Matrix Decomposition Research Articles

Verified Error Bounds for Matrix Decompositions

Verified Error Bounds for Matrix Decompositions

Generalized Fused Lasso for Treatment Pooling in Network Meta-Analysis.

This work develops a generalized fused lasso (GFL) approach to fitting contrast-based network meta-analysis (NMA) models. The GFL method penalizes all pairwise differences between treatment effects, resulting in the pooling of treatments that are not sufficiently different. This approach offers an intriguing avenue for potentially mitigating biases in treatment rankings and reducing sparsity in networks. To fit contrast-based NMA models within the GFL framework, we formulate the models as generalized least squares problems, where the precision matrix depends on the standard error in the data, the estimated between-study heterogeneity and the correlation between contrasts in multi-arm studies. By utilizing a Cholesky decomposition of the precision matrix, we linearly transform the data vector and design matrix to frame NMA within the GFL framework. We demonstrate how to construct the GFL penalty such that every pairwise difference is penalized similarly. The model is straightforward to implement in R via the "genlasso" package, and runs instantaneously, contrary to other regularization approaches that are Bayesian. A two-step GFL-NMA approach is recommended to obtain measures of uncertainty associated with the (pooled) relative treatment effects. Two simulation studies confirm the GFL approach's ability to pool treatments that have the same (or similar) effects while also revealing when incorrect pooling may occur, and its potential benefits against alternative methods. The novel GFL-NMA method is successfully applied to a real-world dataset on diabetes where the standard NMA model was not favored compared to the best-fitting GFL-NMA model with AICc selection of the tuning parameter ( .

A novel damage localization method of Circular Phased Array using Minimum Variance Distortionless Response Beamforming with Autocorrelation Matrix Diagonal Loading

Damage localization methods based on Acoustic Emission (AE) can be classified into time-based and waveform-based. However, the former requires a large number of sensors while the latter is limited to 2D plane localization. In order to address the challenge of achieving more accurate 3D localization using a reduced number of sensors, this paper proposes a Circular Phased Array using Minimum Variance Distortionless Response (MVDR) Beamforming with Autocorrelation Matrix Diagonal Loading (AMDL) method. Firstly, a sparse circular array is utilized to form multiple beamforming for coherent shear wave signals, decomposing the original 3D localization problem into Direction Of Arrival (DOA) estimation. Secondly, azimuth angle, elevation angle and autocorrelation matrix diagonal loading methods are introduced, working in conjunction with the MVDR beamforming algorithm. Finally, spatial integration is performed through matrix decomposition to solve geometric overdetermined equations. The effectiveness of the proposed method is validated through numerical simulations and experimental verifications under various damage conditions. Results indicate that estimation errors for azimuth and elevation angles are both less than 2 %, while 3D damage source localization errors remain within a range of less than 3 %. This proposed method extends beamforming technology from 2D plane localization to 3D localization, significantly reducing the complexity of sensor arrangement and lowering the cost of structural health monitoring systems by utilizing a small number of sensors.

Detection of Traffic Anomalies Based on Their Frame Wavelet Transformations Processing

Relevance. The active transition to a massive digital infrastructure based on Internet of Things (IoT) technology has brought telecommunications networks to the level of dominant information resources. The one-time increase in the number of existing Internet services is inextricably linked to the growing variety of network anomalies on telecommunications equipment. In turn, existing methods of detecting network threats do not allow timely assessment of network traffic, which is characterized by a large number of parameters, and the detected anomalies from external interference do not have pronounced patterns. The purpose of the study is to increase the efficiency of detecting traffic anomalies based on the results of processing its frame wavelet transform. The scientific task is to develop scientific and methodological approaches that allow effective analysis and timely detection of anomalies in network traffic. A comparative review of search methods for detecting network traffic anomalies, algorithms for detecting uncontrolled anomalies, traffic analysis methods based on local emission factor, binary trees, optical emission spectroscopy. Decision. The results of the study of the possibility of detecting anomalies in the bitstream traffic based on the results of its multiple-variable transformation in the Haar wavelet basis are considered. The choice for further processing of the coefficients of the traffic decomposition matrix along the time shift variable is justified. It is proved that multiple-scale transformations not only increase the structural differences in traffic, but also open up the possibility of localization of anomalies that caused these differences. The scientific novelty of the work is determined by the author's approach to detecting network traffic anomalies during the transition from the direct representation of a signal in the form of its discrete samples to coefficients formed from the matrices of its wavelet transformations, and, as a result, increasing its contrast with other signals with a similar structure. Theoretical significance. The necessity and sufficiency of using wavelet coefficients instead of time samples of signals in the basis of the parent wavelet from the matrix of the generated frame is proved. The relationship between the Hurst indicators and the coefficients of the cross-correlation functions has been established. Practical significance. The results obtained in the work, in the future, can be used in the construction of models for evaluating network traffic in conditions of deliberate, as well as methods for searching and synthesizing effective methods of protection against them.

