Matrix Decomposition Research Articles

Inferring sparse structure in genotype-phenotype maps.

Correlation among multiple phenotypes across related individuals may reflect some pattern of shared genetic architecture: individual genetic loci affect multiple phenotypes (an effect known as pleiotropy), creating observable relationships between phenotypes. A natural hypothesis is that pleiotropic effects reflect a relatively small set of common "core" cellular processes: each genetic locus affects one or a few core processes, and these core processes in turn determine the observed phenotypes. Here, we propose a method to infer such structure in genotype-phenotype data. Our approach, sparse structure discovery (SSD) is based on a penalized matrix decomposition designed to identify latent structure that is low-dimensional (many fewer core processes than phenotypes and genetic loci), locus-sparse (each locus affects few core processes), and/or phenotype-sparse (each phenotype is influenced by few core processes). Our use of sparsity as a guide in the matrix decomposition is motivated by the results of a novel empirical test indicating evidence of sparse structure in several recent genotype-phenotype datasets. First, we use synthetic data to show that our SSD approach can accurately recover core processes if each genetic locus affects few core processes or if each phenotype is affected by few core processes. Next, we apply the method to three datasets spanning adaptive mutations in yeast, genotoxin robustness assay in human cell lines, and genetic loci identified from a yeast cross, and evaluate the biological plausibility of the core process identified. More generally, we propose sparsity as a guiding prior for resolving latent structure in empirical genotype-phenotype maps.

Distributed fusion robust filter for multisensor networked singular control system with uncertain variances and missing measurement

AbstractA distributed fusion time‐varying robust filtering algorithm for multisensor networked singular control system is studied in this paper, mainly aiming at the system with missing measurement and uncertain variances in practical application. First, the singular value decomposition (SVD) method and de‐randomization method are used to transform the singular control system into a standard system only with uncertain variances. Based on the new standard system, a minimax robust local Kalman filter is proposed by using the minimax robust estimation principle, which ensures that the actual filtering error variance has the corresponding minimum upper bound for all allowable uncertainties. Further, the robust local and distributed fusion filters for original singular control systems are proposed, and the actual and conservative filtering error variances are obtained. Their robustness is proved by Lyapunov equation method and nonnegative definite matrix decomposition method. A simulation example of two‐loop system verifies the effectiveness of the proposed results.

Can multipartite entanglement be characterized by two-point connected correlation functions?

We discuss under which conditions multipartite entanglement in mixed quantum states can be characterized only in terms of two-point connected correlation functions, as it is the case for pure states. In turn, the latter correlations are defined via a suitable combination of (disconnected) one- and two-point correlation functions. In contrast to the case of pure states, conditions to be satisfied turn out to be rather severe. However, we were able to identify some interesting cases, as when the point-independence is valid of the one-point correlations in each possible decomposition of the density matrix, or when the operators that enter in the correlations are (semi-)positive/negative defined.

The dual index and dual core generalized inverse

Abstract In this article, we introduce the dual index and dual core generalized inverse (DCGI). By applying rank equation, generalized inverse, and matrix decomposition, we give several characterizations of the dual index when it is equal to 1. We realize that if DCGI exists, then it is unique. We derive a compact formula for DCGI and a series of equivalent characterizations of the existence of the inverse. It is worth noting that the dual index of A ^ \widehat{A} is equal to 1 if and only if its DCGI exists. When the dual index of A ^ \widehat{A} is equal to 1, we study dual Moore-Penrose generalized inverse (DMPGI) and dual group generalized inverse (DGGI) and consider the relationships among DCGI, DMPGI, DGGI, Moore-Penrose dual generalized inverse, and other dual generalized inverses. In addition, we consider symmetric dual matrix and its dual generalized inverses. Finally, two examples are given to illustrate the application of DCGI in linear dual equations.

