Matrix Decomposition Method Research Articles

Mueller matrix analysis of a biologically sourced engineered tissue construct as polarimetric phantom.

The polarimetric properties of biological tissues are often difficult to ascertain independent of their complex structural and organizational features. Conventional polarimetric tissue phantoms have well-characterized optical properties but are overly simplified. We demonstrate that an innovative, biologically sourced, engineered tissue construct better recapitulates the desired structural and polarimetric properties of native collagenous tissues, with the added benefit of potential tunability of the polarimetric response. We bridge the gap between non-biological polarimetric phantoms and native tissues. We aim to evaluate a synthesized tissue construct for its effectiveness as a phantom that mimics the polarimetric properties in typical collagenous tissues. We use a fibroblast-derived, ring-shaped engineered tissue construct as an innovative tissue phantom for polarimetric imaging. We perform polarimetry measurements and subsequent analysis using the Mueller matrix decomposition and Mueller matrix transformation methods. Scalar polarimetric parameters of the engineered tissue are analyzed at different time points for both a control group and for those treated with the transforming growth factor . Second-harmonic generation (SHG) imaging and three-dimensional collagen fiber organization analysis are also applied. We identify linear retardance and circular depolarization as the parameters that are most sensitive to the tissue culture time and the addition of . Aside from a statistically significant increase over time, the behavior of linear retardance and circular depolarization indicates that the addition of accelerates the growth of the engineered tissue, which is consistent with expectations. We also find through SHG images that collagen fiber organization becomes more aligned over time but is not susceptible to the addition of . The engineered tissue construct exhibits changes in polarimetric properties, especially linear retardance and circular depolarization, over culture time and under treatments. This tissue construct has the potential to act as a controlled modular optical phantom for polarimetric-based methods.

Efficient Random Field Generation With Rotational Anisotropy for Probabilistic SPH Analysis of Slope Failure

ABSTRACTDue to geological processes such as sedimentation, tectonic movement, and backfilling, natural soil often exhibits characteristics of rotated anisotropy. Recent studies have shown the significant impact of rotated anisotropy on slope stability. However, little research has explored how this rotated anisotropy affects the large deformations occurring after slope failure. Therefore, this study integrates rotated random field theory with smoothed particle hydrodynamics (SPH) to investigate its influence on post‐failure slope behavior. Focusing on a typical slope scenario, this research utilizes graphics processing unit (GPU)–accelerated covariance matrix decomposition (CMD) method to create rotated anisotropy random fields and applies the SPH framework for analysis. It examines the influence of rotated anisotropy angles and the cross‐correlation between cohesion and internal friction angle on landslides. The results indicate that the rotational anisotropy of the slope significantly influences post‐failure behavior. When the rotation angle is close to the slope surface, it tends to amplify both the magnitude and variability of slope failure. Furthermore, the study evaluates the efficiency of generating these random fields and emphasizes the substantial computational speed improvements achieved with GPU acceleration. These findings offer a robust approach for probabilistic analysis of slope large deformations considering rotated anisotropy. They provide a theoretical foundation for accurately assessing the risk of slope collapse, holding significant practical implications for geotechnical engineering.

A short-term wind power forecasting model based on CUR

Abstract Wind power forecasting plays a crucial role in the contemporary renewable energy system. During the process of forecasting wind power, the establishment of LSTM models requires a lot of time and effort, and the interpretability of prediction results is poor, making it difficult to understand and verify the results. To accomplish interpretable and precise wind power predictions, this paper introduces a wind power prediction algorithm model leveraging CUR matrix decomposition. The CUR matrix decomposition method first obtains the original matrix A (wind power data matrix). The statistical influence scores of rows and columns in A are calculated, and several columns and rows with higher scores are selected to form a low dimensional matrix C and R. Matrix C contains the main characteristic factors that affect wind power, while matrix R contains time series features. Then, the matrix U is approximated by A, C, and R to transform the preference feature extraction problem in high-dimensional space into a matrix analysis problem in low-dimensional space, making it more interpretable and accurate. The efficacy of the wind power forecasting approach utilizing CUR matrix decomposition is assessed and confirmed on openly accessible datasets. The results indicate that the CUR matrix decomposition method has good prediction accuracy and interpretability.