Visualize the Gas Spreading Over Time as Separate Trajectories with Matrix Decomposition Based on the Linearity of LSPR Gas Sensor Response

Visualize the Gas Spreading Over Time as Separate Trajectories with Matrix Decomposition Based on the Linearity of LSPR Gas Sensor Response

Boosted Whittaker–Henderson Graduation

The Whittaker–Henderson (WH) graduation is a smoothing method for equally spaced one-dimensional data such as time series. It includes the Bohlmann filter, the Hodrick–Prescott (HP) filter, and the Whittaker graduation as special cases. Among them, the HP filter is the most prominent trend-cycle decomposition method for macroeconomic time series such as real gross domestic product. Recently, a modification of the HP filter, the boosted HP (bHP) filter, has been developed, and several studies have been conducted. The basic idea of the modification is to achieve more desirable smoothing by extracting long-term fluctuations remaining in the smoothing residuals. Inspired by the modification, this paper develops the boosted version of the WH graduation, which includes the bHP filter as a special case. Then, we establish its properties that are fundamental for applied work. To investigate the properties, we use a spectral decomposition of the penalty matrix of the WH graduation

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.

Population-aware permutation-based significance thresholds for genome-wide association studies

Abstract Motivation Permutation-based significance thresholds have been shown to be a robust alternative to classical Bonferroni significance thresholds in genome-wide association studies for skewed phenotype distributions. The recently published method permGWAS introduced a batch-wise approach to efficiently compute permutation-based genome-wide association studies. However, running multiple univariate tests in parallel leads to many repetitive computations and increased computational resources. More importantly, traditional permutation methods that permute only the phenotype break the underlying population structure. Results We propose permGWAS2, an improved method that does not break the population structure during permutations and uses an elegant block matrix decomposition to optimize computations, thereby reducing redundancies. We show on synthetic data that this improved approach yields a lower false discovery rate for skewed phenotype distributions compared to the previous version and the commonly used Bonferroni correction. In addition, we re-analyze a dataset covering phenotypic variation in 86 traits in a population of 615 wild sunflowers (Helianthus annuus L.). This led to the identification of dozens of novel associations with putatively adaptive traits, and removed several likely false-positive associations with limited biological support. Availability permGWAS2 is open-source and publicly available on GitHub for download: https://github.com/grimmlab/permGWAS. Supplementary information Supplementary data are available at Bioinformatics Advances online.

Constitutive modeling of thermo-chemical decomposition and thermo-mechanical deformation, coupled with transient heat conduction, in ablative matrix composite

Several thermal protection systems employ sacrificial composite layer that undergoes thermo-chemical decomposition in high-temperature environment. This results in the pyrolysis gas formation (endothermic reaction) that gets trapped inside the voids generated in the ablative matrix phase. These trapped gases apply pore pressure on the structure, along with the mechanical loading, thus significantly influencing the structure failure. A novel thermo-chemical (TC) decomposition and thermo-mechanical (TM) deformation-based coupled multi-physics formulation, applicable to ablative composite systems, is thus presented. A novel shrinkage expression, due to ablative matrix decomposition, is derived. The TC + TM coupled formulation is converted to stress update process, and its results are validated against the available experimental data. The proposed formulation is also converted to boundary value problem employing non-linear finite element framework (NL-FEM). The Jacobian matrices, for one- and two-dimensional cases, are systematically derived, and the proposed NL-FEM formulation is successfully verified against several benchmark problems.The transient heat conduction equation is finally coupled with the proposed TC + TM formulation (one-way coupling) thus enabling the analysis of more realistic situations where the constant heating rate assumption is not valid. The coupled formulation is finally implemented for several test cases and it is demonstrated that, it has a significant influence on pore pressure and porosity evolution (through pore volumetric strain) within the ablative matrix phase.

