On the Computational Intractability of Exact and Approximate Dictionary Learning

Tillmann, Andreas M.

doi:10.1109/lsp.2014.2345761

Cited by 77 publications

(44 citation statements)

References 39 publications

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“…The minimization program presented in Eq. 2 is NPhard [21], but there are common methods to approximate it and come up with workable solutions. In our work we employ convex relaxation by replacing the 0 -"norm" with its closest convex norm, the 1 -norm.…”

Section: Sparse Codingmentioning

confidence: 99%

AF Classification from ECG Recording Using Feature Ensemble and Sparse Coding

Whitaker¹,

Rizwan²,

Aydemir³

et al. 2017

Computing in Cardiology Conference (CinC)

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Introduction: The aim of the Physionet/CinC Challenge 2017 is to automatically classify atrial fibrillation (AF) from a short single lead ECG recording. The Challenge provides 8,528 labeled ECG recordings; each recording was labeled as normal, AF, other, or noisy. In addition, the Challenge provides sample code which includes an R-peak detector and a simple classifier.Algorithm: We use an ensemble of features extracted from the ECG signals to create a four-class support vector machine (SVM) classifier. Included in the feature set are statistics obtained from the ECG signal, its spectrum, and the RR-intervals. In addition, we learn a 32-element sparse coding dictionary on the sorted RR-intervals of the ECG signals. Using the dictionary, we calculate a sparse coefficient vector for each training sample and put these through a soft-margin linear SVM. The soft-margin scores are used as additional features in the final classifier.Results: Our algorithm achieves cross-validated F1 scores of 0.874, 0.756, and 0.689 (for normal, AF, and other files, respectively), resulting in a final crossvalidated challenge score of 0.773. The score when tested on a subset of the unknown data is 0.78 (with F1 scores of 0.88, 0.80, 0.65). The official challenge score was 0.77.Conclusions: We developed an algorithm to classify ECG recordings as normal, AF, other, or noisy. Our results show that sparse coding is an effective way to define discriminating features from a list of sorted RR-intervals. In addition, these sparse codes complement more commonly used features in the classification task. Further work will attempt to increase the accuracy of the algorithm by exploring other features and classifiers while still using sparse coding as an unsupervised feature extractor.

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Section: Sparse Codingmentioning

confidence: 99%

AF Classification from ECG Recording Using Feature Ensemble and Sparse Coding

Whitaker¹,

Rizwan²,

Aydemir³

et al. 2017

Computing in Cardiology Conference (CinC)

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“…Given a training dataset with N samples Y ∈ R n×N , the dictionary learning problem can be stated as the NP-hard [5], non-convex optimization problem…”

Section: Introductionmentioning

confidence: 99%

Learning fast sparsifying overcomplete dictionaries

Rusu

Thompson

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-In this paper we propose a dictionary learning method that builds an overcomplete dictionary that is computationally efficient to manipulate, i.e., sparse approximation algorithms have sub-quadratic computationally complexity. To achieve this we consider two factors (both to be learned from data) in order to design the dictionary: an orthonormal component made up of a fixed number of fast fundamental orthonormal transforms and a sparse component that builds linear combinations of elements from the first, orthonormal component. We show how effective the proposed technique is to encode image data and compare against a previously proposed method from the literature. We expect the current work to contribute to the spread of sparsity and dictionary learning techniques to hardware scenarios where there are hard limits on the computational capabilities and energy consumption of the computer systems.

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“…Dictionary design is adapted to selffeature the vibration signals to match well with the high-level structures of the impulses. As far as sparse representation is concerned, the exact resolution of sparse representation proves to be an NP-hard problem [32], and the approximate solutions based on greedy-based matching pursuit [33] and convex optimal-based basis pursuit [34] are considered instead. Dictionary construction includes manually predefined dictionary and dictionary learning.…”

Section: Introductionmentioning

confidence: 99%

Fault Detection of High-Speed Train Wheelset Bearing Based on Impulse-Envelope Manifold

Zhuang

Ding

Tan

et al. 2017

Shock and Vibration

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A novel fault detection method employing the impulse-envelope manifold is proposed in this paper which is based on the combination of convolution sparse representation (CSR) and Hilbert transform manifold learning. The impulses with different sparse characteristics are extracted by the CSR with different penalty parameters. The impulse-envelope space is constructed through Hilbert transform on the extracted impulses. The manifold based on impulse-envelope space (impulse-envelope manifold) is executed to learn the low-dimensionality intrinsic envelope of vibration signals for fault detection. The analyzed results based on simulations, experimental tests, and practical applications show that (1) the impulse-envelope manifold with both isometric mapping (Isomap) and locally linear coordination (LLC) can be successfully used to extract the intrinsic envelope of the impulses where local tangent space analysis (LTSA) fails to perform and (2) the impulse-envelope manifold with Isomap outperforms those with LLC in terms of strengthening envelopes and the number of extracted harmonics. The proposed impulse-envelope manifold with Isomap is superior in extracting the intrinsic envelope, strengthening the amplitude of intrinsic envelope spectra, and enlarging the harmonic number of fault-characteristic frequency. The proposed technique is highly suitable for extracting intrinsic envelopes for bearing fault detection.

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On the Computational Intractability of Exact and Approximate Dictionary Learning

Cited by 77 publications

References 39 publications

AF Classification from ECG Recording Using Feature Ensemble and Sparse Coding

AF Classification from ECG Recording Using Feature Ensemble and Sparse Coding

Learning fast sparsifying overcomplete dictionaries

Fault Detection of High-Speed Train Wheelset Bearing Based on Impulse-Envelope Manifold

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