Singular Value Decomposition Algorithm Research Articles

Urban mobility analytics amid COVID-19 pandemic: A framework for promoting work resumption based on mobile phone data

The Corona Virus Disease 2019 (COVID-19) pandemic had a pernicious influence on the whole world, so that the international community implemented various travel policies to inhibit the viral spread. With the COVID-19 pandemic under control, the overly lenient measures allowed the new variant to take advantage. Also, it is difficult to determine the geographical scope of transport policy that has the least impact on work resumption. Therefore, it is necessary to find policies to promote work resumption while preventing and controlling the pandemic in a geographical perspective. In this paper, a framework based on mobile phone data is proposed for promoting work resumption during the pandemic. First, human mobility networks are constructed through the origin-destination flow extracted from mobile phone data. Second, the singular value decomposition (SVD) algorithm is utilized to recognize the mobility patterns and explore the urban mobility dynamics of work-resumption-related travel during the pandemic. Third, the nonoverlapping community detection algorithm is used to generate policy zoning for work-resumption-related travel. Finally, the policy zoning is validated by public health data based on the overlay analysis and spatial statistics method, and policy implications are proposed. A case study of Shanghai, China is applied to verify the proposed framework. The results show that the framework can capture the mobility patterns and implement the policy zoning based on mobile phone data to balance the economic activity and public health during the pandemic, and the proposed framework can be applied to other cities with future public health events.

Personalised Outfit Recommendation System Using Deep Learning

Abstract: Fashion engineering presents a significant challenge in efficiently coordinating outfits to suit personal preferences. In this study, we introduce a Fashion Coordination Assistant featuring a hybrid recommendation system. Our approach combines content-based and collaborative filtering techniques, utilizing Singular Value Decomposition (SVD) and Non-negative Matrix Factorization (NMF) algorithms. By thoroughly analyzing clothing characteristics and user behavior, we address the technical complexities of fashion coordination. Leveraging the latent features identified by SVD and the non-linear relationships captured by NMF, our system generates tailored outfit suggestions based on individual preferences and style profiles. Extensive testing validates the system's ability to provide diverse and efficient recommendations. By integrating innovative recommendation methods, the Fashion Coordination Assistant adapts to evolving fashion trends and user preferences, enhancing its practical utility in real-world scenarios

AI Based Personalized Recommendation of Career Guidance for Students

This paper is devoted to solving the problem of determining the career guidance of student using Artificial Intelligence systems. This paper proposes an AI-based web application approach for personalized career recommendations, leveraging the strengths of Singular Value Decomposition (SVD) and XG Boost algorithms. By integrating these techniques, the proposed system aims to overcome limitations of existing methods and deliver more accurate, contextually relevant Career suggestions to students. The web application was developed by Python and uses Keras ,Numpy,Pandas libraries. Result of this paper can be used to inform the students with informed career choices that align with their unique attributes and aspirations, thereby enhancing their successful career.

Hybrid watermarking and encryption techniques for securing three-dimensional information

A hybrid digital watermarking and encryption technique based on the Computer Generated Holography (CGH) and fractional Fourier transform (FRFT) combined with singular value decomposition (SVD) algorithm is proposed for securing three-dimensional (3D) information. Initially, hierarchical 3D information is encrypted using the angular spectrum diffraction method and a random phase key. This process yields a binary real valued CGH, where incorporating a random phase key broadens the key space and adds complexity, effectively scrambling and concealing the 3D information. Subsequently, the encrypted binary real valued CGH is embedded into the host image as a watermark using the FRFT-SVD algorithm. This hybrid approach enhances the security of the watermarking process. In the final step, the CGH watermark is extracted using the inverse operation of the embedding algorithm. Applying the correct optical key and angular spectrum inverse algorithm successfully reconstructs the 3D information. The watermark algorithm’s efficiency significantly improves by leveraging the rapid computational speed and high focusing capabilities of the FRFT. Additionally, integrating SVD enhances the image’s resistance to geometric attacks, thereby improving the algorithm’s invisibility and robustness. The proposed scheme effectively achieves the encryption and digital watermarking of 3D information. Simulation results substantiate the presented watermarking scheme’s efficacy and robustness.

