Classical Matrix Research Articles

Structured Joint Sparse Orthogonal Nonnegative Matrix Factorization for Fault Detection

As modern industrial processes become complicated, and some faults are difficult to be detected due to noises and nonlinearity of data, data-driven fault detection has been extensively used to detect abnormal events in functional units. In order to obtain the better fault detection performance of nonnegative matrix factorization, this paper first proposes a fault detection method using the structured joint sparse orthogonal nonnegative matrix factorization. The core idea is to incorporate the graph regularization, sparsity and orthogonality constraints into the classical nonnegative matrix factorization, which enjoys stronger discriminative ability, removes redundancy of different basis vectors and improves the fault interpretability. More importantly, an optimization algorithm based on the proximal alternating nonnegative least squares is developed, which can guarantee and speed up the convergence. Finally, the effectiveness of the proposed method is demonstrated by the experiments on the benchmark Tennessee Eastman Process and two practical bearing datasets. Particularly, compared with the classical nonnegative matrix factorization, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> statistic has a gain of 33.13% for the fault IDV(16) on the Tennessee Eastman Process. The results show that the proposed model and algorithms are promising for the fault detection.

МЕТОДИЧНІ ТА ПРИКЛАДНІ АСПЕКТИ ВИКОРИСТАННЯ МАТРИЦІ BCG

The BCG method is a portfolio analysis tool. It is used to effectively manage a business. This method helps to identify which businesses should be invested in and which should be disposed of. Nowadays BCG method is a popular tool for planning corporate product portfolios. However, this method has come under a lot of criticism, with many academics drawing attention to methodological weaknesses of product portfolio analysis based on the BCG matrix. The relevance of further research of the BCG matrix method leads to methodological and practical issues. They arise when the assortment of the entity in a particular market is evaluated. The following research methods are used: monographic (in the study of theoretical and methodological foundations of the classical method Boston Consulting Group Matrix); dialectical, abstract-logical (for theoretical generalizations to identify methodological shortcomings and ways to overcome them, the formulation of conclusions), graphic and tabular (to present research results). We have proved that the use of the traditional BCG matrix methodology can be impossible in practice because of the lack of accurate data on competitors and their sales volumes of certain products. The main problems arising in the construction of the BCG matrix: the lack of clear criteria for classifying businesses to a particular market, the existence of alternative methodologies for calculating the market share of the product, the lack of unambiguous quantitative criteria for classifying products as «high» or «low» market share, the lack of unambiguous quantitative criteria for classifying products as having «high» or «low» growth rates, the failure to compare only two years to evaluate the market growth. The objectives of the study are to adapt the classical matrix for use in an uncertain market environment. The proposed refinements to the use of the BCG matrix deserve to be implemented in the practice of strategic management of companies. The results of the analysis using the modified BCG matrix can be used in financial strategic planning and in the development of the marketing strategy, in particular when planning advertising campaigns.

An Amplitude-Phase Representation of the North-East-Down Kinematic Differential Equations

The overall goal of the paper is to derive a kinematic model for vehicle path-following systems, where the pitch and yaw angles <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\theta, \psi)$ </tex-math></inline-formula> together with the surge velocity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$u$ </tex-math></inline-formula> can be treated as control inputs. Then the outer control loop can be designed as a nonlinear path-following guidance law. At the same time, the inner control loops can be stabilized using commercial autopilot systems to control the pitch and yaw angles. The main result of the paper is a novel kinematic amplitude-phase representation of the North-East-Down (NED) positional rates, which can replace the classical Euler angle rotation matrix representation. The proposed kinematic model gives equivalent NED positional rates as the rotation matrix representation for all combinations of the Euler angles and the linear velocities. The main advantage of the kinematic amplitude-phase representation is the design of vehicle guidance laws using nonlinear control theory and Lyapunov stability analysis. Furthermore, it is shown that nonlinear guidance laws can be designed for path following and that the proposed methods guarantee that the origins are uniformly semiglobally exponentially stable (USGES). A case study of an unmanned surface vehicle (USV) demonstrates how a path-following control system can be designed using the amplitude-phase representation.

