Matrix Decomposition Research Articles

Exploration of Imaging Genetic Biomarkers of Alzheimer's Disease Based on a Machine Learning Method.

Alzheimer's disease (AD) is an irreversible primary brain disease with insidious onset. The rise of imaging genetics research has led numerous researchers to examine the complex association between genes and brain phenotypes from the perspective of computational biology. Given that most previous studies have assumed that imaging data and genetic data are linearly related and are therefore unable to explore their nonlinear relationship, our study applied a joint depth semi-supervised nonnegative matrix decomposition (JDSNMF) algorithm to solve this problem. The JDSNMF algorithm jointly decomposed multimodal imaging genetics data into both a standard basis matrix and multiple feature matrices. During the decomposition process, the coefficient matrix A multilayer nonlinear transformation was performed using a neural network to capture nonlinear features. The results using a real dataset demonstrated that the algorithm can fully exploit the association between strongly correlated image genetics data and effectively detect biomarkers of AD. Our results might provide a reference for identifying biologically significant imaging genetic correlations, and help to elucidate disease-related mechanisms. The diagnostic model constructed by the top features of the three modality data sets mined by the algorithm has high accuracy, and these features are expected to become new therapeutic targets for AD.

In situ compressive behavior of carbon fibers reinforced PolyEtherEther Ketone laminates exposed to one-sided heat flux

This study investigates the influence of a combined thermal heat flux (imposed by a cone calorimeter) and a compressive loading on the deformation and damage mechanisms within quasi-isotropic carbon fibers reinforced PolyEtherEther Ketone laminates. Thermogravimetric Analyses conducted at increasing heating rates under nitrogen (from 5 to 500°C/min) provide valuable information on the thermal decomposition of C/PEEK that ranges from 550°C to 627°C, with a corresponding mass loss ranging from 20 to 26%. From the thermo-mechanical coupling standpoint, the softening and the thermal decomposition of the PEEK matrix under a 50 kW/m2 heat flux result in the micro-buckling of fibers bundles in matrix-rich areas at the ply scale. Ultimately, it leads to the formation and propagation in the transverse direction of plastic kink bands at the laminates scale. Post-failure observations show that this macroscopic kinking propagates specifically according to the PEEK matrix pyrolysis.

Stochastic nested primal-dual method for nonconvex constrained composition optimization

In this paper we study the nonconvex constrained composition optimization, in which the objective contains a composition of two expected-value functions whose accurate information is normally expensive to calculate. We propose a STochastic nEsted Primal-dual (STEP) method for such problems. In each iteration, with an auxiliary variable introduced to track the inner layer function values we compute stochastic gradients of the nested function using a subsampling strategy. To alleviate difficulties caused by possibly nonconvex constraints, we construct a stochastic approximation to the linearized augmented Lagrangian function to update the primal variable, which further motivates to update the dual variable in a weighted-average way. Moreover, to better understand the asymptotic dynamics of the update schemes we consider a deterministic continuous-time system from the perspective of ordinary differential equation (ODE). We analyze the Karush-Kuhn-Tucker measure at the output by the STEP method with constant parameters and establish its iteration and sample complexities to find an ϵ \epsilon -stationary point, ensuring that expected stationarity, feasibility as well as complementary slackness are below accuracy ϵ \epsilon . To leverage the benefit of the (near) initial feasibility in the STEP method, we propose a two-stage framework incorporating a feasibility-seeking phase, aiming to locate a nearly feasible initial point. Moreover, to enhance the adaptivity of the STEP algorithm, we propose an adaptive variant by adaptively adjusting its parameters, along with a complexity analysis. Numerical results on a risk-averse portfolio optimization problem and an orthogonal nonnegative matrix decomposition reveal the effectiveness of the proposed algorithms.

Asymmetric Cryptography Based on the Tropical Jones Matrix

In recent years, the tropical polynomial factorization problem, the tropical matrix decomposition problem, and the tropical multivariate quadratic equation solving problem have been proved to be NP-hard. Some asymmetric cryptographic systems based on tropical semirings have been proposed, but most of them are insecure and have been successfully attacked. In this paper, a new key exchange protocol and a new encryption protocol are proposed based on the difficulty of finding the multiple exponentiation problem of the tropical Jones matrices. The analysis results indicate that our protocol can resist various existing attacks. The complexity of attacking an MEP by adversaries is raised due to the larger number of combinations in the tropical Jones matrices compared to regular matrix polynomials. Furthermore, the index semiring is the non-negative integer cyclic matrix semiring, leading to a higher efficiency in key generation.