Low-rank tensor completion based on tensor train rank with partially overlapped sub-blocks and total variation

Recently, the low-rank tensor completion method based on tensor train (TT) rank has achieved promising performance. Ket augmentation (KA) is commonly used in TT rank-based methods to improve the performance by converting low-dimensional tensors to higher-dimensional tensors. However, block artifacts are caused since KA also destroys the original structure and image continuity of original low-dimensional tensors. To tackle this issue, a low-rank tensor completion method based on TT rank with tensor augmentation by partially overlapped sub-blocks (TAPOS) and total variation (TV) is proposed in this paper. The proposed TAPOS preserves the image continuity of the original tensor and enhances the low-rankness of the generated higher-dimensional tensors, and a weighted de-augmentation method is used to assign different weights to the elements of sub-blocks and further reduce the block artifacts. To further alleviate the block artifacts and improve reconstruction accuracy, TV is introduced in the TAPOS-based model to add the piecewise smooth prior. The parallel matrix decomposition method is introduced to estimate the TT rank to reduce the computational cost. Numerical experiments show that the proposed method outperforms the existing state-of-the-art methods.

Prediction of miRNA-disease Associations by Deep Matrix Decomposition Method based on Fused Similarity Information

Prediction of miRNA-disease Associations by Deep Matrix Decomposition Method based on Fused Similarity Information

Characterization of polarization properties of colorectal cancer using decomposition Mueller matrix method

Rectal cancer is the third most prevalent cancer diagnosed and is traditionally screened using colonoscopy. Meanwhile, polarization characteristic measurement has emerged as an attractive alternative in recent years owing to its deep analysis of the structure of samples and non-invasive nature. Accordingly, this study employed the Mueller matrix decomposition method to measure the effective optical parameters of 100 slices from 20 healthy rectal tissue samples and 100 slices from 20 cancerous rectal tissue samples. The mean values and expression levels of the linear birefringence, circular birefringence, linear dichroism, circular dichroism, and depolarization index properties of the samples were compared using t-tests and ANOVA tests. The experimental results showed that the linear birefringence, orientation angle of linear dichroism, and values of linear dichroism and circular dichroism showed significant differences between the different tissue types. Thus, these parameters may serve as useful biomarkers for the diagnosis of rectal cancer.