A novel structure-preserving algorithm for the singular value decomposition of biquaternion matrices

In this paper, we study the singular value decomposition of biquaternion matrices. We prove that the singular value decomposition of biquaternion matrices can be equivalently converted to the singular value decomposition of quaternion adjoint matrices. By means of the Cheng product, we propose a novel representation called Q -representation and design a Q structure-preserving algorithm to deal with the singular value decomposition of quaternion matrices, which makes use of high-level operations. The algorithm is more efficient than that in quaternion toolbox for matlab using quaternion arithmetics and real structure-preserving algorithm. The Q structure-preserving algorithm for singular value decomposition of biquaternion matrices is presented through the application of the Q structure-preserving algorithm for singular value decomposition of quaternion matrices. Numerical experiments are provided to demonstrate the efficiency of the Q structure-preserving algorithm. We apply the Q structure-preserving algorithm of quaternion singular value decomposition to improve the image denoising process.

Performance analysis of three recommendation algorithms on Amazon datasets

Recommendation systems play a crucial role in enhancing user satisfaction and driving sales for businesses. They are essential in todays marketplaces, as they are able to suggest products and services that may interest a particular individual based on their past purchases. In this paper, empirical research is conducted on three distinct subsets of the Amazon dataset, namely Sports & Outdoors, Movies & TV, and Video Games, to comprehensively evaluate the performance of three distinct recommendation methods based on deep learning algorithms. These methods include the dot product method, (an updated version of the singular value decomposition algorithm), the neural network method, and the neural collaborative filtering model with natural language processing method. The results of this study reveal that deep learning-based recommendation systems can achieve more accurate results compared to traditional recommendation systems for three types of products. The implementation of these methods on Amazons dataset can help improve sales by correctly identifying customers interests and suggesting relevant items.

Performance comparison and analysis of SVD and ALS in recommendation system

This research predominantly focuses on the electronic segment of the Amazon dataset. In this setting, this studys primary objective is to use this particular dataset to carry out a detailed comparative analysis of two matrix factorization-based collaborative filtering techniques, namely Singular Value Decomposition (SVD) and Alternating Least Squares (ALS). The findings stemming from this investigation reveal a notable contrast in the performance of these algorithms. Specifically, the SVD algorithm demonstrates significantly higher overall accuracy when compared to ALS. This observation suggests that in scenarios characterized by denser and smaller datasets, the SVD algorithm outperforms ALS by a considerable margin. The implications of these results underscore the significance of algorithm selection in recommender systems, emphasizing that the performance of collaborative filtering methods can vary markedly depending on the datasets characteristics. Additionally, this research highlights the potential limitations of ALS in scenarios similar to the one explored here, shedding light on the importance of tailoring algorithmic choices to the specific data environment. Overall, these findings contribute valuable insights to the field of recommendation systems and provide guidance for algorithm selection based on dataset properties.

Fixed-precision randomized quaternion singular value decomposition algorithm for low-rank quaternion matrix approximations

The fixed-precision randomized quaternion singular value decomposition algorithm (FPRQSVD) is presented to compute the low-rank quaternion matrix approximation. The FPRQSVD algorithm estimates the appropriate rank according to the given tolerance without a predetermined rank parameter, and computes the corresponding low-rank quaternion matrix approximation automatically. Error analysis indicates that the FPRQSVD algorithm is mathematically equivalent to the randomized quaternion singular value decomposition algorithm. Numerical experiments are given to demonstrate that the FPRQSVD algorithm is feasible and effective. Moreover, we use it to deal with the problem of color image inpainting.

Singular Value Decomposition-Driven Non-negative Matrix Factorization with Application to Identify the Association Patterns of Sarcoma Recurrence.