Cross-domain information fusion and personalized recommendation in artificial intelligence recommendation system based on mathematical matrix decomposition

Given the challenges of inter-domain information fusion and data sparsity in collaborative filtering algorithms, this paper proposes a cross-domain information fusion matrix decomposition algorithm to enhance the accuracy of personalized recommendations in artificial intelligence recommendation systems. The study begins by collecting Douban movie rating data and social network information. To ensure data integrity, Levenshtein distance detection is employed to remove duplicate scores, while natural language processing technology is utilized to extract keywords and topic information from social texts. Additionally, graph convolutional networks are utilized to convert user relationships into feature vectors, and a unique thermal coding method is used to convert discrete user and movie information into binary matrices. To prevent overfitting, the Ridge regularization method is introduced to gradually optimize potential feature vectors. Weighted average and feature connection techniques are then applied to integrate features from different fields. Moreover, the paper combines the item-based collaborative filtering algorithm with merged user characteristics to generate personalized recommendation lists.In the experimental stage, the paper conducts cross-domain information fusion optimization on four mainstream mathematical matrix decomposition algorithms: alternating least squares method, non-negative matrix decomposition, singular value decomposition, and latent factor model (LFM). It compares these algorithms with the non-fused approach. The results indicate a significant improvement in score accuracy, with mean absolute error and root mean squared error reduced by 12.8% and 13.2% respectively across the four algorithms. Additionally, when k = 10, the average F1 score reaches 0.97, and the ranking accuracy coverage of the LFM algorithm increases by 54.2%. Overall, the mathematical matrix decomposition algorithm combined with cross-domain information fusion demonstrates clear advantages in accuracy, prediction performance, recommendation diversity, and ranking quality, and improves the accuracy and diversity of the recommendation system. By effectively addressing collaborative filtering challenges through the integration of diverse techniques, it significantly surpasses traditional models in recommendation accuracy and variety.

Electronic Coherences Excited by an Ultra Short Pulse Are Robust with Respect to Averaging over Randomly Oriented Molecules as Shown by Singular Value Decomposition.

We report a methodology for averaging quantum photoexcitation vibronic dynamics over the initial orientations of the molecules with respect to an ultrashort light pulse. We use singular value decomposition of the ensemble density matrix of the excited molecules, which allows the identification of the few dominant principal molecular orientations with respect to the polarization direction of the electric field. The principal orientations provide insights into the specific stereodynamics of the corresponding principal molecular vibronic states. The massive compaction of the vibronic density matrix of the ensemble of randomly oriented pumped molecules enables a most efficient fully quantum mechanical time propagation scheme. Two examples are discussed for the quantum dynamics of the LiH molecule in the manifolds of its electronically excited Σ and Π states. Our results show that electronic and vibrational coherences between excited states of the same symmetry are resilient to averaging over an ensemble of molecular orientations and can be selectively excited at the ensemble level by tuning the pulse parameters.

Analysis of multiple-faults of high-voltage circuit breakers based on non-negative matrix decomposition

High-voltage circuit breakers are the core equipment in power networks, and to a certain extent, are related to the safe and reliable operation of power systems. However, their core components are prone to mechanical faults. This study proposes a component separation method to detect multiple mechanical faults in circuit breakers that can achieve online real-time monitoring. First, a model and strategy are presented for obtaining mechanical voiceprint signals from circuit breakers. Subsequently, the component separation method was used to decompose the voiceprint signals of multiple faults into individual component signals. Based on this, the recognition of the features of a single-fault voiceprint signal can be achieved. Finally, multiple faults in high-voltage circuit breakers were identified through an experimental simulation and verification of the circuit breaker voiceprint signals collected from the substation site. The research results indicate that the proposed method exhibits excellent performance for multiple mechanical faults, such as spring structures and loose internal components of circuit breakers. In addition, it provides a reference method for the real-time online monitoring of high-voltage circuit breakers.