Weakly-supervised content-based video moment retrieval using low-rank video representation

Content-based video moment retrieval (CVMR) aims to localize a successive sequence of frames in an untrimmed reference video, called target moment, that is semantically corresponding to a given query video. Current state-of-the-art CVMR methods are mainly developed using frame-level annotation, which is often quite expensive to collect. In this paper, we aim to develop a weakly-supervised CVMR method, which uses coarse-grained video-level annotations during training. Under weak supervision, video localizers require more discriminative frame-level video features. To achieve this goal, we proposed a novel prior, termed low-rank prior, based on an observation that the frame-level feature of a video should have low-rank properties. We demonstrated that the low-rank features are more discriminative and are beneficial to accurately localize the action boundaries. To produce a low-rank feature, we designed a low-rank feature reconstruction (LFR) operator. A new differentiable matrix decomposition approach is proposed to generate the low-rank reconstruction of the input matrix, meanwhile ensuring that the matrix decomposition process is differentiable. Based on the LFR, we developed a new weakly-supervised CVMR model which produces low-rank video representation and performs semantic consistency measures to discover the semantically matched segment in the reference video to the query video. Extensive experiments demonstrate that our method outperforms state-of-the-art weakly-supervised methods consistently and even achieves competing performance to fully-supervised baselines.

Precision Heart Rate Estimation Using a PPG Sensor Patch Equipped with New Algorithms of Pre-Quality Checking and Hankel Decomposition.

A new method for accurately estimating heart rates based on a single photoplethysmography (PPG) signal and accelerations is proposed in this study, considering motion artifacts due to subjects' hand motions and walking. The method comprises two sub-algorithms: pre-quality checking and motion artifact removal (MAR) via Hankel decomposition. PPGs and accelerations were collected using a wearable device equipped with a PPG sensor patch and a 3-axis accelerometer. The motion artifacts caused by hand movements and walking were effectively mitigated by the two aforementioned sub-algorithms. The first sub-algorithm utilized a new quality-assessment criterion to identify highly noise-contaminated PPG signals and exclude them from subsequent processing. The second sub-algorithm employed the Hankel matrix and singular value decomposition (SVD) to effectively identify, decompose, and remove motion artifacts. Experimental data collected during hand-moving and walking were considered for evaluation. The performance of the proposed algorithms was assessed using the datasets from the IEEE Signal Processing Cup 2015. The obtained results demonstrated an average error of merely 0.7345 ± 8.1129 beats per minute (bpm) and a mean absolute error of 1.86 bpm for walking, making it the second most accurate method to date that employs a single PPG and a 3-axis accelerometer. The proposed method also achieved the best accuracy of 3.78 bpm in mean absolute errors among all previously reported studies for hand-moving scenarios.

LncRNAs associated with vascular mimicry establish a novel molecular subtype and prognostic model for pancreatic cancer.

Vascular mimicry (VM) epitomizes an innovative tumor angiogenesis pathway, potentially serving as an alternate conduit under the assumption of traditional tumor angiogenesis pathway inhibition. The role of VM in pancreatic cancer (PC), however, remains unexplored. Using differential analysis and Spearman correlation, we identified key long non-coding RNAs (lncRNAs) signatures in PC from the collected set of VM-associated genes in the literature. We identified optimal clusters using the non-negative matrix decomposition (NMF) algorithm, and then compared clinicopathological features and prognostic differences between clusters. We also assessed tumor microenvironmental (TME) differences between clusters using multiple algorithms. Using univariate Cox regression analyses as well as lasso regression, we constructed and validated new lncRNA prognostic risk models for PC. We used Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) to analyze model-enriched functions and pathways. Nomograms were then developed to predict patient survival in association with clinicopathological factors. In addition, single-cell RNA-sequencing (scRNA-seq) analysis was used to analyze the expression patterns of VM-related genes and lncRNAs in the PC of TME. Finally, we used the Connectivity Map (cMap) database to predict local anaesthetics that could modify the VM of PC. In this study, we developed a novel three-cluster molecular subtype using the identified VM-associated lncRNA signatures of PC. The different subtypes have significantly different clinical characteristics and prognostic value, and also show differential treatment response and TME. Following an in-depth analysis, we constructed and validated a novel prognostic risk model for PC based on the VM-associated lncRNA signatures. Enrichment analysis suggested that high riskscores were significantly associated with functions and pathways, including extracellular matrix remodeling, et al. In addition, we predicted eight local anaesthetics that could modulate VM in PC. Finally, we discovered differential expression of VM-related genes and lncRNAs across various cell types within pancreatic cancer. VM has a critical role in PC. This study pioneers the development of a VM-based molecular subtype that demonstrates substantial differentiation in PC populations. Furthermore, we highlighted the significance of VM within the immune microenvironment of PC. Moreover, VM might contribute to PC tumorigenesis through its mediation of mesenchymal remodeling and endothelial transdifferentiation-related pathways, which offers a new perspective on its role in PC.

