Singular Value Decomposition Algorithm Research Articles

A singular value decomposition approach for detecting and delineating harmful algal blooms in the Red Sea

Harmful algal blooms (HABs) have adverse effects on marine ecosystems. An effective approach for detecting, monitoring, and eventually predicting the occurrences of such events is required. By combining a singular value decomposition (SVD) approach and satellite remote sensing observations, we propose a remote sensing algorithm to detect and delineate species-specific HABs. We implemented and tested the proposed SVD algorithm to detect HABs associated with the mixed assemblages of different phytoplankton functional type (PFT) groupings in the Red Sea. The results were validated with concurrent in-situ data from surface samples, demonstrating that the SVD-model performs remarkably well at detecting and distinguishing HAB species in the Red Sea basin. The proposed SVD-model offers a cost-effective tool for implementing an automated remote-sensing monitoring system for detecting HAB species in the basin. Such a monitoring system could be used for predicting HAB outbreaks based on near real-time measurements, essential to support aquaculture industries, desalination plants, tourism, and public health.

Improved Tucker decomposition algorithm for noise suppression of 3D GPR data in road detection

AbstractThe echo data of ground‐penetrating radar (GPR) have a low signal‐to‐noise ratio. Denoising and interference suppression are important for improving the accuracy of underground target recognition and detection. In this paper, a new method of noise analysis and suppression of 3D GPR is proposed, transforming the problem of noise reduction into an optimization problem regarding a third‐order tensor. This method is improved with the following features; a bidimensional empirical mode decomposition (BEMD) algorithm is employed to decompose the 3D GPR noise. The main source of the noise is determined by computing the standard deviation of each component decomposed. For the shortcoming of the existing GPR denoising methods that reduce the dimension of 3D GPR data, the proposed approach can denoise 3D GPR data directly to avoid the loss of data caused by reducing the dimension. This preserves the desired signal and extracts noise through the Tucker decomposition of 3D GPR data. An improved high‐order orthogonal iteration algorithm is utilized to optimize the decomposition. The peak signal‐to‐noise ratio (PSNR) of the signal for each survey line is calculated to evaluate the effectiveness of noise reduction. Simulations and real data sets are provided to compare the performance of algorithms. The results show that the mean PSNR after noise suppression with our method is 8.915 dB and 16.458 dB higher than wavelet transform and singular value decomposition algorithms, respectively. This demonstrates that the proposed approach can better suppress 3D GPR noise and provides technical support for improving 3D GPR data quality and road detection accuracy.

An efficient audio watermarking scheme with scrambled medical images for secure medical internet of things systems.

In recent times, the security of communication channels between healthcare entities in Medical Internet of Things (MIoT) systems becomes a significant issue to facilitate and guarantee the exchange of medical image and expertise securely. This paper presents an efficient audio watermarking scheme employing professionally Wavelet-based Image Fusion, Arnold transforms, and Singular Value Decomposition (SVD) for the secure transmission of medical images and reports in the MIoT applications. The essential consequence of the proposed scheme is to first syndicate two medical watermarks into a fused watermark to upsurge the payload of the inserted medical images. The fused watermark is then scrambled utilizing Arnold transform. Lastly, the Arnold fused watermark is inserted in the audio signal using the SVD algorithm following converting it into a 2D format. The choice of the Arnold transform for watermark is ascribed to settling robustness that skirmishes respective types of severe attacks. Several assessment metrics such as SNR, LLR, SNRseg, SD, and Cr are used to evaluate the audio watermarked signal and extracted watermarks The results reveal that the proposed audio watermarking scheme increases the capacity with more embedded medical images and security of implanted medical images transmission deprived of affecting the quality of audio signals, especially for IoT-based Telemedicine systems.