Decomposition Matrix for the projective Characters S_28, p=11

In this work, we compute the decomposition matrix to the spin characteristics of S_28 for a given field of characteristic p=11, the connections between the irreducible modular spin characters and the irreducible spin characters of S_28. The technique employed in this study is (r,r ̅ )-inducing, which creates projective characters for S_28 by using the projective characters of S_27. Maple was used to seeing all available columns and then choosing the potentially appropriate columns of them. In order to explore irreducible modular spin characteristics, general correlations and theorems will be discovered as a result of this research.

Analysis of Structural Change for the Kyrgyz Republic Economy: Evidence from Decomposition of Output Changes and Multiplier Product Matrix

Input-output analyses, which investigate intersectoral interdependencies and structural changes, are critical to sectoral planning by providing policymakers with significant information. This study draws on the input-output tables calculated by the Asian Development Bank for Asian and Pacific countries, specifically for the Kyrgyz Republic. The decomposition of output changes and the multiplier product matrix are employed to identify any structural changes in the country’s economy. The empirical findings indicate that a major structural change has occurred in the Kyrgyz economy, led by the financial intermediation sector.

Vision SLAM algorithm for wheeled robots integrating multiple sensors.

Wheeled robots play a crucial role in driving the autonomy and intelligence of robotics. However, they often encounter challenges such as tracking loss and poor real-time performance in low-texture environments. In response to these issues, this research proposes a real-time localization and mapping algorithm based on the fusion of multiple features, utilizing point, line, surface, and matrix decomposition characteristics. Building upon this foundation, the algorithm integrates multiple sensors to design a vision-based real-time localization and mapping algorithm for wheeled robots. The study concludes with experimental validation on a two-wheeled robot platform. The results indicated that the multi-feature fusion algorithm achieved the highest average accuracy in both conventional indoor datasets (84.57%) and sparse-feature indoor datasets (82.37%). In indoor scenarios, the vision-based algorithm integrating multiple sensors achieved an average accuracy of 85.4% with a processing time of 64.4 ms. In outdoor scenarios, the proposed algorithm exhibited a 14.51% accuracy improvement over a vision-based algorithm without closed-loop detection. In summary, the proposed method demonstrated outstanding accuracy and real-time performance, exhibiting favorable application effects across various practical scenarios.

Fast identification of coherent sound sources with the covariance matrix fitting method based on non-synchronous measurements

The Non-Synchronous Measurements is particularly effective at expanding the operating frequency range of a single microphone array. The completed cross-spectral matrix of the synthetic array, when combined with high-resolution imaging algorithms, can yield accurate sound source identification results. However, when matrix completion algorithms are applied to large synthetic arrays, their computational complexity increases significantly. Furthermore, existing integrations with high-resolution imaging algorithms often encounter difficulties in the presence of coherent sound sources. To address this problem, this paper introduces the accelerated gradient descent algorithm for the covariance matrix fitting by orthogonal least squares. The matrix completion model for non-synchronous measurements is initially simplified through matrix decomposition, thereby enabling the rapid completion of the cross-spectral matrix using the accelerated gradient descent algorithm. This is then followed by the application of the covariance matrix fitting by orthogonal least squares to achieve quick and precise identification of coherent sound sources employing the completed cross-spectral matrix. The performance of the algorithm is evaluated using numerical simulations and validated through loudspeaker experiments in an anechoic chamber. The results from these simulations and experiments reveal that the proposed algorithm not only improves matrix completion performance on large synthetic arrays but also accurately identifies the locations and correlation coefficients of coherent sound sources.

SAM-PARSER: Fine-Tuning SAM Efficiently by Parameter Space Reconstruction

Segment Anything Model (SAM) has received remarkable attention as it offers a powerful and versatile solution for object segmentation in images. However, fine-tuning SAM for downstream segmentation tasks under different scenarios remains a challenge, as the varied characteristics of different scenarios naturally requires diverse model parameter spaces. Most existing fine-tuning methods attempt to bridge the gaps among different scenarios by introducing a set of new parameters to modify SAM's original parameter space. Unlike these works, in this paper, we propose fine-tuning SAM efficiently by parameter space reconstruction (SAM-PARSER), which introduce nearly zero trainable parameters during fine-tuning. In SAM-PARSER, we assume that SAM's original parameter space is relatively complete, so that its bases are able to reconstruct the parameter space of a new scenario. We obtain the bases by matrix decomposition, and fine-tuning the coefficients to reconstruct the parameter space tailored to the new scenario by an optimal linear combination of the bases. Experimental results show that SAM-PARSER exhibits superior segmentation performance across various scenarios, while reducing the number of trainable parameters by approximately 290 times compared with current parameter-efficient fine-tuning methods.