Graph Regularized Nonnegative Matrix Factorization for Community Detection in Attributed Networks

Community detection has become an important research topic in machine learning due to the proliferation of network data. However, most existing methods have been developed based on only exploiting the topology structures of the network, which can result in missing the advantage of using the nodes' attribute information. As a result, it is expected that much valuable information that could be used to improve the quality of discovered communities will be ignored. To solve this limitation, we propose a novel Augment Graph Regularization Nonnegative Matrix Factorization for Attributed Networks (AGNMF-AN) method, which is simple yet effective. Firstly, Augment Attributed Graph (AAG) is applied to combine both the topological structure and attributed nodes of the network. Secondly, we introduced an effective framework to update the affinity matrix, in which the affinity matrix's weight in each iteration is modified adaptively instead of using a fixed affinity matrix in the classical graph regularization-based nonnegative matrix factorization methods. Thirdly, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{2,1}$</tex-math></inline-formula> -norm is utilized to reduce the effect of random noise and outliers in the quality of structure community. Experimental results show that our method performs unexpectedly well in comparison to existing state-of-the-art methods in attributed networks.

An innovative fuzzy parameterized MADM approach to site selection for dam construction based on sv-complex neutrosophic hypersoft set

&lt;abstract&gt;&lt;p&gt;Dams are water reservoirs that provide adequate freshwater to residential, industrial, and mining sites. They are widely used to generate electricity, control flooding, and irrigate agricultural lands. Due to recent urbanization trends, industrialization, and climatic changes, the construction of dams is in dire need, which is planning intensive, quite expensive, and time-consuming. Moreover, finding an appropriate site to construct dams is also considered a challenging task for decision-makers. The dam site selection problem (DSSP) has already been considered a multi-criteria decision-making (MCDM) problem under uncertain (fuzzy set) environments by several researchers. However, they ignored some essential evaluating features (e.g., (a) fuzzy parameterized grades, which assess the vague nature of parameters and sub-parameters, (b) the hypersoft setting, which provides multi-argument-based domains for the approximation of alternatives, (c) the complex setting which tackles the periodicity of data, and (d) the single-valued neutrosophic setting which facilitates the decision makers to provide their opinions in three-dimensional aspects) that can be used in DSSP to make it more reliable and trustworthy. Thus this study aims to employ a robust fuzzy parameterized algebraic approach which starts with the characterization of a novel structure "fuzzy parameterized single valued complex neutrosophic hypersoft set ($ \tilde{\lambda} $-set)" that is competent to deal with the above-mentioned features jointly. After that, it integrates the concept of fuzzy parameterization, decision-makers opinions in terms of single-valued complex neutrosophic numbers, and the classical matrix theory to compute the score values for evaluating alternatives. Based on the stages of the proposed approach, an algorithm is proposed, which is further explained by an illustrative example in which DSSP is considered a multiple attributes decision-making (MADM) scenario. The computed score values are then used to evaluate some suitable sites (regions) for dam construction. The computational results of the proposed algorithm are found to be precise and consistent through their comparison with some already developed approaches.&lt;/p&gt;&lt;/abstract&gt;

Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing

The block-term tensor decomposition model with multilinear rank- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(L_{r},L_{r},1)$</tex-math></inline-formula> terms (or the “ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula> tensor decomposition” in short) offers a valuable alternative formulation for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hyperspectral unmixing</i> (HU), which ensures the identifiability of the endmembers/abundances in cases where classic matrix factorization (MF) approaches cannot provide such guarantees. However, the existing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula> -tensor-decomposition-based HU algorithms use a three-factor parameterization of the tensor (i.e., the hyperspectral image cube), which causes difficulties in incorporating structural prior information arising in HU. Consequently, their algorithms often exhibit high per-iteration complexity and slow convergence. This article focuses on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula> tensor decomposition under structural constraints and regularization terms in HU. Our algorithm uses a two-factor reparameterization of the tensor model. Like in the MF-based approaches, the factors correspond to the endmembers and abundances in the context of HU. Thus, the proposed framework is natural to incorporate physics-motivated priors in HU. To tackle the formulated optimization problem, a two-block alternating <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gradient projection</i> (GP)-based algorithm is proposed. Carefully designed projection solvers are proposed to implement the GP algorithm with a relatively low per-iteration complexity. An extrapolation-based acceleration strategy is proposed to expedite the GP algorithm. Such an extrapolated multiblock algorithm only had asymptotic convergence assurances in the literature. Our analysis shows that the algorithm converges to the vicinity of a stationary point within finite iterations, under reasonable conditions. Empirical study shows that the proposed algorithm often attains orders-of-magnitude speedup and substantial HU performance gains compared with the existing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula> -decomposition-based HU algorithms.