High-Dimensional Generalized Orthogonal Matching Pursuit With Singular Value Decomposition

Matching pursuit (MP) is an algorithm which can reconstruct signal accurately, and is widely used in signal processing. However, MP algorithm has efficiency problem in processing large amount of data like five-dimensional (5D) seismic data. Generalized orthogonal matching pursuit with singular value decomposition (SVD_GOMP) is an algorithm which can improve the calculation efficiency a lot, and keeps the advantage of high accuracy. In this study, a redundant atom dictionary includes incident angles and azimuth is built. Then the five-dimensional seismic data is reconstructed efficiently and accurately by the generalize orthogonal matching pursuit with singular value decomposition algorithm. Compared with traditional matching pursuit method, the proposed method decomposes the five-dimensional seismic data at the same time and recovers the angle information efficiently. The reconstructed results of synthetic and field data examples are utilized to demonstrate the feasibility, computational efficiency and precision of the proposed method.

Ionospheric Tomography: A Compressed Sensing Technique Based on Dictionary Learning

GNSS (Global Navigation Satellite System) observation insufficiency limits the development of the voxel-based computerized ionospheric tomography (CIT) technique. Electron densities of voxels without observation cannot be accurately estimated by the commonly used algebraic reconstruction techniques. In this study, we proposed a compressed sensing technique (CST) based on dictionary learning for ionospheric tomography. Specifically, the K-SVD (singular value decomposition) algorithm was used for dictionary learning based on training sets that are derived from the NeQuick model, hereafter referred to as the CST_NeQuick algorithm. K-SVD uses the orthogonal matching pursuit (OMP) for sparse coding and the SVD approach for dictionary updating. Both simulations and real experiments demonstrated the feasibility and superiority of the CST algorithm when compared to the widely used multiplicative algebraic reconstruction technique (MART). It was found that the CST_NeQuick algorithm’s tomographic performances were mostly superior to those of the MART algorithm in comparison with the independent slant total electron content (STEC) references. Another CST-based tomographic experiment was performed by using the MART-based solutions for dictionary learning, hereafter referred to as the CST_MART algorithm. It showed that the CST_MART algorithm can reduce the average root mean square (RMS) of the CIT-derived STEC by 37.3 % and 20.2 %, respectively, when compared to the MART and CST_NeQuick algorithms. Besides, the CST_MART algorithm’s electron density profiles also showed more agreement with the electron density profiles that were derived from radio occultation data.

Обчислення сингулярного розкладу матриць з використанням графічного процесора

In this research paper we present an implementation of a singular value decomposition algorithm designed specifically for the graphics processing unit. It consists of two parts: orthogonal matrix decomposition and matrix diagonalization. Presented an implementation of bidiagonalization algorithm where we calculate the main bidiagonal matrix and two orthogonal multipliers using a series of House- holder transformations, as well as diagonalization algorithm with the help of Givens rotation matrices. Bothe these parts are implemented in jCUDA environment. Experiments have been conducted, the results of which have been thoroughly investigated on the matter of time consumption and calculations error. We’ve also compared our implementation with alternatives both on central and graphic processors.

Data Optimization for Industrial IoT-Based Recommendation Systems

The most common problems that arise when working with big data for intelligent production are analyzed in the article. The work of recommendation systems for finding the most relevant user information was considered. The features of the singular-value decomposition (SVD) and Funk SVD algorithms for reducing the dimensionality of data and providing quick recommendations were determined. An improvement of the Funk SVD algorithm using a smaller required amount of user data for analysis was proposed. According to the results of the experiments, the proposed modification improves the speed of data processing on average by 50–70% depending on the number of users and allows spending fewer computing resources. As follows, recommendations to users are provided in a shorter period and are more relevant. The faster calculation of modified Funk SVD to exchange the optimal parameters between nodes was proposed. It was determined that execution time can be reduced on average by 75% for using ten nodes exchanging the optimal decomposition parameter compared to using one. Using Spark technology for faster calculation on average by 20% compared to Hadoop was proposed. The architecture of the IIoT system was proposed, which uses a modified Funk SVD algorithm to optimize data on edge devices and monitors the effectiveness of providing recommendations using control centers and cloud resources.

