Non-negative Matrix Factorization using weighted beta divergence and equality constraints for industrial source apportionment

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

doi:10.1109/mlsp.2013.6661903

Cited by 9 publications

(33 citation statements)

References 15 publications

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“…We thus propose a parameterization which takes into account this knowledge. It extends our previous parameterization [12] which only considered equality constraints.…”

Section: Parameterization Of Constraintsmentioning

confidence: 89%

“…In this paper, we extend our previous work [12] by (i) investigating and discussing several β-divergence expressions, (ii) exploring different data normalization procedures (as profiles are chemical species proportions, the rows of F are normalized), and (iii) adding maximum and minimum bounds to some of the unknown values of F . The relevance of the proposed approaches is shown on simulations of particulate matter source apportionment.…”

Section: Introductionmentioning

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%

See 2 more Smart Citations

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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“…We thus propose a parameterization which takes into account this knowledge. It extends our previous parameterization [12] which only considered equality constraints.…”

Section: Parameterization Of Constraintsmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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)

Self Cite

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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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“…Remarkably, none of the algorithms used above is informed with any prior knowledge about the location of the noise. As a complementary experiment, we informed ISNMF with this knowledge by incorporating a mask containing the position of the noise into the NMF, resulting into a weighted ISNMF [28]. The blind Lévy NMF still leads to better results than the informed ISNMF.…”

Section: B Music Spectrogram Inpaintingmentioning

confidence: 99%

Lévy NMF for robust nonnegative source separation

Magron

Badeau

2017

2017 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA)

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Source separation, which consists in decomposing data into meaningful structured components, is an active research topic in many areas, such as music and image signal processing, applied physics and text mining. In this paper, we introduce the Positive α-stable (PαS) distributions to model the latent sources, which are a subclass of the stable distributions family. They notably permit us to model random variables that are both nonnegative and impulsive. Considering the Lévy distribution, the only PαS distribution whose density is tractable, we propose a mixture model called Lévy Nonnegative Matrix Factorization (Lévy NMF). This model accounts for low-rank structures in nonnegative data that possibly has high variability or is corrupted by very adverse noise. The model parameters are estimated in a maximum-likelihood sense. We also derive an estimator of the sources given the parameters, which extends the validity of the generalized Wiener filtering to the PαS case. Experiments on synthetic data show that Lévy NMF compares favorably with state-of-the art techniques in terms of robustness to impulsive noise. The analysis of two types of realistic signals is also considered: musical spectrograms and fluorescence spectra of chemical species. The results highlight the potential of the Lévy NMF model for decomposing nonnegative data.

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Non-negative Matrix Factorization using weighted beta divergence and equality constraints for industrial source apportionment

Cited by 9 publications

References 15 publications

Bound constrained weighted NMF for industrial source apportionment

Bound constrained weighted NMF for industrial source apportionment

Outlier-robust calibration method for sensor networks

Lévy NMF for robust nonnegative source separation

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