Unsupervised feature selection regression model with nonnegative sparsity constraints

Selecting appropriate features can better describe the characteristics and structure of data, which play an important role in further improving models and algorithms whether for supervised or unsupervised learning. In this paper, a new unsupervised feature selection regression model with nonnegative sparse constraints (URNS) is proposed. The algorithm combines nonnegative orthogonal constraint, L2,1-norm minimum optimization and spectral clustering. Firstly, the linear regression model between the features and the pseudo labels is given, and the indicator matrix, which describes feature weight, is subject to nonnegative and orthogonal constraints to select better features. Secondly, in order to reduce redundant and even noisy features, L2,1-norm for indicator matrix is added to the regression model for exploring the correlation between pseudo labels and features by the row sparsity property of L2,1-norm. Finally, pseudo labels of all samples are established by spectral clustering. In order to solve the regression model efficiently and simply, the method of nonnegative matrix decomposition is used and the complexity of the given algorithm is analysed. Moreover, a large number of experiments and analyses have been carried out on several public datasets to verify the superiority of the given model.

Channel Customization for Limited Feedback in RIS-Assisted FDD Systems

Reconfigurable intelligent surfaces (RISs) represent a pioneering technology to realize smart electromagnetic environments by reshaping the wireless channel. Jointly designing the transceiver and RIS relies on the channel state information (CSI), whose feedback has not been investigated in multi-RIS-assisted frequency division duplexing systems. In this study, the limited feedback of the RIS-assisted wireless channel is examined by capitalizing on the ability of the RIS in channel customization. By configuring the phase shifters of the surfaces using statistical CSI, we customize a sparse channel in rich-scattering environments, which significantly reduces the feedback overhead in designing the transceiver and RISs. Since the channel is customized in terms of singular value decomposition (SVD) with full-rank, the optimal SVD transceiver can be approached without a matrix decomposition and feeding back the complete channel parameters. The theoretical spectral efficiency (SE) loss of the proposed transceiver and RIS design is derived by considering the limited CSI quantization. To minimize the SE loss, a bit partitioning algorithm that splits the limited number of bits to quantize the CSI is developed. Extensive numerical results show that the channel customization-based transceiver with reduced CSI can achieve satisfactory performance compared with the optimal transceiver with full CSI. Given the limited number of feedback bits, the bit partitioning algorithm can minimize the SE loss by adaptively allocating bits to quantize the channel parameters.

Experimental Testing of a Tensegrity Simplex: Self-Stress Implementation and Static Loading

A physical model of the simplest three-dimensional tensegrity unit was built at human scale out of aluminum. Self-stress implementation and static loading tests were performed on this model. At each step, accurate measurements were obtained for all nodal positions and element forces. For the prestressing phase, elongations were imposed, via mechanical devices, in different combinations of elements, called prestress scenarios. Experimental results are compared to the theoretical self-stress state obtained by singular value decomposition of the equilibrium matrix and to numerical simulations using the dynamic relaxation method. It is shown that internal forces follow the same linear trend for all prestress scenarios even if the geometry is significantly impacted. Compressive tests were conducted by hanging masses from the top nodes. It is shown that there exists a unique load-displacement relation that follows the infinitesimal mechanism direction for a finite distance, which depends on the self-stress level. The paper provides a detailed overview of the simplex’s structural behavior using both experimental and numerical results while discussing the limitations of the analysis methods explored.

On the Common AOA Error in CKM-Based Integrated Sensing and Communications

In integrated sensing and communications (ISAC), the channel information can be acquired via the channel knowledge map (CKM). However, due to the lack of the precise knowledge of the user equipment’s heading, angle of arrival (AOA) estimations of all paths share an identical error, which is defined as the common AOA error (CAE). In this letter, we prove that the CAE imposes rotational effects on the unitary matrices of the singular value decomposition (SVD) of the channel matrix, leading to non-orthogonality among data layers for the SVD-based precoding. Then we develop two algorithms utilizing the rotational effect to estimate and eliminate the CAE. The two algorithms are suitable for scenarios with low and high Rician K-factors, respectively. By applying the proposed algorithms, accurate wideband channel information can be attained based on narrowband reference signals. Simulation results show that the proposed algorithms obtain higher precoding performance than the baseline method.