Credit Card-Not-Present Fraud Detection and Prevention Using Big Data Analytics Algorithms

Currently, fraud detection is employed in numerous domains, including banking, finance, insurance, government organizations, law enforcement, and so on. The amount of fraud attempts has recently grown significantly, making fraud detection critical when it comes to protecting your personal information or sensitive data. There are several forms of fraud issues, such as stolen credit cards, forged checks, deceptive accounting practices, card-not-present fraud (CNP), and so on. This article introduces the credit card-not-present fraud detection and prevention (CCFDP) method for dealing with CNP fraud utilizing big data analytics. In order to deal with suspicious behavior, the proposed CCFDP includes two steps: the fraud detection Process (FDP) and the fraud prevention process (FPP). The FDP examines the system to detect harmful behavior, after which the FPP assists in preventing malicious activity. Five cutting-edge methods are used in the FDP step: random undersampling (RU), t-distributed stochastic neighbor embedding (t-SNE), principal component analysis (PCA), singular value decomposition (SVD), and logistic regression learning (LRL). For conducting experiments, the FDP needs to balance the dataset. In order to overcome this issue, Random Undersampling is used. Furthermore, in order to better data presentation, FDP must lower the dimensionality characteristics. This procedure employs the t-SNE, PCA, and SVD algorithms, resulting in a speedier data training process and improved accuracy. The logistic regression learning (LRL) model is used by the FPP to evaluate the success and failure probability of CNP fraud. Python is used to implement the suggested CCFDP mechanism. We validate the efficacy of the hypothesized CCFDP mechanism based on the testing results.

Harmonic Source Location and Characterization Based on Permissible Current Limits by Using Deep Learning and Image Processing

Identification of harmonic sources contributing to harmonic distortion, and characterization of harmonic current injected by them, are crucial tasks in harmonic analysis of modern power systems. In this paper, these tasks are addressed based on the permissible current limits recommended by IEEE 519 Standard, with a determination of whether or not injected harmonics are within these limits. If limits are violated, the extent of the violations are characterized to provide information about harmonic current levels in the power system and facilitate remedial actions if necessary. A novel feature extraction method is proposed, whereby each set of harmonic measurements in a power system are transformed into a unique RGB image. Harmonic State Estimation (HSE) is discretized as a classification problem. Classifiers based on deep learning have been developed to subsequently locate and characterize harmonic sources. The approach has been demonstrated effectively both on the IEEE 14-bus system, and on a real transmission network where harmonics have been measured. A comparative study indicates that the proposed technique outperforms state-of-the-art techniques for HSE, including Bayesian Learning (BL), Singular Value Decomposition (SVD) and hybrid Genetic Algorithm Least Square (GALS) method in terms of accuracy and limited number of monitors.

An improved stochastic configuration network for concentration prediction in wastewater treatment process

A learner model with fast learning and compact architecture is expected for industrial data modeling. To achieve these goals during stochastic configuration networks (SCNs) construction, we propose an improved version of SCNs in this paper. Unlike the original SCNs, the improved one employs a new inequality constraint in the construction process. In addition, to speed up the construction efficiency of SCNs, a node selection method is proposed to adaptively select nodes from a candidate pool. Moreover, to reduce the redundant nodes of the built SCNs model, we further compress the model based on the singular value decomposition algorithm. The improved SCNs are compared with other methods over four datasets and then applied to the ammonia–nitrogen concentration prediction task in the wastewater treatment process. Experimental results indicate that the proposed method has good potential for industrial data analytics.

