A convergent algorithm for orthogonal nonnegative matrix factorization

Mirzal, Andri

doi:10.1016/j.cam.2013.09.022

Cited by 39 publications

(37 citation statements)

References 44 publications

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“…If an algorithm minimizes an objective function with a weighting parameter and if the value is not appropriately chosen, then the algorithm would fail in either acceptable degree of approximation or orthogonality. Such a failure has often been reported in past experimental results (Li et al 2010;Mirzal 2014;Pompili et al 2012). Ding et al (2006) proposed the first ONMF algorithm based on the MU algorithm (Lee and Seung 2000).…”

Section: Orthogonal Nmfmentioning

confidence: 72%

“…He proposed two algorithms in Mirzal (2014), one of which is the same as the one by Li et al (2010). The first algorithm introduced a weighting parameter α instead of the Lagrangian multiplier λ in (4).…”

Section: With a Weighting Parametermentioning

confidence: 99%

“…The zero-lock problem is resolved by [ ] + operation as it is in Mirzal (2014). The proposed HALS-ONMF algorithm is shown in Algorithm 1.…”

Section: Algorithm 1 Fast Hals-orthogonal Nmfmentioning

confidence: 99%

“…We also noted that their algorithm was slowest among all the compared algorithms. For the weighting parameter α in Li's ONMF (Li et al 2010) and Mirzal's ONMF (Mirzal 2014), we used α = 1, because the value worked satisfactorily on most datasets.…”

Section: Compared Algorithms and Evaluation Measuresmentioning

confidence: 99%

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A column-wise update algorithm for nonnegative matrix factorization in Bregman divergence with an orthogonal constraint

2016

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Recently orthogonal nonnegative matrix factorization (ONMF), imposing an orthogonal constraint into NMF, has been attracting a great deal of attention. ONMF is more appropriate than standard NMF for a clustering task because the constrained matrix can be considered as an indicator matrix. Several iterative ONMF algorithms have been proposed, but they suffer from slow convergence because of their matrix-wise updating. In this paper, therefore, a column-wise update algorithm is proposed for speeding up ONMF. To make the idea possible, we transform the matrix-based orthogonal constraint into a set of column-wise orthogonal constraints. The algorithm is stated first with the Frobenius norm and then with Bregman divergence, both for measuring the degree of approximation. Experiments on one artificial and six real-life datasets showed that the proposed algorithms converge faster than the other conventional ONMF algorithms, more than four times in the best cases, due to their smaller numbers of iterations.

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Section: Orthogonal Nmfmentioning

confidence: 72%

Section: With a Weighting Parametermentioning

confidence: 99%

“…The zero-lock problem is resolved by [ ] + operation as it is in Mirzal (2014). The proposed HALS-ONMF algorithm is shown in Algorithm 1.…”

Section: Algorithm 1 Fast Hals-orthogonal Nmfmentioning

confidence: 99%

Section: Compared Algorithms and Evaluation Measuresmentioning

confidence: 99%

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A column-wise update algorithm for nonnegative matrix factorization in Bregman divergence with an orthogonal constraint

2016

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“…Therefore, for specific data types and applications, a dimensionality reduction method which can decompose non-negative data, while the decomposed data is still keeping non-negative is needed. The nonnegative matrix factorization is a decompositon method to meet this requirement.. NMF(Non-negative Matrix Factorization) is an algorithm for data dimensionality reduction and feature extraction by looking for a low dimensional feature space of non-negative factors, which has the advantage of clear principle, simple structure and good interpretive results [7][8] Now NMF has been widely used in various fields of pattern recognition, image procssing, text retrieval, etc., it is also very suitable for multivariate analysis in chemometrics.…”

Section: Introductionmentioning

confidence: 99%

NIR Spectroscopy and NMF Algorithm for Identification of Oil Pollutants in Water

Tan¹,

Zhao²,

Guo³

2014

Proceedings of the 2014 International Conference on Mechatronics, Electronic, Industrial and Control Engineering

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Abstract-Oil pollutants is one of the major pollution sources in water. Accurate, rapid, and convenient detection method of oil pollutants in water has very important theoretical value and practical significance. The combination of near-infrared spectroscopy (NIR) and chemometrics is ideal for such a situation. NIR spectroscopy is a powerful and effective technique. traditional NIR methods do not take full account of the absorbance data non-negative characteristics, resulting in the analysis lack of reasonable explanation. In this paper, the qualitative discriminate method of single species oil contaminants based on nonnegative matrix factorization feature extraction combined with support vector machine classification algorithm is studied. Non-negative matrix factorization algorithm and support vector machine classifier parameters on classification accuracy are discussed in depth to optimize NIR qualitative classification model. The present method has a good identification effect and strong generalization ability ， and can work as a new method for rapid identification of oil pollutants in water．

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A constrained proper orthogonal decomposition model for upscaling permeability

Onimisi

Lashore

Akanji

et al. 2023

Numerical Methods in Fluids

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Reservoir modeling and simulation are vital components of modern reservoir management processes. Despite the advances in computing power and the advent of smart technologies, the implementation of model-based operational/control strategies has been limited by the inherent complexity of reservoir models. Thus, reduce order models that not only reduce the cost of the implementation but also provide geological consistent prediction are essential. This article introduces reduced-order models based on the proper orthogonal decomposition (POD) coupled with linear interpolation for upscaling. First, using POD-based models, low rank approximate (LRA) are obtained by projecting the high dimensional permeability dataset to a low dimensional subspace spanned by its trajectories to decorrelate the dataset. Next, the LRA is integrated into the interpolation algorithm to generate upscaled values. This technique is highly scalable since low-rank approximations are achieved by the variation in the number of modes used for reconstruction. To test the validity and reliability of the model, we show its application to the practical dataset from SPE10 benchmark case2. From statistics of the error analysis, the classical POD algorithm seems to be more preferred for LRA; however, since non-negativity of the permeability data set is a priority, the constrained POD (non-negative POD) algorithm described in this article is more appropriate. Finally, we compared the POD-based models to a traditional industry-standard upscaling technique (e.g., arithmetic mean) to highlight our model benefits/performance. Results show that the POD-based models, particularly the non-negative POD model, produce considerably less error than the arithmetic mean model in the upscaling process.

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A convergent algorithm for orthogonal nonnegative matrix factorization

Cited by 39 publications

References 44 publications

A column-wise update algorithm for nonnegative matrix factorization in Bregman divergence with an orthogonal constraint

A column-wise update algorithm for nonnegative matrix factorization in Bregman divergence with an orthogonal constraint

NIR Spectroscopy and NMF Algorithm for Identification of Oil Pollutants in Water

A constrained proper orthogonal decomposition model for upscaling permeability

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