Performance evaluation of LU matrix decomposition using the SYCL standard

The object of this study is the performance of the SYCL standard tools when solving the LU matrix decomposition problem. SYCL is a fairly new technology for parallel computing in heterogeneous systems, so the topic of evaluating the performance of the standard on specific tasks in the field of parallel computing is relevant. In the study, the algorithm of parallelized LU decomposition of a square matrix was implemented by means of the SYCL standard and standard C++, and an experiment was conducted to test the implementation in a heterogeneous system with several types of processors. During testing, the program received square matrices of various dimensions as input, and the output was the execution time of the LU schedule on the selected processor. The obtained results, presented in the form of tabular and graphic data, show the advantage of the implementation of the SYCL standard over ordinary C++ by more than 2 times when using a graphics processor. It was experimentally shown that the implementation on SYCL is almost not inferior in speed to the implementation on ordinary C++ when executed on a central processor. Such results are caused both by the high possibility of parallelizing the LU schedule algorithm itself, and by the great work of the developers of the standard on its optimization. The obtained results indicate the possibility of speeding up the solution of the LU decomposition of the matrix and similar algorithms by means of SYCL when using heterogeneous systems with processors optimized for data parallelism. The results of the study can be used in justifying the choice of technology for solving LU matrix decomposition problems or problems with a similar parallelization scheme.

A complex structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix and its applications

A complex structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix and its applications

Spin Characters' Decomposition Matrix, S24 modulo, p=7

In this work, we compute decomposition matrix for the spin characters , connected between irreducible spin characters and irreducible modular spin characters, when the field characteristic equal to 7. The method used in this work is -inducing in a way to generate projective character for by projective character of and used maple program to see all the possible of columns and then choose the possible the right columns of them. The aim of this research is to pave the way for finding general relationships and theorems to study irreducible modular spin characters.

High-dimensional data analytics in civil engineering: A review on matrix and tensor decomposition

Recent developments in sensing and monitoring techniques have led to the generation of high-dimensional data in the field of civil engineering. High-dimensional data analytics methods have thus been developed to interpret such complex data. Among the different high-dimensional data analytics techniques, matrix and tensor decomposition methods have acquired a notable interest in the civil engineering community over the past decade. Due to their unique ability to deal with highly redundant and correlated data, these methods are establishing themselves as promising and efficient tools to analyze high-dimensional data in the civil engineering arena. In this paper, high-dimensional data is referred to as a data set in which the number of features is comparable or larger than the number of observations. This review paper aims to summarize the applications of matrix and tensor decomposition methods in civil engineering over the last decade. The survey begins with a general overview of matrix and tensor decomposition followed by highlighting their significance in the field. Afterward, various applications of these high-dimensional data analytics methods in civil engineering are presented, while the advantages offered by these methods are discussed. Finally, challenges and potential research avenues for employing matrix and tensor decomposition and future emerging trends for their novel use are highlighted.

On the Decomposition Matrix for the Spin Characters S_29 Modulo p=11

Background:
 In this work, we compute the decomposition matrix to the spin (projective) characters of , which is the correlations between the irreducible spin characters and the irreducible modular spin characters of , for a given field characteristic of . We may obtain it by figuring out all irreducible spin characters for , by fixing all bar partitions, as well as all irreducible modular spin characters for , , where we generate projective character for by projective character of and used Maple program to see all the possible of columns to choose the possible the right columns of them. The aim of this study is to pave the way for finding general relationships and theorems to study irreducible modular spin characters.
 Materials and Methods:
 We have used the -inducing to generate projective character by projective character of and Maple program to choose the possible the right columns
 Results:
 We find decomposition matrix to the spin (projective) characteristics of for a given field characteristic of which equals … 
 Conclusions:
 We have conducted multiple studies to get sufficient data to identify new characteristics and theorems if the field characteristic is prime because there is no standard approach for researching the issue, especially when we prove the field and the change of groups. Prior scholars achieved this when they looked at the division matrix in the field where the characteristic is 0, We used the -inducing also, we used Maple programming to view every possible columns.