Vertices of Suborbital Graph $F_{u,N}$ under Lorentz Matrix Multiplication

In this study, suborbital graphs, $G_{u,N}$ and $F_{u,N}$ are examined. Modular group $\Gamma$ and its act on $\widehat{\mathbb{Q}}$ are studied. Lorentz matrix that gives the vertices obtained under the classical matrix multiplication in the suborbital graph $F_{u,N}$ is analysed with the Lorentz matrix multiplication. Lorentz matrix written as Möbius transform is normalized and the type of the transform is researched. Moreover, a different element of Modular group $\Gamma$ is scrutinized. The vertices on the path starting with $\infty$ are obtained under this element and the Lorentz matrix multiplication. For this path, it is shown that the vertices obtained in $F_{u,N}$ under the Lorentz matrix multiplication with the Lorentz matrix satisfied the farthest vertex condition for the previous vertex.

Quantum simulation of the N -flavor Gross-Neveu model

We discuss the use of quantum simulation to study an $N$-flavor theory of interacting relativistic fermions in ($1+1$) dimensions on noisy intermediate-scale quantum (NISQ)-era machines. The case of two flavors is particularly interesting as it can be mapped to the Hubbard model. We derive the appropriate qubit Hamiltonians and associated quantum circuits. We compare classical simulation and density matrix renormalization group/time-evolving blocked decimation calculations with the results of quantum simulation on various platforms for $N=2$ and 4-flavors. We demonstrate that the four steps needed for calculations of real-time scattering can be implemented using current NISQ devices.

Molecular polariton electroabsorption

We investigate electroabsorption (EA) in organic semiconductor microcavities to understand whether strong light-matter coupling non-trivially alters their nonlinear optical [{chi }^{(3)}left(omega,{{{{mathrm{0,0}}}}}right)] response. Focusing on strongly-absorbing squaraine (SQ) molecules dispersed in a wide-gap host matrix, we find that classical transfer matrix modeling accurately captures the EA response of low concentration SQ microcavities with a vacuum Rabi splitting of hslash Omega approx 200 meV, but fails for high concentration cavities with hslash Omega approx 420 meV. Rather than new physics in the ultrastrong coupling regime, however, we attribute the discrepancy at high SQ concentration to a nearly dark H-aggregate state below the SQ exciton transition, which goes undetected in the optical constant dispersion on which the transfer matrix model is based, but nonetheless interacts with and enhances the EA response of the lower polariton mode. These results indicate that strong coupling can be used to manipulate EA (and presumably other optical nonlinearities) from organic microcavities by controlling the energy of polariton modes relative to other states in the system, but it does not alter the intrinsic optical nonlinearity of the organic semiconductor inside the cavity.

Exploiting temporal features in multicriteria decision analysis by means of a tensorial formulation of the TOPSIS method

A number of Multiple Criteria Decision Analysis (MCDA) methods have been developed to rank alternatives based on several decision criteria. Usually, MCDA methods deal with the criteria value at the time the decision is made without considering their evolution over time. However, it may be relevant to consider the criteria’ time-series since it can provide essential information for the decision-making (e.g., an improvement of the criteria). To deal with this issue, we propose a new approach to rank the alternatives based on the criteria time-series features (trend, variance, etc.). In this novel approach, the data is structured in three dimensions, which require a more complex data structure, as the tensors, instead of the classical matrix representation used in MCDA. For this, we propose an extension of the TOPSIS method to handle tensors rather than matrices. Computational results confirm that the proposed approach allows to rank the alternatives from a new perspective that can be meaningful to the decision-maker.