On Kursov's theorem for matrices over division rings

Let D be a division ring with center F and multiplicative group D×, where each element of the commutator subgroup of D× can be expressed as a product of at most s commutators. A known theorem of Kursov states that if D is finite-dimensional over F, then every element of the commutator subgroup of the general linear group over D can be expressed as a product of at most s+1 commutators. We show that this result remains valid when F has a sufficiently large number of elements, without requiring D to be finite-dimensional. Our approach not only improves upon recent results on matrix decompositions over division rings but also provides a look at the Engel word map for matrices over arbitrary algebras.

Distributional hypothesis as isomorphism between word-word co-occurrence and analogical parallelograms.

Most of the modern natural language processing (NLP) techniques are based on the vector space models of language, in which each word is represented by a vector in a high dimensional space. One of the earliest successes was demonstrated by the four-term analogical reasoning task: what is to C as B is to A? The trained word vectors form "parallelograms" representing the quadruple of words in analogy. This discovery in NLP offers us insight into our understanding of human semantic representation of words via analogical reasoning. Despite successful applications of the large-scale language models, it has not been fully understood why such parallelograms emerge by learning through natural language data. As the vector space model is not optimized to form parallelograms, the key structure related to geometric shapes of word vectors is expected to be in the data, rather than the models. In the present article, we test our hypothesis that such parallelogram arrangement of word vectors readily exists in the co-occurrence statistics of language. Our approach focuses more on the data itself, and it is different from the existing theoretical approach trying to find the mechanism of parallelogram formation in the algorithms and/or vector arithmetic operations on word vectors. First, our analysis suggested that analogical reasoning is possible by decomposition of the bigram co-occurrence matrix. Second, we demonstrated the formation of a parallelepiped, a more structured geometric object than a parallelogram, by creating a small artificial corpus and its word vectors. With these results, we propose a refined form of distributional hypothesis pointing out an isomorphism between a sort of symmetry or exchangeability and word co-occurrence statistics.

Practical consensus of T-S fuzzy positive multi-agent systems using linear programming

This paper presents the practical consensus of T-S fuzzy positive multi-agent systems with interval type-1 and type-2 fuzzy sets using observer-based control protocols. A fuzzy positive observer is first constructed for the systems. An observer-based fuzzy control protocol is designed, where an additional constant term is introduced. Some linear programming conditions are established to achieve the positivity of the original system and its observer. Then, the practical consensus of the original system is transformed into the stability of a dynamic system, where a set of new variables is defined by combining the constant term and the states of the agents. In the first step, the positivity of the new variables is guaranteed. In the second step, the stability of the dynamic system consisting new variables is addressed by using a fuzzy copositive Lyapunov function. The gain matrices of observer and control protocols are formulated based on a matrix decomposition approach. All positive and consensus conditions are described via linear programming. Finally, two examples are provided to verify the validity of the obtained results.

Joint range and velocity super-resolution estimation with Doppler effects for innovative OFDM-based RFA RadCom system