Sarcomas are malignant tumors from mesenchymal tissue and are characterized by their complexity and diversity. The high recurrence rate making it important to understand the mechanisms behind their recurrence and to develop personalized treatments and drugs. However, previous studies on the association patterns of multi-modal data on sarcoma recurrence have overlooked the fact that genes do not act independently, but rather function within signaling pathways. Therefore, this study collected 290 whole solid images, 869 gene and 1387 pathway data of over 260 sarcoma samples from UCSC and TCGA to identify the association patterns of gene-pathway-cell related to sarcoma recurrences. Meanwhile, considering that most multi-modal data fusion methods based on the joint non-negative matrix factorization (NMF) model led to poor experimental repeatability due to random initialization of factorization parameters, the study proposed the singular value decomposition (SVD)-driven joint NMF model by applying the SVD method to calculate initialized weight and coefficient matrices to achieve the reproducibility of the results. The results of the experimental comparison indicated that the SVD algorithm enhances the performance of the joint NMF algorithm. Furthermore, the representative module indicated a significant relationship between genes in pathways and image features. Multi-level analysis provided valuable insights into the connections between biological processes, cellular features, and sarcoma recurrence. In addition, potential biomarkers were uncovered, while various mechanisms of sarcoma recurrence were identified from an imaging genetic perspective. Overall, the SVD-NMF model affords a novel perspective on combining multi-omics data to explore the association related to sarcoma recurrence.

A failure diagnosis method of ball bearing based on optimized multiscale variational modal extraction with synchro squeezing transformation

When a compound failure occurs in a bearing, the failure information included in vibration signals is featured by being weak, complex and combined. This fact makes it difficult to identify a compound failure precisely. Variational mode extraction (VME) solves the problem of variational mode decomposition (VMD) in being difficult to determine the number of decomposition layers and has certain applications in the identification of bearing failures. However, the initial expected central frequency of VME and option of penalty factor is crucial to the extraction of expected mode. To precisely determine the central frequency and penalty factor of VME and fulfill the correct extraction of feature information of compound failures in bearing, the paper has proposed a method based on synchro squeezing transform (SST) and information entropy to adaptively determine the parameters in VME (SST-VME). Firstly, SST is used to make time-frequency analysis of original vibration signals and characteristic frequency bands with larger energy are chosen from time-frequency spectrum to adaptively determine the expected central frequency of VME. Secondly, as information entropy has representation capacity for information included in the signal, penalty factor of VME was adaptively determined according to information entropy. Thirdly, original signals were subjected to VME according to expected central frequency and penalty factor adaptively determined; the expectation mode obtained was denoised by singular value decomposition algorithm. Finally, the type of compound failures of bearing is determined according to the frequency spectrum of denoised signals. To verify the effectiveness of proposed method, a comparison with VMD algorithm is conducted. As indicated by the result, the proposed method is more precise and comprehensive than VMD algorithm to extract the feature information corresponding to compound faults of bearing, and thereby correctly determines the type of compound failures.

Fast computation of the eigensystem of genomic similarity matrices

The computation of a similarity measure for genomic data is a standard tool in computational genetics. The principal components of such matrices are routinely used to correct for biases due to confounding by population stratification, for instance in linear regressions. However, the calculation of both a similarity matrix and its singular value decomposition (SVD) are computationally intensive. The contribution of this article is threefold. First, we demonstrate that the calculation of three matrices (called the covariance matrix, the weighted Jaccard matrix, and the genomic relationship matrix) can be reformulated in a unified way which allows for the application of a randomized SVD algorithm, which is faster than the traditional computation. The fast SVD algorithm we present is adapted from an existing randomized SVD algorithm and ensures that all computations are carried out in sparse matrix algebra. The algorithm only assumes that row-wise and column-wise subtraction and multiplication of a vector with a sparse matrix is available, an operation that is efficiently implemented in common sparse matrix packages. An exception is the so-called Jaccard matrix, which does not have a structure applicable for the fast SVD algorithm. Second, an approximate Jaccard matrix is introduced to which the fast SVD computation is applicable. Third, we establish guaranteed theoretical bounds on the accuracy (in L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_2$$\\end{document} norm and angle) between the principal components of the Jaccard matrix and the ones of our proposed approximation, thus putting the proposed Jaccard approximation on a solid mathematical foundation, and derive the theoretical runtime of our algorithm. We illustrate that the approximation error is low in practice and empirically verify the theoretical runtime scalings on both simulated data and data of the 1000 Genome Project.

