Non-Negative Matrix Factorization Based Uncertainty Quantification Method for Complex Networked Systems

The behavior of large networked systems with underlying complex nonlinear dynamic are hard to predict. With increasing number of states, the problem becomes even harder. Quantifying uncertainty in such systems by conventional methods requires high computational time and the accuracy obtained in estimating the state variables can also be low. This paper presents a novel computational Uncertainty Quantifying (UQ) method for complex networked systems. Our approach is to represent the complex systems as networks (graphs) whose nodes represent the dynamical units, and whose links stand for the interactions between them. First, we apply Non-negative Matrix Factorization (NMF) based decomposition method to partition the domain of the dynamical system into clusters, such that the inter-cluster interaction is minimized and the intra-cluster interaction is maximized. The decomposition method takes into account the dynamics of individual nodes to perform system decomposition. Initial validation results on two well-known dynamical systems have been performed. The validation results show that uncertainty propagation error quantified by RMS errors obtained through our algorithms are competitive or often better, compared to existing methods.

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Infrared Non-Destructive Testing via Semi-Nonnegative Matrix Factorization

Proceedings ◽

10.3390/proceedings2019027013 ◽

2019 ◽

Vol 27 (1) ◽

pp. 13 ◽

Cited By ~ 1

Author(s):

Yousefi ◽

Ibarra-Castanedo ◽

Maldague

Keyword(s):

Matrix Factorization ◽

Nonnegative Matrix ◽

Principal Component ◽

Computational Time ◽

Detection Accuracy ◽

Non Destructive Testing ◽

Destructive Testing ◽

Non Destructive ◽

Non Negative Matrix Factorization ◽

Subsurface Defects

Detection of subsurface defects is undeniably a growing subfield of infrared non-destructive testing (IR-NDT). There are many algorithms used for this purpose, where non-negative matrix factorization (NMF) is considered to be an interesting alternative to principal component analysis (PCA) by having no negative basis in matrix decomposition. Here, an application of Semi non-negative matrix factorization (Semi-NMF) in IR-NDT is presented to determine the subsurface defects of an Aluminum plate specimen through active thermographic method. To benchmark, the defect detection accuracy and computational load of the Semi-NMF approach is compared to state-of-the-art thermography processing approaches such as: principal component thermography (PCT), Candid Covariance-Free Incremental Principal Component Thermography (CCIPCT), Sparse PCT, Sparse NMF and standard NMF with gradient descend (GD) and non-negative least square (NNLS). The results show 86% accuracy for 27.5s computational time for SemiNMF, which conclusively indicate the promising performance of the approach in the field of IR-NDT.

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The Effect of ICA and Non-negative Matrix Factorization Analysis for EMG Signals Recorded From Multi-Channel EMG Sensors

Frontiers in Neuroscience ◽

10.3389/fnins.2020.600804 ◽

2020 ◽

Vol 14 ◽

Author(s):

Yeongdae Kim ◽

Sorawit Stapornchaisit ◽

Makoto Miyakoshi ◽

Natsue Yoshimura ◽

Yasuharu Koike

Keyword(s):

Matrix Factorization ◽

Decomposition Method ◽

Index Finger ◽

Power Source ◽

Classification Performance ◽

Emg Signal ◽

Movement Artifacts ◽

Low Dimensional ◽

Sensor Positions ◽

Non Negative Matrix Factorization

Surface electromyography (EMG) measurements are affected by various noises such as power source and movement artifacts and adjacent muscle activities. Hardware solutions have been found that use multi-channel EMG signal to attenuate noise signals related to sensor positions. However, studies addressing the overcoming of crosstalk from EMG and the division of overlaid superficial and deep muscles are scarce. In this study, two signal decompositions—independent component analysis and non-negative matrix factorization—were used to create a low-dimensional input signal that divides noise, surface muscles, and deep muscles and utilizes them for movement classification based on direction. In the case of index finger movement, it was confirmed that the proposed decomposition method improved the classification performance with the least input dimensions. These results suggest a new method to analyze more dexterous movements of the hand by separating superficial and deep muscles in the future using multi-channel EMG signals.

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Gene Expression Analysis through Parallel Non-Negative Matrix Factorization

Computation ◽

10.3390/computation9100106 ◽

2021 ◽

Vol 9 (10) ◽

pp. 106

Author(s):

Angelica Alejandra Serrano-Rubio ◽

Guillermo B. Morales-Luna ◽

Amilcar Meneses-Viveros

Keyword(s):

Gene Expression ◽

Expression Analysis ◽

Matrix Factorization ◽

Clustering Algorithm ◽

Gene Selection ◽

Clustering Algorithms ◽

Biological Data ◽

Dimensional Structure ◽

Computational Time ◽

Non Negative Matrix Factorization

Genetic expression analysis is a principal tool to explain the behavior of genes in an organism when exposed to different experimental conditions. In the state of art, many clustering algorithms have been proposed. It is overwhelming the amount of biological data whose high-dimensional structure exceeds mostly current computational architectures. The computational time and memory consumption optimization actually become decisive factors in choosing clustering algorithms. We propose a clustering algorithm based on Non-negative Matrix Factorization and K-means to reduce data dimensionality but whilst preserving the biological context and prioritizing gene selection, and it is implemented within parallel GPU-based environments through the CUDA library. A well-known dataset is used in our tests and the quality of the results is measured through the Rand and Accuracy Index. The results show an increase in the acceleration of 6.22× compared to the sequential version. The algorithm is competitive in the biological datasets analysis and it is invariant with respect to the classes number and the size of the gene expression matrix.

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Image Encryption Based on Matrix Factorization

International Journal of Safety and Security Engineering ◽

10.18280/ijsse.100510 ◽

2020 ◽

Vol 10 (5) ◽

pp. 655-661

Author(s):

Vivek Khalane ◽

Shekhar Suralkar ◽

Umesh Bhadade

Keyword(s):

Image Encryption ◽

Matrix Factorization ◽

Decomposition Method ◽

Computation Time ◽

Matrix Decomposition ◽

Input Image ◽

Decomposition Techniques ◽

Encryption Method ◽

State Of Art ◽

Non Negative Matrix Factorization

In this paper, we present a matrix decomposition-based approach for image cryptography. The proposed method consists of decomposing the image into different component and scrambling the components to form the image encryption technique. We use two different type of matrix decomposition techniques to check the efficiency of proposed encryption method. The decomposition techniques used are Independent component analysis (ICA) and Non-Negative Matrix factorization (NMF). The proposed technique has unique user defined parameters (key) such as decomposition method, number of decomposition components and order in which the components are arranged. The unique encryption technique is designed on the basis of these key parameters. The original image can be reconstructed at the decryption end only if the selected parameters are known to the user. The design examples for both decomposition approaches are presented for illustration purpose. We analyze the complexity and encryption time of cryptography system. Results prove that the proposed scheme is more secure as it has less correlation between the input image and the encrypted version of the same as compared to state-of-art methods. The computation time of the proposed approach is found to be comparable.

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