was supported by PhLAMES chair (ENS Paris‐Saclay).
Funding
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ISSN:1932-1864
1932-1872
DOI:10.1002/sam.70000