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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Vydané v:	Statistical analysis and data mining Ročník 17; číslo 6
Hlavní autori:	Truong, Charles, Moreau, Thomas
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.12.2024 Wiley Subscription Services, Inc Wiley
Predmet:	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
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Popis
Shrnutí:	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.
Bibliografia:	This work was supported by PhLAMES chair (ENS Paris‐Saclay). Funding ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1932-1864 1932-1872
DOI:	10.1002/sam.70000