APPLICATION OF THE SINGULAR DECOMPOSITION OF THE MATRIX IN SOLVING INCORRECT GEODESIC PROBLEMS

The most reliable method for solving linear equations of the least squares principle, which can be used to solve incorrect geodetic problems, is based on matrix factorization, which is called a singular expansion. Some other methods require less machine time and memory. However, they are less effective in taking into account the errors of the source information, rounding errors, and linear dependence. The methodology of such research is that for any matrix A and any two orthogonal matrices U and V, there is a matrix , which is determined as T U AV  . The idea of a singular decomposition is that by choosing the right matrices U and V, you can convert most elements of the matrix  to zero and make it diagonal with non-negative elements. The novelty and relevance of scientific solutions lie in the feasibility of using a singular decomposition of the matrix to obtain linear equations of the least squares method, which can be used to solve incorrect geodetic problems. The purpose of scientific research is to obtain a stable solution of parametric equations of corrections to the results of mea- surements in incorrect geodetic problems. Based on the performed research on the application of the singular decomposition method for solving incorrect geodetic problems, we can summarize the following results. A singular expansion of a real matrix A is any factorization T A U W  of a matrix with orthogonal columns U, an orthogonal matrix W , and a diagonal matrix , the elements of which are called singular numbers of the matrix A, and the columns of matrices U and W — left and right singular vectors. If the matrix A has a full rank, then its solution will be unique and stable, which can be obtained by different methods. However, the method of singular decomposition, in contrast to other methods, makes it possible to solve problems with incomplete rank. Research shows that the method of solving normal equations by sequential exclusion of unknowns (Gaussian method), which is quite common in geod- esy, does not provide stable solutions for poorly conditioned or incorrect geodetic problems. Therefore, in the case of unstable systems of equations, it is proposed to use the method of singular matrix decomposition, which in computational mathematics is called SVD. The SVD singular decomposition method makes it possible to obtain stable solutions to both stable and by nature unstable problems. This possibility to solve incorrect geodetic problems is associated with the application of some limit , the choice of which can be made by the relative errors of the matrix of coefficients of parametric equations of corrections A and the vector of results of geodetic measurements L . Moreover, the solution of the system of normal equations obtained by the SVD method will have the shortest length. Thus, applying the apparatus of the singular decomposition of the matrix of coefficients of parametric equations of correc- tions to the results of geodetic measurements, we obtained new formulas for estimating the accuracy of the least squares method in solving incorrect geodetic problems. The derived formulas have a compact form and allow the easy calculation of elements  and XQ estimates of accuracy, almost ignoring the complex procedure of rotation of the matrix of coefficients of normal equations.

A Proportional–Integral Observer-Based Dynamic Event-Triggered Consensus Protocol for Nonlinear Positive Multi-Agent Systems

This paper investigates the state estimation and event-triggered control for positive nonlinear multi-agent systems. Firstly, a proportional–integral observer is established to estimate the states of the considered nonlinear positive multi-agent systems based on the matrix decomposition method. Then, a dynamic event-triggered mechanism is constructed, and a control protocol is proposed based on the proportional–integral observer and event-triggered mechanism. By combining linear programming with linear co-positive Lyapunov functions, the considered multi-agent systems are guaranteed to be positive and achieve consensus. Moreover, by introducing three new variables and a finite vector, the final convergence point can be changed based on the given vector. Finally, two illustrative examples demonstrate the validity of the proposed theoretical results.

RPCA-based thermoacoustic imaging for microwave ablation monitoring

Microwave ablation (MWA) is a potent cancer treatment tool, but its effectiveness can be hindered by the lack of visual feedback. This paper validates the feasibility of using microwave-induced thermoacoustic imaging (TAI) technique to monitor the MWA process. A feasibility analysis was conducted at the principle level and a high-performance real-time TAI system was introduced. To address the interference caused by MWA, a robust principal component analysis (RPCA)-based method for TAI was proposed. This method leverages the correlation between multiple signal frames to eliminate interference. RPCA’s effectiveness in TAI was demonstrated through three sets of different experiments. Experiments demonstrated that TAI can effectively monitors the MWA process. This work represents the first application of RPCA-related matrix decomposition methods in TAI, paving the way for the application of TAI in more complex clinical scenarios. By providing rapid and accurate visual feedback, this research advances MWA technology.

Full‐Parameter Symmetric Jones Matrix Construction and Non‐Orthogonal‐Polarization Multiplexed Wavefront Shaping Over a Lossy Metasurface

AbstractAccurate full‐parameter construction of the Jones matrix is of great significance for encoding multiple functions in a single metasurface. Supercells composed of several elements are used for this purpose through coherent superposition. But all the elements in the reported studies should be lossless with near‐unity transmission, which limits the material system and restricts the Jones matrix construction in a unitary manner. Here a non‐unitary matrix decomposition method is proposed to build the supercell using a pair of 0°‐oriented rods and a pair of 45°‐oriented rods for on‐demand design of arbitrary symmetric Jones matrices. This method is applicable for lossy metasurfaces and offers straightforward physical guidance for structure design without optimization. The accuracy of the on‐demand Jones matrix generation is demonstrated by several 3D‐printed alumina metalenses with 3‐, 4‐, and 6‐channel polarization‐multiplexed focusing. The study opens a new pathway for non‐silicon meta‐optics and holds great potential for dynamic or switchable applications.