A memory-efficient MultiVector Quasi-Newton method for black-box Fluid-Structure Interaction coupling

In this work we present a novel Quasi-Newton technique for the black-box partitioned coupling of interface coupled problems. The new RandomiZed Multi-Vector Quasi-Newton method stems from the combination of the original Multi-Vector Quasi-Newton technique with the randomized Singular Value Decomposition algorithm, avoiding thus any dense DOFs-sized square matrix operation. This results in a reduction from quadratic to linear complexity in terms of the number of DOFs. Besides this, the need of storing the old inverse Jacobian is also avoided. Instead, only two very “thin” matrices are required to be saved, thus implying a much smaller memory footprint. Furthermore, our proposal can be used free of any user-defined parameter. The article describes the application of the method to the FSI interface residual equations in both Interface Quasi-Newton and Interface Block Quasi-Newton forms. For the latter, we also derive a closed form expression for the update, thus avoiding any linear system of equations resolution, by applying the Woodbury matrix identity to the inverse Jacobian decomposition matrices.

An enhanced algorithm for online Proper Orthogonal Decomposition and its parallelization for unsteady simulations

Proper Orthogonal Decomposition (POD) plays an important role in the analysis of complex nonlinear systems governed by partial differential equations (PDEs), since it can describe the full-order system in a simplified but representative way using a handful of dominant dynamic modes. However, determining a POD from the results of complex unsteady simulations is often impractical using traditional approaches due to the need to store a large number of high-dimensional solutions. As an alternative, the incremental Singular Value Decomposition (SVD) has been developed, which can be used to avoid the storage problem by performing the POD analysis on the fly using a single-pass updating algorithm. Nevertheless, the total computing cost of incremental SVD is more than traditional approaches. In order to reduce this total cost, we incorporate POD mode truncation into the incremental procedure, leading to an enhanced algorithm for incremental SVD. Two error estimators are formulated for this enhanced incremental SVD based on an aggregated expression of the snapshot solutions, equipping the proposed algorithm with criteria for choosing the truncation number. The effectiveness of these estimators and the parallel efficiency of the enhanced algorithm are demonstrated using transient solutions from representative model problems. Numerical results show that the enhanced algorithm can significantly improve the computing efficiency for different kinds of datasets, and that the proposed algorithm is scalable in both the strong and weak sense. • An enhanced algorithm based on incremental SVD is developed for online POD. • Two lower-bound error estimators are derived for the energy captured by the enhanced incremental SVD. • The proposed enhanced algorithm scales well in parallel. • Accurate estimates of the algorithm's computational efficiency are provided by a priori analysis.

A new bootstrap technique to quantify uncertainty in estimates of ground surface temperature and ground heat flux histories from geothermal data

Abstract. Estimates of the past thermal state of the land surface are crucial to assess the magnitude of current anthropogenic climate change as well as to assess the ability of Earth System Models (ESMs) to forecast the evolution of the climate near the ground, which is not included in standard meteorological records. Subsurface temperature reacts to long-term changes in surface energy balance – from decadal to millennial time scales – thus constituting an important record of the dynamics of the climate system that contributes, with low-frequency information, to proxy-based paleoclimatic reconstructions. Broadly used techniques to retrieve past temperature and heat flux histories from subsurface temperature profiles based on a singular value decomposition (SVD) algorithm were able to provide robust global estimates for the last millennium, but the approaches used to derive the corresponding 95 % confidence interval were wrong from a statistical point of view in addition to being difficult to interpret. To alleviate the lack of a meaningful framework for estimating uncertainties in past temperature and heat flux histories at regional and global scales, we combine a new bootstrapping sampling strategy with the broadly used SVD algorithm and assess its performance against the original SVD technique and another technique based on generating perturbed parameter ensembles of inversions. The new bootstrap approach is able to reproduce the prescribed surface temperature series used to derive an artificial profile. Bootstrap results are also in agreement with the global mean surface temperature history and the global mean heat flux history retrieved in previous studies. Furthermore, the new bootstrap technique provides a meaningful uncertainty range for the inversion of large sets of subsurface temperature profiles. We suggest the use of this new approach particularly for aggregating results from a number of individual profiles, and to this end, we release the programs used to derive all inversions in this study as a suite of codes labeled CIBOR v1: Codes for Inverting BORholes, version 1.

