Fast Nonnegative Matrix Factorization and Completion Using Nesterov Iterations

Dorffer, Clément; Puigt, Matthieu; Delmaire, Gilles; Roussel, Gilles

doi:10.1007/978-3-319-53547-0_3

Cited by 16 publications

(25 citation statements)

References 28 publications

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“…which yieldsslightly different update rules. We proposed in [35] some multiplicative update rules to solve Equation (29) in the case of β-divergence only. The extension to the αβ-divergence is derived in Appendix A.…”

Section: General Problem Formulationmentioning

confidence: 99%

“…Appendix A proposes the update rules for the problem (29). These rules are almost similar to those introduced above as they present some differences in the multiplicative mask.…”

Section: Weighted αβ-Nmf With Set Constraintsmentioning

confidence: 99%

“…The following abbreviations are used in this manuscript: In this appendix, we aim to develop update rules for problem (29), for which we drop the sum-to-one constraint. The structure of the proof follows the same steps as in Section 5.1 within a MM strategy.…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…Lastly, it should be noticed that in receptor models, each data point x ij is provided with an uncertainty measure σ ij and PMF actually solves a weighted optimization problem [4,26]. Weighted extensions of NMF have been also considered, e.g., to enhance the factorization [27] or to deal with missing entries [28,29]. However, it is known than both the PMF [30] and the standard NMF techniques face some convergence issues (however, the convergence of NMF is guaranteed under some separability assumptions [3] which are not satisfied in practice in the considered application and which are thus out of the scope of this paper) [3].…”

Section: Introductionmentioning

confidence: 99%

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Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment

Delmaire

Omidvar

Puigt

et al. 2019

Entropy

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In this paper, we propose informed weighted non-negative matrix factorization (NMF) methods using an α β -divergence cost function. The available information comes from the exact knowledge/boundedness of some components of the factorization—which are used to structure the NMF parameterization—together with the row sum-to-one property of one matrix factor. In this contribution, we extend our previous work which partly involved some of these aspects to α β -divergence cost functions. We derive new update rules which are extendthe previous ones and take into account the available information. Experiments conducted for several operating conditions on realistic simulated mixtures of particulate matter sources show the relevance of these approaches. Results from a real dataset campaign are also presented and validated with expert knowledge.

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Section: General Problem Formulationmentioning

confidence: 99%

“…Appendix A proposes the update rules for the problem (29). These rules are almost similar to those introduced above as they present some differences in the multiplicative mask.…”

Section: Weighted αβ-Nmf With Set Constraintsmentioning

confidence: 99%

Section: Conflicts Of Interestmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment

Delmaire

Omidvar

Puigt

et al. 2019

Entropy

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“…The authors in [16] then proposed an extension of [15] which uses Total Least Square (TLS) to solve Eq. (11). TLS mainly consists of a weighted SVD where the weights allow to take into account the accuracy of each sensor.…”

Section: Nullspace-based Sensor Calibrationmentioning

confidence: 99%

Outlier-robust calibration method for sensor networks

Dorffer¹,

Puigt²,

Delmaire³

et al. 2017

2017 IEEE International Workshop of Electronics, Control, Measurement, Signals and Their Application to Mechatronics (ECMSM)

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Abstract-In this paper, we aim to blindly calibrate the responses of a sensor network whose outputs are possibly corrupted by outliers. In particular, we extend some well-known nullspacebased blind calibration approaches, proposed for fixed sensors with affine responses-i.e., with unknown gain and offset for each sensor-to that difficult case. These state-of-the-art approaches assume that the true data lie in a known lower dimensional subspace, so that in practice sensors can be calibrated by projection of the uncalibrated observations to this subspace. A robust extension was recently proposed in order to provide less sensitivity to noise. In this paper, we show that such methods (including the robust extensions) are very sensitive to outliers and we propose new extensions able to deal with such issues. For that purpose, we assume the outliers to be rare events, which can be modeled as a sparse contribution to the low-rank observed data. Using such an assumption, we separate sparse outliers from the low-rank data, so that we can perform calibration. We show that the proposed approach is able to handle up to 10% of outliers in the data without major impact on the calibration accuracy while state-of-the-art methods are already sensitive to the presence of one unique outlier.

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Low-rank matrix recovery via novel double nonconvex nonsmooth rank minimization with ADMM

Wang

Zhang

2023

Multimed Tools Appl

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Fast Nonnegative Matrix Factorization and Completion Using Nesterov Iterations

Cited by 16 publications

References 28 publications

Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment

Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment

Outlier-robust calibration method for sensor networks

Low-rank matrix recovery via novel double nonconvex nonsmooth rank minimization with ADMM

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