Conventional radar and communication signals face challenges when integrating for accurate sensing in dense electromagnetic environments, especially in scenarios involving high-velocity targets estimation. To address this issue, we propose the random frequency agile-orthogonal frequency division multiplexing-based radar and communication (RFA-OFDM-based RadCom) signal, a novel framework that combines RFA hopping radar signal and OFDM signal. This framework effectively handles high-velocity Doppler scenarios, enhancing electronic countermeasure capabilities. In high-velocity scenarios, achieving accurate range and velocity estimation is crucial. We introduce a comprehensive received signal model that considers intrapulse and intersubcarrier Doppler effects, often overlooked in traditional high-velocity contexts. The proposed two-phase hierarchical perceptual methodology enables joint super-resolution estimation using the shared signal. We transform the shared signal echo model into a uniform linear array-like model and employ the matrix decomposition algorithm based on bidirectional weighted frequency smoothing (BWFS-MD) for decoherence processing. Subsequently, the estimation of signal parameters via rotational invariance techniques (ESPRIT)-complementary integrated subspace fitting (E-CISF) algorithm accurately estimates joint range and velocity. Meanwhile, the contrastive analysis of the mutual impacts between radar and communication functions is conducted. Theoretical analysis and simulation results robustly validate the superior performance of the proposed BWFS-MD algorithm. Furthermore, considering the precision of joint range-velocity estimation, real-time constraints, and super-resolution capability (which is emphasized), the E-CSIF algorithm demonstrates the best overall performance from a comprehensive perspective.

Kinematic calibration of a 5-DOF double-driven parallel mechanism with sub-closed loop on limbs

Abstract This paper proposes a kinematic calibration method of a novel 5-degree-of-freedom double-driven parallel mechanism with the sub-closed loop on limbs. At first, considering the introduction of a sub-closed loop significantly increased the complexity and difficulty of kinematic error modeling, an equivalent transformation method is proposed for the limb with a sub-closed loop. Then kinematic error model of the parallel mechanism is established based on the closed-loop vector method and parasitic motion analysis, which is verified by virtual prototype technology. Because the full kinematic error model is generally redundant, error parameter identifiability analysis is carried out by QR decomposition of the identification Jacobian matrix, and the redundant parameters are removed. Additionally, the Sequence Forward Floating Search algorithm is utilized to optimize measurement configurations to reduce the influence of measurement noise. Finally, with a laser tracker as the measuring device, numerical simulations and experiments are implemented to verify the proposed kinematic calibration method. The experiment results show that average position and orientation errors are reduced from 2.778 mm and 1.115° to 0.263 mm and 0.176°, respectively, within the prescribed workspace.

Gaussian Mixture Regression Model with Sparsity for Clustering of Territory Risk in Auto Insurance

Abstract Insurance rating territory design and accurate estimation of territory risk relativities are fundamental aspects of auto insurance rate regulation. It is crucial to develop methodologies that can facilitate the effective design of rating territories and their risk relativities estimate, as they directly impact the rate filing and the decision support of the rate change review process. This article proposes a Gaussian Mixture Regression model clustering approach for territory design. The proposed method incorporates a linear regression model, taking spatial location as model covariates, which helps estimate the cluster mean more accurately. Also, to further enhance the estimation of territory risk relativities, we impose sparsity through sparse matrix decomposition of the membership coefficient matrix obtained from the Gaussian Mixture Regression model. By transitioning from the current hard clustering method to a soft approach, our methodology could improve the evaluation of territory risk for rate-making purposes. Moreover, using non-negative sparse matrix approximation ensures that the estimation of risk relativities for basic rating units remains smooth, effectively eliminating data noise from the territory risk relativity estimate. Overall, our novel methodology aims to significantly enhance the accuracy and reliability of risk analysis in auto insurance. Furthermore, the proposed method exhibits potential for extension to various other domains that involve spatial clustering of data, thereby broadening its applicability and expanding its usefulness beyond auto insurance rate regulation.

Efficient Distributed Transfer Learning for Large‐Scale Gaussian Graphic Models

ABSTRACTA transfer learning for the large‐scale Gaussian graphical models (GGMs) is considered in a distributed architecture for fitting these target and auxiliary studies scattered across multiple sites. A distributed transfer learning algorithm, DisPower‐Trans‐CLIME, is proposed to learn the target GGMs by incorporating the data from similar and related auxiliary studies. The algorithm is communication efficient via the distributed power method for matrix decomposition. We show that DisPower‐Trans‐CLIME has a fast convergence rate comparable to the centred Trans‐CLIME algorithm. A debiased DisPower‐Trans‐CLIME is constructed and is proved to be element‐wise asymptotically normal for statistical inference. Thus, a multiple testing procedure is developed to detect edge of GGMs with false discovery rate (FDR) control. Extensive simulation experiments have been conducted to demonstrate superior numerical performance of our proposed learning algorithm on estimation and edge detection. It is also applied to infer the regional connection networks in brain regions of interest (ROIs) based on a target hospital site by leveraging the graph from multiple other hospital sites for autism spectrum disorder. We observe that the degrees of regional connectivity in the right brain are balanced, while the ones of the left brain region are extremely uneven because of the presence of multiple strong connections. However, the specific association, between the degrees of connectivity of these regions and ASD disease, is unknown.