On Rotfel'd type inequalities for sectorial matrices

Using a matrix decomposition for sectorial matrices and an AM-GM inequality for singular values, we present a new Rotfel'd type inequality for sectorial matrices, which generalizes and partially improves some results by Zhang. We also give alternative simpler proofs of a main result of a recent paper by Yang, Lu and Chen as well as that by Fu and Liu.

Review of polarization-based technology for biomedical applications

Polarimetry is a powerful optical tool in the biomedical field, providing more comprehensive information on the sub-wavelength micro-physical structure of a sample than traditional light intensity measurement techniques. This review summarizes the concepts and techniques of polarization and its biomedical applications. Specifically, we first briefly describe the basic principles of polarized light and the Mueller matrix (MM) decomposition method, followed by some research progress of polarimetric measurement techniques in recent years. Finally, we introduce some studies on biological tissues and cells, and then illustrate the application value of polarization optical method.

Personalized Intelligent Recommendation Model Construction Based on Online Learning Behavior Features and CNN

The current intelligent recommendation models in online learning systems suffer from data sparsity and cold start problems. To address the data sparsity problem, a collaborative filtering recommendation algorithm model (SACM-CF) based on an automatic coding machine is proposed in the study. The model can extract the online learning behavior features of users and match these features with the learning resource features to improve the recommendation precision. For the cold-start problem, the study proposes a CBCNN model based on CNN, using the language model as the input of the model and the implicit factor as the output of the model. To avoid the problem of over-smoothing the implicit factor model, which affects the recommendation precision, an improved matrix decomposition method is proposed to constrain the output of the CNN and improve the model precision. The RMSE of SACM-CF is 0.844 and the MAE is 0.625. The MAE value of CBCNN is 0.72, the recall value is 0.65, the recommendation precision is 0.954 and the F1-score is 0.84. The metrics of SACM-CF and CBCNN are better than the existing state-of-the-art recommendation models. SACM-CF and CBCNN outperform the existing state-of-the-art intelligent recommendation models in all metrics. Therefore, the SACM-CF model and the CBCNN model can effectively improve the precision of the online learning system in recommending interesting learning resources to users, thus avoiding users' wasted learning time in searching and selecting learning resources and improving users' learning efficiency.

A deep contrastive framework for unsupervised temporal link prediction in dynamic networks

In dynamic networks, temporal link prediction aims to predict the appearance and disappearance of links in future snapshots based on the network structure we have observed. It also plays a crucial role in network analysis and predicting the behavior of the dynamic system. However, most existing studies only focus on supervised temporal link prediction problems, i.e., taking part of the links in future snapshots as supervised information. The ones that can solve the unsupervised temporal link prediction problem are mainly based on matrix decomposition, which lack the capability to automatically extract nonlinear spatial and temporal features from dynamic networks. The most challenging part of this problem is to extract the inherent evolution of the patterns hidden in dynamic networks in unsupervised ways. Inspired by the application and achievement of contrastive learning in network representation learning, we propose a novel deep Contrastive framework for unsupervised Temporal Link Prediction (CTLP). Our framework is based on a deep encoder-decoder architecture, which can capture the nonlinear structure and temporal features automatically and can predict future links of subsequent snapshots of dynamic networks in an unsupervised manner. Besides, CTLP could handle the multi-step temporal link prediction problem of dynamic networks through attenuation modeling across the snapshots. Extensive experiments on temporal link prediction show that our CTLP framework significantly outperforms state-of-the-art unsupervised methods, and even outperforms the supervised methods in some cases.