Dual quaternion hand-eye calibration algorithm for hunter-prey optimization based on twice opposition-learning and random differential variation

In order to solve the problem of noise interference in camera calibration and robot forward kinematics solution, this study proposes a dual quaternion hand-eye calibration algorithm based on twice opposition-learning and random differential variation (ODHPO). The hand-eye calibration equation was innovatively rewritten in the form of dual quaternion, and the F-norm minimization model of the rotation and translation error function was constructed for optimization. At the same time, the penalty function method is introduced to effectively transform the constrained optimization problem in hand-eye calibration into an unconstrained problem, which is further solved by the ODHPO algorithm for global optimization. Compared with the singular value decomposition algorithm based on the traditional dual quaternion method, the ODHPO algorithm performs better in global optimization ability and convergence stability. Through numerical simulation and real robot hand-eye calibration experiments, it is proved that the proposed algorithm is superior to the traditional dual quaternion (CDQ) algorithm, the classical algorithms Tsai method and Navy method in terms of solution accuracy, sensitivity to the number of pose transformations and stability, demonstrating its potential for application and practical significance in robot vision system.

Personalized Sports Health Recommendation System Assisted by Q-Learning Algorithm

In response to the current problem of single sports plan and lack of long-term motivation in recommendation systems, a more intelligent personalized sports health recommendation system was designed by introducing Q-Learning (Quality Learning) algorithm. Firstly, user sports health data was collected, and the user model was constructed to track user sport preferences and historical behavior. Secondly, the sports environment was defined, including different types of sports activities, venues, and weather. Then, the reward function was formulated to reward and punish users based on their sports activities and goals, in order to maximize long-term health benefits. Finally, the Q-Learning algorithm was implemented to continuously iteratively learn and optimize user recommendation models to provide the best personalized sports recommendations. For personalized accuracy, indicators such as precision, recall, F1 value, MAE (Mean Absolute Error), and RMSE (Root Mean Square Error) were used to evaluate, while the system’s participation in sports, user satisfaction, long-term incentive effects, and overall health improvement were collected. The results showed that the average precision of the recommendation system on 10 different datasets was 88%, and the average AUC (Area Under Curve) was 96%, which was 6.7% higher than the SVD (Singular Value Decomposition) algorithm. The user’s sports persistence rate was improved by 25%, and the health score was improved by about 13.3%. These data not only reflect the superior performance of the recommendation system but also highlight its positive impact on long-term user motivation and overall health levels. The results indicate that the proposed personalized exercise health recommendation system, assisted by the Q-Learning algorithm, has significantly improved accuracy. Moreover, it offers users more intelligent and personalized exercise suggestions, effectively increasing long-term participation in physical activities and overall health levels.

Joint Improved Fast Independent Component Analysis and Singular Value Decomposition for Fetal Electrocardiogram Extraction.

Combined the improved fast independent component analysis (FastICA) algorithm with the singular value decomposition algorithm, a single-channel fetal electrocardiogram (fECG) extraction method is proposed. First, the improved FastICA algorithm is used to estimate the maternal ECG component from a single-channel abdominal signal of pregnant women using an overrelaxation factor. Then, a preliminary estimate of the fECG signal is obtained by subtracting from the single-channel abdominal signal. Subsequently, the singular value decomposition algorithm is used to denoise the preliminarily estimated fECG signal to obtain a high signal-to-noise ratio. In addition, in the singular value decomposition algorithm for fetal arrhythmia, an improved method for constructing the ECG signal reconstruction matrix is proposed. Finally, the fECG extraction experiments on synthetic abdominal signals and actual abdominal signals (data from 49 abdominal channels sourced from DAISY database and the non-invasive fECG database in PhysioNet) are carried out. The experimental results show that the method in this paper can effectively improve the signal-to-noise ratio and the accuracy of fECG signal extraction, and is suitable for maternal or fetal arrhythmias. Compared with the FastICA algorithm, the signal-to-noise ratio of the fECG signal extracted by the method in this paper is improved by about 5 dB, and the accuracy of fECG extraction in the PhysioNet database can reach 96.54%.

Fourier Domain Robust Denoising Decomposition and Adaptive Patch MRI Reconstruction.