Multi-interest adaptive unscented Kalman filter based on improved matrix decomposition methods for lithium-ion battery state of charge estimation

Accurately predicting the state of charge (SOC) is crucial to improving Li-ion battery performance. However, available model-based estimation approaches still face challenges in handling model uncertainty and measurement noise effects on parameter identification. Besides, the widely used unscented Kalman filter (UKF) algorithm has limitations in electric vehicles as it requires the error covariance matrix to maintain positive definiteness, limiting its applicability under certain conditions. This study introduces the bias-compensated forgetting factor recursive least squares (BCFFRLS) method for parameter estimation within the second-order RC equivalent circuit model specific to the INR18650-20R battery. Furthermore, we propose a novel algorithm named the optimization multi-interest adaptive unscented Kalman filter (O-MIAUKF). This algorithm is designed to address stability and robustness issues with traditional UKF encounters in dynamic environments. Experimental validation demonstrates that the O-MIAUKF algorithm excels in maintaining strong stability and robustness in various working conditions, accurately estimating SOC even with a non-positive covariance matrix. The SOC estimation error remains stable at 0.8 %, which is lower than that of the current Extended Kalman Filter (EKF), UKF, and Dual Extended Kalman Filter (DEKF).

Heterogeneous graph inference with range constrainted [formula omitted]-collaborative matrix factorization for small molecule-miRNA association prediction

MicroRNAs (miRNAs) play a vital role in regulating gene expression and various biological processes. As a result, they have been identified as effective targets for small molecule (SM) drugs in disease treatment. Heterogeneous graph inference stands as a classical approach for predicting SM-miRNA associations, showcasing commendable convergence accuracy and speed. However, most existing methods do not adequately address the inherent sparsity in SM-miRNA association networks, and imprecise SM/miRNA similarity metrics reduce the accuracy of predicting SM-miRNA associations. In this research, we proposed a heterogeneous graph inference with range constrained L2,1-collaborative matrix factorization (HGIRCLMF) method to predict potential SM-miRNA associations. First, we computed the multi-source similarities of SM/miRNA and integrated these similarity information into a comprehensive SM/miRNA similarity. This step improved the accuracy of SM and miRNA similarity, ensuring reliability for the subsequent inference of the heterogeneity map. Second, we used a range constrained L2,1-collaborative matrix factorization (RCLMF) model to pre-populate the SM-miRNA association matrix with missing values. In this step, we developed a novel matrix decomposition method that enhances the robustness and formative nature of SM-miRNA edges between SM networks and miRNA networks. Next, we built a well-established SM-miRNA heterogeneous network utilizing the processed biological information. Finally, HGIRCLMF used this network data to infer unknown association pair scores. We implemented four cross-validation experiments on two distinct datasets, and HGIRCLMF acquired the highest areas under the curve, surpassing six state-of-the-art computational approaches. Furthermore, we performed three case studies to validate the predictive power of our method in practical application.

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.

Mueller matrix-based characterization of cervical tissue sections: a quantitative comparison of polar and differential decomposition methods.