Study on Inversion Algorithm of NMR T2 Spectrum

Nuclear magnetic resonance (NMR) logging technology is a kind of technology developed gradually in recent decades, which has great significance for the development of logging technology. Nuclear magnetic resonance logging technology compared to traditional logging technology, not only has the ideal signal - hydrogen nuclei, and the exploration of the original signal is not affected by the influence of the rock skeleton, is the only provides information that is unrelated to formation rock porosity, can better provide the formation permeability, movable fluid, oil and gas content, such as information, It is a kind of logging method suitable for low porosity and low permeability and complex special lithology, and overcomes the defects of traditional logging methods .With the development of NMR theory, NMR has been applied to the analysis of well logging data. The original NMR logging data are the spin-echo string observed by the spin echo string, and its amplitude decays with time. The T2 spectrum can be inversely calculated from the measured logging data, and then the T2 spectrum can be further solved to obtain key data such as permeability and porosity. In this paper, a simulated T2 spectrum is constructed by forward modeling, and the inversion is carried out under different SNR. On this basis, the specific relationship between the optimal number of singular values retained and the change of SNR is summarized, and an improved singular value decomposition algorithm is proposed. Inverse problem can be converted to nonlinear fitting optimization problems with nonnegative constraints, linear truncation algorithm on calculation precision has increased significantly, compared with the traditional singular value decomposition inversion algorithm, a new algorithm of signal-to-noise ratio on the solution of smaller and has better stability, and through the improvement of nonnegative constraint processing structure was more rapid inversion iteration algorithm.

A three-dimensional text image watermarking model based on multilayer overlapping of extracted two-dimensional information

Aiming at the problem that watermark information is easy to be lost in two-dimensional text image watermarking, a three-dimensional text image watermarking model is proposed based on multilayer overlapping of extracted two-dimensional information, and a specific method is accordingly realized by means of embedding, extracting and overlapping of multiple watermarks in sequence. We discuss the influence of the sequence order, positional distancing and color difference of the extracted multiple two-dimensional information on displaying a three-dimensional text watermark image. In addition, considering the crucial evaluation indices of the invisibility and robustness for the watermarking algorithm, the selection method for superior embedding regions of multiple watermarks is also constructed to enhance the robust performance of watermarks under the premise of effective invisibility. Moreover, we embed the multiple two-dimensional information into the host image by using the undecimated dual-tree complex wavelet transforms - bidiagonal singular value decomposition algorithm. In this way, the extracted multiple two-dimensional information is automatically overlapped to generate the three-dimensional text watermarking according to the optimal matching parameters. We use standard image processing data set to carry out experiments, the results show that the peak signal to noise ratio before and after embedded watermarks is higher than 39 dB, and the peak signal to noise ratio between the original watermarks and the extracted watermarks is more than 37 dB, which is superior to the current reported watermark model. Therefore, it is suggested that the proposed model shows good invisibility and robustness and can reduce the loss of watermark during transmission and attack as much as possible.

A review on the selection criteria for the truncated SVD in Data Science applications

The Singular Value Decomposition (SVD) is one of the most used factorizations when it comes to Data Science applications. In particular, given the big size of the processed matrices, in most of the cases, a truncated SVD algorithm is employed. In the following manuscript, we review some of the state-of-the-art approaches considered for the selection of the number of components (i.e., singular values) to retain to apply the truncated SVD. Moreover, three new approaches based on the Kullback–Leibler divergence and on unsupervised anomaly detection algorithms, are introduced. The revised methods are then compared on some standard benchmarks in the image processing context.

Optimizing input parameter of the randomized singular value decomposition algorithm for compressing technetium-99m L,L, ethylenedicysteine renal dynamic study in minimum time preserving clinical information.