The sparsity of the Fourier transform domain has been applied to magnetic resonance imaging (MRI) reconstruction in k -space. Although unsupervised adaptive patch optimization methods have shown promise compared to data-driven-based supervised methods, the following challenges exist in MRI reconstruction: 1) in previous k -space MRI reconstruction tasks, MRI with noise interference in the acquisition process is rarely considered. 2) Differences in transform domains should be resolved to achieve the high-quality reconstruction of low undersampled MRI data. 3) Robust patch dictionary learning problems are usually nonconvex and NP-hard, and alternate minimization methods are often computationally expensive. In this article, we propose a method for Fourier domain robust denoising decomposition and adaptive patch MRI reconstruction (DDAPR). DDAPR is a two-step optimization method for MRI reconstruction in the presence of noise and low undersampled data. It includes the low-rank and sparse denoising reconstruction model (LSDRM) and the robust dictionary learning reconstruction model (RDLRM). In the first step, we propose LSDRM for different domains. For the optimization solution, the proximal gradient method is used to optimize LSDRM by singular value decomposition and soft threshold algorithms. In the second step, we propose RDLRM, which is an effective adaptive patch method by introducing a low-rank and sparse penalty adaptive patch dictionary and using a sparse rank-one matrix to approximate the undersampled data. Then, the block coordinate descent (BCD) method is used to optimize the variables. The BCD optimization process involves valid closed-form solutions. Extensive numerical experiments show that the proposed method has a better performance than previous methods in image reconstruction based on compressed sensing or deep learning.

A Combined Noise Reduction Method for Floodgate Vibration Signals Based on Adaptive Singular Value Decomposition and Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise

To address the issue of the vibration characteristic signals of floodgates being affected by background white noise and low-frequency water flow noise, a noise reduction method combining the improved adaptive singular value decomposition algorithm (ASVD) and the improved complete ensemble EMD with adaptive noise (ICEEMDAN) is proposed. Firstly, a Hankel matrix is constructed based on the collected discrete time signals. After performing SVD on the Hankel matrix, the ASVD algorithm is used to automatically select the effective singular values to filter out most of the background white noise and retain the useful frequency components with similar energy in the signal. Then, ICEEMDAN combined with the Spearman correlation coefficient method is used to further filter out residual white noise and low-frequency water flows. The noise reduction performance of this combined method is verified through simulation experiments. Filtered by the ASVD-ICEEMDAN method, the signal-to-noise ratio of the simulation signal (50% noise level) is increased from 4.417 to 16.237, and the root mean square error is reduced from 2.286 to 0.586. Based on the practically measured vibration signals of a floodgate at a large hydropower station, the result shows that the ASVD-ICEEMDAN method exhibits good noise reduction performance and feature information extraction abilities for floodgate vibration signals, and can provide support for operational mode analysis and damage identification of practical structures under complex interference conditions.

A novel committee-based framework for modeling groundwater level fluctuations: A combination of mathematical and machine learning models using the weighted multi-model ensemble mean algorithm

water level (GWL) fluctuations simulation can be divided into three general categories: Analytical solution, conceptual or physical-based models, and data-based or data-driven models. The goal of this research is to develop the MODFLOW conceptual model and the GMDH data-driven model as single models (SMs) for GWL modeling, and then to combine these models to develop a novel mathematical-machine learning model based on a weighted multi-model ensemble mean approach (MMWEM) for a more accurate GWL simulation. For this purpose, the Miqan aquifer, located in northeastern Iran, was selected as a case study. Hydrological and hydrogeological data of the Miqan wetland for ten years (September 2013 to August 2023) with a monthly time step were used to compile models. First, the MODFLOW model was developed for one month (steady-state), then calibrated for nine years (unsteady-state), and finally tested for one year. In the second step, the GMDH model was developed. The grasshopper optimization algorithm (GOA) and the singular value decomposition (SVD) algorithms were used to determine the Ivakhnenko polynomial coefficients of the GMDH (SVD-GMDH and GOA-GMDH). 80% of the data was used to develop SVD-GMDH and GOA-GMDH, and other data was used to test models. Consequently, the sequential forward floating selection (SFFS) method was used to select the best input variables for the SVD-GMDH and GOA-GMDH. The coefficient of determination (R2), root mean squared error (RMSE), and Nash-Sutcliffe Efficiency coefficient (NSE) were used to evaluate the performance of the models. Based on the results of this study, using each of the SMs, GWL can be simulated with acceptable accuracy. However, a closer examination of the results of SMs showed that the MODFLOW has the worst performance among SMs, while the GOA-GMDH has the best function for simulating GWL. In the third step, SMs was used to develop the MMWEM. The GWL of 13 of the 34 piezometers studied in this study was better simulated with the MODFLOW and GOA-GMDH than the SVD-GMDH. Therefore, these models were used to develop the MMWEM for these piezometers. For GWL simulation in 21 piezometers, the SVD-GMDH and GOA-GMDH perform better than the MODFLOW, so these models were used to develop the MMWEM in these piezometers. Finally, the results of the SMs Moreover, the MMWEM were compared with each other. Based on the results of this study, the MMWEM performs better than SMs. In many studies, only the performance of each numerical model and machine learning to simulate groundwater level (GWL) fluctuations is evaluated. Then, their results are compared with each other. However, according to this study, the combination of the results of these models is a big step in improving the accuracy of the groundwater level simulation process. In addition to simulating the groundwater level, this method can simulate other quantitative and qualitative parameters of water resources.