Quantitative optical polarimetry has received considerable recent attention owing to its potential for being an efficient diagnosis and characterizing tool with potential applications in biomedical research and various other disciplines. In this regard, it is crucial to validate various Mueller matrix (MM) decomposition methods, which are utilized to extract and quantify the intrinsic individual polarization anisotropy properties of various complex optical media. To quantitatively compare the performance of both polar and differential MM decomposition methods for probing the structural and morphological changes in complex optical media through analyzing their intrinsic individual polarization parameters, which are extracted using the respective decomposition algorithms. We also intend to utilize the decomposition-derived anisotropy parameters to distinguish among the cervical tissues with different grades of cervical intraepithelial neoplasia (CIN) and to characterize the healing efficiency of an organic crystal. Polarization MM of the cervical tissues with different grades of CIN and the different stages of the self-healing crystal are recorded with a home-built MM imaging setup in the transmission detection geometry with a spatial resolution of . The measured MMs are then processed with both the polar and differential MM decomposition methods to extract the individual polarization parameters of the respective samples. The derived polarization parameters are further analyzed to validate and compare the performance of both the MM decomposition methods for probing and characterizing the structural changes in the respective investigated optical media through their decomposition-derived intrinsic individual polarization properties. Pronounced differences in the decomposed-derived polarization anisotropy parameters are observed for cervical tissue sections with different grades of CIN. While a significant increase in the depolarization parameter is obtained with the increment of CIN stages for both the polar [ for CIN grade one (CIN-I) and for CIN grade two (CIN-II))] and differential ( for CIN-I and for CIN-II) decomposition methods, a trend reversal is seen for the linear diattenuation parameter , indicating the structural distortion in the cervical morphology due to the CIN disease. More importantly, with the differential decomposition algorithm, the magnitude of the derived parameter decreases from 0.26 to 0.19 with the progression of CIN, which was not being probed by the polar decomposition method. Our results demonstrate that the differential decomposition of MM holds certain advantages over the polar decomposition method to characterize and probe the structural changes in the cervical tissues with different grades of CIN. Although the quantified individual polarization parameters obtained through both the MM decomposition methods can be used as useful metrics to characterize various optical media, in case of complex turbid media such as biological tissues, incorporation of the differential decomposition technique may yield more efficient information. Also, the study highlights the utilization of MM polarimetry with an appropriate decomposition technique as an efficient diagnostic and characterizing tool in the realm of biomedical clinical research, and various other disciplines.

MDSVDNV: predicting microbe-drug associations by singular value decomposition and Node2vec.

Recent researches have demonstrated that microbes are crucial for the growth and development of the human body, the movement of nutrients, and human health. Diseases may arise as a result of disruptions and imbalances in the microbiome. The pathological investigation of associated diseases and the advancement of clinical medicine can both benefit from the identification of drug-associated microbes. In this article, we proposed a new prediction model called MDSVDNV to infer potential microbe-drug associations, in which the Node2vec network embedding approach and the singular value decomposition (SVD) matrix decomposition method were first adopted to produce linear and non-linear representations of microbe interactions. Compared with state-of-the-art competitive methods, intensive experimental results demonstrated that MDSVDNV could achieve the best AUC value of 98.51% under a 5-fold CV, which indicated that MDSVDNV outperformed existing competing models and may be an effective method for discovering latent microbe-drug associations in the future.

Decomposition Mueller matrix polarimetry for enhanced miRNA detection with antimonene-based surface plasmon resonance sensor and DNA-linked gold nanoparticle signal amplification

A decomposition Mueller matrix method is proposed for detection of miRNA and enhanced by using a surface plasmon resonance (SPR). In the proposed approach, a Mueller matrix decomposition method is employed to extract the linear birefringence (LB) and circular dichroism (CD) properties of the miRNA sample. The accuracy of the LB and CD measurements is enhanced through the use of a high-resolution antimonene-based SPR prism coupler with DNA-linked gold nanoparticles (AuNPs). The feasibility of the proposed method is demonstrated by measuring the LB orientation angle (α) and CD property (R) of two miRNA aqueous solutions (hsa-miR-125-5p and hsa-miR-21-5p) over the concentration range of 0∼1000 fM in both cases. The results show that, for both samples, α and R vary linearly with the change in the miRNA concentration. Furthermore, the values of α and R obtained for the two samples are quantifiably different, and hence the selectivity of the proposed SPR sensor is confirmed. Overall, the results highlight the potential of the proposed sensor as a valuable tool for miRNA detection with prospective applications in cancer diagnosis.

