Bound constrained weighted NMF for industrial source apportionment

Omidvar

et al. 2019

Entropy

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.

Section: Weighted αβ-Nmf With Set Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

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

Omidvar

et al. 2019

Entropy

“…It should be noticed that normalizing the rows of F is classical in matrix factorization and is usually performed after each update of F [42] or within the optimization problem [52]. Informed NMF with normalization was also investigated in [53], [54]. However, such a normalization implies rows of F to be exactly equal to the chosen means, which may lead to calibration errors in the case of an inexact knowledge of the mean parameters in the considered application.…”

Section: Average-constrained Extension Of In-calmentioning

confidence: 99%

Informed Nonnegative Matrix Factorization Methods for Mobile Sensor Network Calibration

Dorffer

IEEE Trans. on Signal and Inf. Process. over Networks

et al. 2018

In 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 propose to revisit blind sensor calibration as an informed Nonnegative Matrix Factorization (NMF) problem with missing entries. In the considered framework, one matrix factor contains the calibration structure of the sensors-and especially the values of the sensed phenomenon-while the other one contains the calibration parameters of the whole sensor network. The available information is taken into account by using a specific parameterization of the NMF problem. Moreover, we also consider additional NMF constraints which can be independently taken into account, i.e., an approximate constraint over the mean calibration parameters and a sparse approximation of the sensed phenomenon over a known dictionary. The enhancement of our proposed approaches is investigated through more than 5000 simulations and is shown to be accurate for the considered application and to outperform a multi-hop micro-calibration technique as well as a method based on low-rank matrix completion and nonnegative least squares.

“…Moreover, blind NMF methods for source apportionment may result in solutions without physical meaning [11], especially when some source profiles are geometrically close to each other. To overcome these drawbacks, we recently proposed some informed NMF approaches [12][13][14][15] which take into account some prior information-e.g., some set values in the profile matrix provided by chemical experts-together with the row sum-to-one property. In [12,13], the constraints were alternatingly satisfied along iterations and only the limit matrix was fulfilling both of them.…”

Section: Introductionmentioning

confidence: 99%

“…To overcome these drawbacks, we recently proposed some informed NMF approaches [12][13][14][15] which take into account some prior information-e.g., some set values in the profile matrix provided by chemical experts-together with the row sum-to-one property. In [12,13], the constraints were alternatingly satisfied along iterations and only the limit matrix was fulfilling both of them. We recently proposed a new parameterization [14,15] which fulfills both constraints at the same time, and we then derived informed NMF methods using the split gradient strategy [16].…”

Section: Introductionmentioning

confidence: 99%

Informed Split Gradient Non-negative Matrix factorization using Huber cost function for source apportionment

Chreiky

2016 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT)

et al. 2016

Source apportionment is usually tackled with blind Positive/Non-negative Matrix factorization (PMF/NMF) methods. However, the obtained results may be poor due to the dependence between some rows of the second factor. We recently proposed to inform the estimation of this factor using some prior knowledge provided by chemists-some entries are set to some fixed values-and the sum-to-one property of each row. These constraints were recently taken into account by using a parameterization which gathers all of them. In this paper, a novel robust NMF approach able to cope with outliers is proposed. For that purpose, we consider the Huber loss function-a 2-1 cost function-which is robust to outliers, contrary to the Frobenius norm classically met in NMF. We thus propose new update rules for the informed Huber NMF in the framework of the split gradient techniques. The choice of the adaptive cutoff parameter-which links both single cost functions-is discussed along this paper. The proposed approach is shown to outperform state-of-the-art methods on several source apportionment simulations involving various input SNRs and outliers.