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.

Latent Archetypes of the Spatial Patterns of Cancer.

The cancer atlas edited by several countries is the main resource for the analysis of the geographic variation of cancer risk. Correlating the observed spatial patterns with known or hypothesized risk factors is time-consuming work for epidemiologists who need to deal with each cancer separately, breaking down the patterns according to sex and race. The recent literature has proposed to study more than one cancer simultaneously looking for common spatial risk factors. However, this previous work has two constraints: they consider only a very small (2-4) number of cancers previously known to share risk factors. In this article, we propose an exploratory method to search for latent spatial risk factors of a large number of supposedly unrelated cancers. The method is based on the singular value decomposition and nonnegative matrix factorization, it is computationally efficient, scaling easily with the number of regions and cancers. We carried out a simulation study to evaluate the method's performance and apply it to cancer atlas from the USA, England, France, Australia, Spain, and Brazil. We conclude that with very few latent maps, which can represent a reduction of up to 90% of atlas maps, most of the spatial variability is conserved. By concentrating on the epidemiological analysis of these few latent maps a substantial amount of work is saved and, at the same time, high-level explanations affecting many cancers simultaneously can be reached.

Flowfield reconstruction in a supersonic isolator based on proper orthogonal decomposition and sensor compression coupling under variable Mach numbers

The supersonic inflow passes through the shock train in the isolator of the scramjet to complete deceleration and pressurization, followed by combustion and energy release, providing strong thrust. When the back pressure generated by combustion is disturbed forward, the location of shock train leading edge (STLE) will also change accordingly. Once it moves to the entrance of the isolator, it will cause unstart. Accurately detecting STLE in the isolator of a scramjet is crucial for controlling the shock train and preventing the inlet from unstart. Therefore, based on the sparse reconstruction of compressive sensing and sensor compression coupling, a supersonic flowfield reconstruction model (POD-STLE) based on proper orthogonal decomposition (POD) was constructed to reconstruct the supersonic flowfield and detect the location of STLE in the supersonic isolator. The experiments were conducted on the shock oscillation under variable Mach numbers and back pressures, to construct the experimental dataset. Combining supersonic flowfield reconstruction and matrix decomposition, different sensor layouts were constructed, which can ensure accuracy and stability while saving sensor resources. The POD-STLE was applied to the flowfield reconstruction of the supersonic isolator, and the location of STLE was detected under variable and constant conditions, ultimately achieving the expected reconstruction effect and detection accuracy. This study provides a new research method for detecting the location of STLE in the supersonic isolator of a scramjet and provides technical for exploring supersonic flowfield.

Facile Design of Bi2S3‐Doped CeO2/Dihydroxybenzoate Composite as Highly Efficient UV‐Shielding Agents

AbstractIn this study, bismuth sulfide (Bi2S3)‐doped cerium oxide (CeO2) was prepared via hydrothermal method, and by depositing ethyl 3,4‐dihydroxybenzoate (EDHB) on the surface of Bi2S3/CeO2 (Bi2S3/CeO2/EDHB and BCE). The samples were characterized by FTIR, XRD, TEM, and UV–vis absorption spectrum means. According to the characterizations, Bi2S3 was successfully incorporated into the CeO2 structure (Bi2S3/CeO2), and the prepared BCE/PVC composite films display excellent UV‐shielding property. Moreover, the result of thermogravimetric analysis (TGA) tests indicated that BCE also was barely catalytic thermal decomposition of PVC matrix. This work not only paves an attractive way for the design of the CeO2‐based UV‐shielding agent, but also provides valuable insights into the inspiration to construct high‐performance UV‐shielding composites.