Application of singular value decomposition in image compression

The field of computer graphics and multimedia technologies places significant emphasis on the study path of image compression. The increasing prevalence of digital photographs has led to a significant growth in the size of image files, hence presenting storage and transmission issues. The Singular Value Decomposition (SVD) is a matrix decomposition method that possesses significant computational capacity and finds utility in various domains. In recent years, SVD has emerged as a prevalent technique in the domain of image processing, particularly in the context of image compression, yielding notable outcomes. This work primarily employs a literature review research methodology to explore the application of SVD. Specifically, SVD is applied to image compression using Matlab. The approach holds significance due to its ability to achieve efficient compression of digital images, hence enhancing transmission efficiency without compromising image quality.

A novel efficient Rank-Revealing QR matrix and Schur decomposition method for big data mining and clustering (RRQR-SDM)

Big Data is an emerging technology with enormous potential to develop business and its administration. Due to the enormous volume, efficient data mining and clustering methods are crucial to extracting meaningful insights and patterns from large-scale datasets. Problems may arise from the need to analyze, capture, share, store, and visualize the data. Several methods have already been proposed for mining knowledge from big data. It is practically inefficient or impossible to handle these massive data using the proposed methods in a single machine because big data are frequently acquired from dispersed locations and stored on several machines. Matrix decomposition is one of the critical strategies to retrieve knowledge from diverse, noisy, huge data generated by modern applications and stored in dispersed locations. This study proposes a novel approach called the Rank-Revealing QR Matrix and Schur Decomposition Method (RRQR-SDM) specifically designed for big data mining and clustering tasks. The RRQR-SDM is designed to reveal the rank of the data matrix in a computationally efficient manner by using a modified QR decomposition, eliminating the need for expensive Singular Value Decomposition (SVD) computations. The proposed RRQR-SDM method offers several advantages over existing approaches. Firstly, exploiting the inherent low-rank structure reduces the computational complexity associated with large-scale datasets. By revealing the rank of the input matrix, it enables dimensionality reduction and efficient data compression. Secondly, the Schur decomposition enhances the interpretability of the data by providing a clear separation between the relevant and irrelevant components. This feature makes the RRQR-SDM method particularly suitable for data mining and clustering tasks where identifying the most significant features is essential. To evaluate the performance of the RRQR-SDM method, extensive experiments were conducted on various big data datasets. The results demonstrate that the proposed method outperforms state-of-the-art computational efficiency and clustering accuracy techniques.

Enhancing the SVD compression losslessly

Orthonormality is the foundation of a number of matrix decomposition methods. For example, Singular Value Decomposition (SVD) implements the compression by factoring a matrix with orthonormal parts and is pervasively utilized in various fields. Orthonormality, however, inherently includes constraints that would induce redundant information, preventing SVD from deeper compression and even making it frustrated as the data fidelity is strictly required. In this paper, we theoretically prove that these redundances resulted by orthonormality can be completely eliminated in a lossless manner. An enhanced version of SVD, namely E-SVD, is accordingly established to losslessly and quickly release constraints and recover the orthonormal parts in SVD. According to our theory, advantages of E-SVD over SVD become increasingly evident with the rising requirement of data fidelity. In particular, E-SVD will reduce 25% storage units as SVD reaches its limitation and fails to compress data. Empirical evidences from remote sensing and internet of things justify our theory by demonstrating the consistent compression superiority of E-SVD over SVD, and the additional calculation cost of E-SVD is of the same magnitude with SVD. Digital image compression experiment with typical size 375 × 500 also shows that E-SVD needs the least storage space as compared to alternative compression solutions when the rank is sufficient to maintain a good visual quality. The presented theory sheds insightful lights on the constraint solution in orthonormal matrices and E-SVD, guaranteed by which will profoundly enhance the SVD-based compression in the context of explosive growth in both data acquisition and fidelity levels.