Non-negative Matrix Factorization under equality constraints—a study of industrial source identification

Limem, Abdelhakim; Delmaire, Gilles; Puigt, Matthieu; Roussel, Gilles; Courcot, Dominique

doi:10.1016/j.apnum.2014.05.009

Cited by 23 publications

(36 citation statements)

References 29 publications

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“…In future work, we will investigate some outlier-robust extensions of these approaches, using a similar low-rank modeling. We will compare such a formalism to robust informed matrix factorization using parametric divergences [24], [25] or the Huber norm [26], that we recently proposed for another application [27]. Moreover, the proposed techniques need to know the low-rank subspace where the sensed phenomenon lie.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

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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“…In the considered application, the rows of the profile matrix are summed to 1. As a consequence, in our previous work [11,12], we used to normalize the matrices G and F in each iteration, after estimating them. In this paper, we investigate an alternative normalization procedure.…”

Section: Normalization Proceduresmentioning

confidence: 99%

“…As a consequence, we investigated in our recent work [11][12][13] the enhancement provided by informed NMF which takes into consideration the known values of some terms of F [11,12] or G [13] in order to improve the separation. In [11], we introduced a specific parameterization for NMF methods using a Frobenius norm while we extended this approach to a Constrained Weighted NMF method using a β-divergence (β-CWNMF) in [12]. These approaches should be considered as a flexible NMF counterpart of [14] in between BSS-where no information on F is provided-and regression, where F is fully known.…”

Section: Introductionmentioning

confidence: 99%

Bound constrained weighted NMF for industrial source apportionment

Limem

Puigt

Delmaire

et al. 2014

2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP)

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In our recent work, we introduced a constrained weighted Non-negative Matrix Factorization (NMF) method using a βdivergence cost function. We assumed that some components of the factorization were known and were used to inform our NMF algorithm. In this paper, we are provided some intervals of possible values for some factorization components. We thus introduce an extended version of our previous work combining an improved divergence expression and some matrix normalizations while using the known / bounded information. Some experiments on simulated mixtures of particulate matter sources show the relevance of these approaches.

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“…This turns out to be a WINMF problem which can be tackled by, e.g., the approach in [14]-extending the multiplicative update NMF approaches in [15][16][17]-that we used and generalized in [12]. Indeed, the last columns in G and F are perfectly known as well as some entries in the first column of G. This information can be used as a specific parameterization where only the free parts of G and F are updated [12,14]. WINMF then reads…”

Section: Previously Proposed Bmsc Methodsmentioning

confidence: 99%

“…Using these matrices, it is then straightforward to see that the problems (14) and (8) are equivalent-except that we respectively replace W , X, and F by W, X , and F in Eq. (8)-so that we can use the update rules (10).…”

Section: Bmsc With Relaxed Rendezvousmentioning

confidence: 99%

Blind mobile sensor calibration using an informed nonnegative matrix factorization with a relaxed rendezvous model

Dorffer

Puigt

Delmaire

et al. 2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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To cite this version:Clément Dorffer, Matthieu Puigt, Gilles Delmaire, Gilles Roussel. Blind mobile sensor calibration using an informed nonnegative matrix factorization with a relaxed rendezvous model. 41st IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2016) ABSTRACTIn this paper, we consider the problem of blindly calibrating a mobile sensor network-i.e., determining the gain and the offset of each sensor-from heterogeneous observations on a defined spatial area over time. For that purpose, we previously proposed a blind sensor calibration method based on Weighted Informed Nonnegative Matrix Factorization with missing entries. It required a minimum number of rendezvous-i.e., data sensed by different sensors at almost the same time and place-which might be difficult to satisfy in practice.In this paper we relax the rendezvous requirement by using a sparse decomposition of the signal of interest with respect to a known dictionary. The calibration can thus be performed if sensors share some common support in the dictionary, and provides a consistent performance even if no sensors are in exact rendezvous.Index Terms-Blind calibration, mobile sensor networks, informed nonnegative matrix factorization, sparse data analysis

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Non-negative Matrix Factorization under equality constraints—a study of industrial source identification

Cited by 23 publications

References 29 publications

Outlier-robust calibration method for sensor networks

Outlier-robust calibration method for sensor networks

Bound constrained weighted NMF for industrial source apportionment

Blind mobile sensor calibration using an informed nonnegative matrix factorization with a relaxed rendezvous model

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