Fault diagnosis of horizontal centrifugal pump orifice ring wear and blade fracture based on complete ensemble empirical mode decomposition with adaptive noise-singular value decomposition algorithm

Horizontal centrifugal pump orifice ring wear and blade fracture failure will not only affect the hydraulic performance but also affect the safety and stability of the whole unit. In this paper, the horizontal centrifugal pump orifice ring wear and blade fracture failure are studied, and carry out condition monitoring and fault identification through the vibration signal under the failure. Combined with the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Singular Value Decomposition algorithm of adaptive noise, a vibration feature extraction method of horizontal centrifugal pump based on intrinsic mode singular value is proposed. Through the BP neural network, based on the time domain, frequency domain, wavelet packet-AR spectrum, and intrinsic mode singular value characteristics of single-point and double-point vibration, the identification model is constructed and the identification effect is compared. The research shows that the vibration feature recognition effect of CEEMDAN-SVD decomposition is verified based on BP neural network model, and the BP neural network is improved by Particle Swarm Optimization to further improve the recognition effect and speed, which provides the diagnosis model for the design of subsequent diagnosis system.

Fault Feature Extraction Method of Ball Screw Based on Singular Value Decomposition, CEEMDAN and 1.5DTES

In this article, a method is proposed to effectively extract weak fault features and accurately diagnose faults in ball screws, even in the presence of strong background noise. This method combines singular value decomposition (SVD), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), and the 1.5-dimensional spectrum (1.5D) to process and analyze fault vibration signals. The first step involves decomposing the fault signal using the SVD algorithm. The singular values are then screened, and the part of the screen containing more noise information is extracted to complete the first denoising step. The second step involves decomposing the signal after the initial denoising process using CEEMDAN and removing some of the false components from the intrinsic mode function (IMF) components, based on the kurtosis correlation function index. The signal is then reconstructed to complete the second denoising step. Finally, the denoised signal is analyzed using Teager energy operator demodulation and 1.5D spectral analysis to extract the fault frequency and determine the location of the fault in the ball screw. This method has been compared with other denoising methods, such as wavelet packet decomposition combined with CEEMDAN or SVD combined with variational mode decomposition (VMD), and the results show that under the condition of strong background noise, the proposed method can better extract the fault frequency of ball screw.

Federated singular value decomposition for high-dimensional data

Federated learning (FL) is emerging as a privacy-aware alternative to classical cloud-based machine learning. In FL, the sensitive data remains in data silos and only aggregated parameters are exchanged. Hospitals and research institutions which are not willing to share their data can join a federated study without breaching confidentiality. In addition to the extreme sensitivity of biomedical data, the high dimensionality poses a challenge in the context of federated genome-wide association studies (GWAS). In this article, we present a federated singular value decomposition algorithm, suitable for the privacy-related and computational requirements of GWAS. Notably, the algorithm has a transmission cost independent of the number of samples and is only weakly dependent on the number of features, because the singular vectors corresponding to the samples are never exchanged and the vectors associated with the features are only transmitted to an aggregator for a fixed number of iterations. Although motivated by GWAS, the algorithm is generically applicable for both horizontally and vertically partitioned data.