The SVDsketch [MATLAB function which implements a randomized singular value decomposition (rSVD) algorithm] uses tolerance (tol) to adaptively determine the rank of the matrix sketch approximation. As the tol gets larger, fewer features of input image matrix are used in the matrix sketch. The objective of this study was to optimize the value of tol for compressing technetium-99m (Tc-99m) L,L, ethylenedicysteine (LLEC) renal dynamic (RD) study in minimum time preserving clinical information. At different values of tol [0.00012(default), 0.1, 0.01, and 0.05] 50 Tc-99m LLEC RD studies were compressed. Two nuclear medicine (NM) physicians compared compressed images at tol = 0.1 with its input images. The SVD computation time and compression factor were calculated for each study. The image quality metrics: Error, structural similarity index for measuring image quality, brightness, global contrast factor (GCF), contrast per pixel (CPP), and blur were used for objective assessment of image quality. Percentage error in split function estimated from compressed and original images was calculated. Wilcoxon signed-rank test was applied to find statistically significant difference between renal split function, blur, GCF, CPP, and brightness of the compressed image and the original image at . As per NM physicians, compressed images estimated with tol = 0.1 were identical to the original images. Based on image quality metrics, compressed images were significantly less noisy, brighter, and have better contrast compared with its input images. There was insignificant difference in split renal function estimated from compressed RD study at tol = 0.1 and its original study. The SVD computation and percentage compression per study were found to be 0.04725 s and up to 74.53%. The optimized value of tol for compressing Tc-99m LLEC RD study preserving clinical information was found to be 0.1, and SVD computation time: 0.04725 s.

Neural Embedding Singular Value Decomposition for Collaborative Filtering.

Singular value decomposition (SVD) is one of the most effective algorithms in recommender systems (RSs). Due to the iterative nature of SVD algorithms, one big challenge is initialization that has a major impact on the convergence and performance of RSs. Unfortunately, existing SVD algorithms in the literature typically initialize the user and item features in a random manner; thus, data information is not fully utilized. This work addresses the challenge of developing an efficient initialization method for SVD algorithms. We propose a general neural embedding initialization framework, where a low-complexity probabilistic autoencoder neural network initializes the features of user and item. This framework supports explicit and implicit feedback data sets. The design details of our proposed framework are elaborated and discussed. Experimental results show that RSs based on our proposed initialization framework outperform the state-of-the-art methods in rating prediction. Moreover, regarding item ranking, our proposed framework shows an improvement of at least 2.20% ~5.74% than existing SVD algorithms and other matrix factorization methods in the literature.

Rapid detection of copper ore grade based on visible-infrared spectroscopy and TSVD-IVTELM

The rapidity of ore grade identification is key to speeding up the beneficiation process in the mining process. Traditional ore grade detection mostly relies on chemical methods. Although these methods have high accuracy, they take a long time, and the cost of detection has always been high. Therefore, this paper proposes a detection method for ore grade using visible-infrared spectroscopy and an incremental two hidden layer extreme learning machine with variable hidden layer nodes based on the truncated singular value decomposition (TSVD-IVTELM) algorithm. Firstly, the spectral data of each sample are obtained by spectrometer. Then, Monte Carlo cross-validation is used to eliminate abnormal samples, and partial least squares regression is used to extract the latent variables of the spectral data to reduce the data dimension. Finally, TSVD-IVTELM is used for regression analysis. TSVD-IVTELM is proved to have the smallest root mean square error and best fitting performance after comparison experiments.

Singular value decomposition model application for e-commerce recommendation system

A recommendation system is one of the most important things in today’s technology. It can suggest products that match the user’s preferences. Many fields utilize this system, including e-commerce, using various algorithms. This paper used the matrix factorization-based algorithm, singular value decomposition (SVD), to make a recommendation system based on users’ similarities. Afterward, we implement the model against the ModCloth Amazon dataset. The results imply that the SVD algorithm yields the best accuracy compared to other matrix factorization-based algorithms with root mean square error (RMSE) of 1.055586. Then, we optimized the SVD algorithm by changing the hyperparameters of the algorithm to generate better accuracy and yield a model with an RMSE value of 1.041784.