Symmetric circulant matrix decomposition-based multivariable group sparse coding for rolling bearing fault diagnosis

Singular value decomposition technique proves its effectiveness in mechanical signal analysis by decomposing the test signal into a series of singular spectral components of different frequency bands. Nevertheless, how to adapt this technology to the needs of cyclo-nonstationary signal and how to set the decomposition number while maintaining detailed features to obtain the optimal component containing the most fault information, remains an important issue that needs to be addressed in the field of mechanical fault diagnosis. To overcome these disadvantages, the symmetric circulant matrix decomposition (SCMD) is presented. Two main ideas structure the present technique. Firstly, symmetric circulant matrix is used to generate eigenvectors, which will better adapt to the cyclo-nonstationary signal associated with the structural symmetry of rotating machinery. Then, an impulse fluctuation measure is established to adaptively search for the decomposition number and extract the optimal component. Moreover, to better improve the impulse extraction effect of SCMD, the multivariate group sparse coding based on the multivariate correlation characteristics and intra group sparsity characteristics of impulse signals is proposed, which can enhance impulse features while preserving fault details as much as possible. The reliability and feasibility of the proposed method are verified by the experimental signals. The comparison with several classic methods shows that this method is more effectiveness in weak feature extraction.

An image quality assessment method based on edge extraction and singular value for blurriness

The automatic assessment of perceived image quality is crucial in the field of image processing. To achieve this idea, we propose an image quality assessment (IQA) method for blurriness. The features of gradient and singular value were extracted in this method instead of the single feature in the traditional IQA algorithms. According to the insufficient size of existing public image quality assessment datasets to support deep learning, machine learning was introduced to fuse the features of multiple domains, and a new no-reference (NR) IQA method for blurriness denoted Feature fusion IQA(Ffu-IQA) was proposed. The Ffu-IQA uses a probabilistic model to estimate the probability of each edge detection blur in the image, and then uses machine learning to aggregate the probability information to obtain the edge quality score. After that uses the singular value obtained by singular value decomposition of the image matrix to calculate the singular value score. Finally, machine learning pooling is used to obtain the true quality score. Ffu-IQA achieves PLCC scores of 0.9570 and 0.9616 on CSIQ and TID2013, respectively, and SROCC scores of 0.9380 and 0.9531, which are better than most traditional image quality assessment methods for blurriness.

Landmark-based k-factorization multi-view subspace clustering

Multi-view subspace clustering (MSC) has gained significant popularity due to its ability to overcome noise and bias present in single views by fusing information from multiple views. MSC enhances the accuracy and robustness of clustering. However, many existing MSC methods suffer from high computational costs and sub-optimal performance on large-scale datasets, since they often construct a fused graph directly from high-dimensional data and then apply spectral clustering. To address these challenges, we propose a framework called Landmark-based k-Factorization Multi-view Subspace Clustering (LKMSC). Our framework tackles these issues by generating a small number of landmarks p≪n for each view, which form a landmark graph. We represent each entire view as a linear combination of these landmarks, where n is the number of data points. To address inconsistencies that naturally occur in landmark graphs due to multiple views, we utilize Landmark Graphs Alignment. This technique incorporates both feature and structural information to capture the correspondence between landmarks. The aligned graphs are then factorized into consensus k groups, emphasizing structural sparsity. LKMSC efficiently extracts features and reduces dimensionality of the input dataset. It eliminates the need for learning large-scale affinity matrix and feature decomposition. Our approach exhibits linear computational complexity and has demonstrated promising results in numerous experimental evaluations across a range of datasets. The source codes and datasets are available at https://github.com/FY0109/LKMSC.

Randomized two-sided subspace iteration for low-rank matrix and tensor decomposition

The low-rank approximation of big data matrices and tensors plays a pivotal role in many modern applications. Although, a truncated version of the singular value decomposition (SVD) furnishes the best approximation, its computation is challenging on modern, multicore architectures. Recently, the randomized subspace iteration has shown to be a powerful tool in approximating large-scale matrices. In this paper we present a two-sided variant of the randomized subspace iteration. Novel in our work is the exploitation of the unpivoted QR factorization, rather than the SVD, for factorizing the compressed matrix. Hence our algorithm is a randomized rank-revealing URV decomposition. We prove the rank-revealingness of our algorithm by establishing bounds for the singular values as well as the other blocks of the compressed matrix. We further provide bounds on the error of the low-rank approximations of the proposed algorithm, in both 2- and Frobenius norm. In addition, we employ the proposed algorithm to efficiently compute low rank tensor decompositions: we present two randomized algorithms, one for the truncated higher-order SVD, and the other for the tensor SVD. We conduct numerical tests on (i) various classes of matrices, and (ii) synthetic tensors and real datasets to demonstrate the efficacy of the proposed algorithms.