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

Chreiky, Robert; Delmaire, Gilles; Puigt, Matthieu; Roussel, Gilles; Abche, Antoine

doi:10.1109/isspit.2016.7886011

Cited by 3 publications

(3 citation statements)

References 20 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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“…where c represents the threshold parameter of the data using the L 1 -norm or the L 2 -norm. This function is a bounded and convex function that minimizes the effects of a single anomaly point (Chreiky et al, 2016). Huber losses often apply to the insensitive outliers and noise contained in the data, which are often difficult to find using the squared loss function (Du et al, 2012).…”

Section: Related Workmentioning

confidence: 99%

Sparse Graph Regularization Non-Negative Matrix Factorization Based on Huber Loss Model for Cancer Data Analysis

Wang

Liu

et al. 2019

Front. Genet.

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Non-negative matrix factorization (NMF) is a matrix decomposition method based on the square loss function. To exploit cancer information, cancer gene expression data often uses the NMF method to reduce dimensionality. Gene expression data usually have some noise and outliers, while the original NMF loss function is very sensitive to non-Gaussian noise. To improve the robustness and clustering performance of the algorithm, we propose a sparse graph regularization NMF based on Huber loss model for cancer data analysis (Huber-SGNMF). Huber loss is a function between L 1-norm and L 2-norm that can effectively handle non-Gaussian noise and outliers. Taking into account the sparsity matrix and data geometry information, sparse penalty and graph regularization terms are introduced into the model to enhance matrix sparsity and capture data manifold structure. Before the experiment, we first analyzed the robustness of Huber-SGNMF and other models. Experiments on The Cancer Genome Atlas (TCGA) data have shown that Huber-SGNMF performs better than other most advanced methods in sample clustering and differentially expressed gene selection.

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“…As a consequence, robust NMF methods were proposed to deal with a predefined number of outliers. While some of them decompose the data matrix into the sum of a low-rank and a sparse matrix-where the latter contains the outlying component [18]-most ones consider some modified cost functions as dissimilarity measures which gave rise to flexible and robust algorithms, e.g., Bregman-NMF [19], α-NMF [20], β-NMF [21,22], αβ-NMF [23], Correntropy-NMF [24], Huber-NMF [25] (it should be noticed that the Huber cost function has also been considered for robust PMF [26]).…”

Section: Introductionmentioning

confidence: 99%

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

Cited by 3 publications

References 20 publications

Outlier-robust calibration method for sensor networks

Outlier-robust calibration method for sensor networks

Sparse Graph Regularization Non-Negative Matrix Factorization Based on Huber Loss Model for Cancer Data Analysis

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

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