Variable projection methods for separable nonlinear inverse problems with general-form Tikhonov regularization

The variable projection (VarPro) method is an efficient method to solve separable nonlinear least squares problems. In this paper, we propose a modified VarPro method for solving separable nonlinear least squares problems with general-form Tikhonov regularization. In particular, we apply the Gauss–Newton method to the corresponding reduced problem and investigate its convergence when different approximations of the Jacobian matrix are used. For special cases when computing the generalized singular value decomposition is feasible or a joint spectral decomposition of both forward and regularization operators exists, we provide efficient ways to compute the Jacobians and the solution of the linear subproblems. For large-scale problems, where matrix decompositions are not an option, we compute a reduced Jacobian and apply projection-based iterative methods and generalized Krylov subspace methods to solve the linear subproblems. In all cases, the regularization parameter can be computed automatically at each iteration using generalized cross validation. Several numerical examples highlight the proposed approach’s performance in the quality of the reconstructed image and the reconstructed forward operator, including large-scale two-dimensional imaging problems arising from semi-blind deblurring.

A robust direction-of-arrival estimation method for impulsive noise environments

The performance of conventional direction-of-arrival (DOA) estimation methods degrades greatly when there are few snapshots and the noise model is mismatched, especially in impulsive noise environments. To solve this problem, this paper proposes a robust DOA estimation method, which is robust to the probability density function of impulsive noise. First, by exploiting the low-rank decomposition of the residual fitting error matrix and the characteristics of impulsive noise, three conditions of a good cost function in impulsive noise environments are proposed, and a unified cost function framework is established. Based on this, a robust cost function is designed to suppress the contribution of samples with impulsive noise to the cost function. Then, a bi-iterative complex fixed-point algorithm (BI-CFPA) is developed for the nonconvex optimization problem of signal subspace estimation based on the proposed robust cost function. Theoretical analyses indicate that the BI-CFPA has excellent numerical stability and low computational complexity. Finally, with the estimated signal subspace, the multiple signal classification technique is employed to obtain DOA estimates. Simulation results show that the proposed DOA estimator performs better than existing methods in three typical impulsive noise environments, especially under fairly strong impulsive noise.

Модальный синтез системы управления полиномиальным методом для перевернутого маятника с двумя степенями свободы

An example of calculating an automatic control system for a multi-channel linearized model of a control object is given ‒ a 2-degree of freedom pendulum on a cart with the ability to move, for a mobile board and a support rack, in two planes. This model is described by a non-square matrix transfer function with a large number of output parameters compared to the number of input parameters. A description of a linear model of an object is obtained through the state space and through a matrix transfer function. According to the obtained descriptions, it can be seen that for a linearized version of the description of the object, for different coordinate axes, the description of the system is symmetrical. In this regard, there is an approach to synthesizing the control system for each coordinate of the mobile platform separately. However, with the further transition to a nonlinear description of the system, the symmetry of the description will be violated and it will be problematic to apply the obtained regulators for a nonlinear object in some cases. In this article, the work of the algorithm for the synthesis of the control system of the mobile platform for stabilizing the support rack to a vertical position and bringing the mobile platform to a given position at both coordinates at the same time is illustrated. The calculation was carried out using the algorithm of synthesis of the controller by a modular method using a polynomial matrix decomposition of the matrix transfer functions of the object and the controller. The simulation of the operation of the resulting automatic control system shows that the controller copes with the task of stabilizing the angle of the support post in the vertical position and bringing the mobile platform to the desired position.

FDD based modal identification of structures using least squares approach

In the conventional frequency domain modal identification procedures, modal parameters are attempted to be identified using power spectral density matrix decomposition. As it is well stated in the literature, the quality of estimated mode shapes significantly increases when an average PSD matrix over a selected frequency band is utilized in the identification procedure. In this context, this study aims at deriving a weighted average for the PSD matrix to increase the quality of the estimated mode shapes by using an FDD-based modal model. Then, the remaining modal parameters comprising modal frequency, damping ratio and spectral density of modal exciting force are calculated through a least squares equation. Moreover, the presented FDD based approach is also adapted to the solution of multiple setup problem. The proposed method for single and multiple setup cases is validated by making use of one numerical and two field data examples. The obtained results reveal that the presented frequency domain technique can successfully achieve high quality of modal estimates in the presence of measurement noise, and it can be easily implemented to field applications.