Recent Advances in Organic Room Temperature Phosphorescence of Triphenylamine‐Based Doping Systems

AbstractThe host–guest doping strategy has become one of the most effective approaches to realize pure organic room temperature phosphorescence (RTP). Crystalline small molecules can provide a rigid environment that restricts the molecular motion of luminescent guests, thus enhancing phosphorescence emission. Triphenylamine (TPA) is a classic crystalline small molecule matrix that, when doped with designed guest molecules, enables tunable RTP properties and diverse functionalities. These properties afford TPA‐based doping systems with numerous applications in anticounterfeiting, bio‐imaging, and multiple responsive sensing. In this concept, design strategies, luminescence mechanisms, and applications of TPA‐based host‐guest doping systems are summarized. Moreover, the future prospects of TPA‐based RTP materials are proposed.

Rethinking the Knowledge Transfer Process Through the Use of Metaverse: A Qualitative Study of Organizational Learning Approach for Remote Workplace

Abstract This paper aims to explore the possibilities of implementing the tacit knowledge transfer process and practices in the metaverse and remote workplaces. Tacit knowledge transfer is crucial for organizational knowledge management and maintaining an organization's sustainable development. The research team believes that the use of the metaverse in remote workplaces is expected to revolutionize established organizational learning, knowledge management, and tacit knowledge transfer models. This research attempts to understand employees’ experiences from three perspectives: (1) the acceptance by both senior and junior staff of using the metaverse for training; (2) the experiences of tacit knowledge transfer over the metaverse; and (3) the role of immersion and interactivity during the knowledge transfer process. The significance of this research is the theoretical investigation of the tacit knowledge transfer model in the metaverse. This research is explorative in nature; therefore, this research is not going to generalize or prove the effectiveness of using the metaverse in the tacit knowledge transfer process, but rather explore the factors and deepen our understanding of these fundamental attributes. The findings of this research suggest a modification of the classical model SECI Matrix by adding a new component of “integration” in the transfer process.

Density matrix formulation of dynamical systems.

Physical systems that are dissipating, mixing, and developing turbulence also irreversibly transport statistical density. However, predicting the evolution of density from atomic and molecular scale dynamics is challenging for nonsteady, open, and driven nonequilibrium processes. Here, we establish a theory to address this challenge for classical dynamical systems that is analogous to the density matrix formulation of quantum mechanics. We show that a classical density matrix is similar to the phase-space metric and evolves in time according to generalizations of Liouville's theorem and Liouville's equationfor non-Hamiltonian systems. The traditional Liouvillian forms are recovered in the absence of dissipation or driving by imposing trace preservation or by considering Hamiltonian dynamics. Local measures of dynamical instability and chaos are embedded in classical commutators and anticommutators and directly related to Poisson brackets when the dynamics are Hamiltonian. Because the classical density matrix is built from the Lyapunov vectors that underlie classical chaos, it offers an alternative computationally tractable basis for the statistical mechanics of nonequilibrium processes that applies to systems that are driven, transient, dissipative, regular, and chaotic.

Description of Microwave Circuits via the Reduced-Basis Method Giving Physical Insight

A description of electromagnetics by means of the reduced-basis method (RBM), which gives physical insight, is detailed. Contrary to what has been previously done to get further insights from the electromagnetic behavior, a reliable reduced-order model completely describing a microwave circuit in a frequency band of interest is carried out. Following a theoretical analysis starting from time-harmonic Maxwell’s equations, we identify the dominant contributions to electromagnetics in a band of analysis. Making use of the reliable reduced-order model, we present the electromagnetic information in that reduced-order model in a more insightful manner, using a specific dynamical system representation of electromagnetics. As a result, a full-wave coupling matrix completely describing electromagnetics in the band of analysis is identified, where no narrowband approximation is considered, such as it is the case in classical coupling matrix circuit theory. No approximation is taken into account other than carrying out the analysis in a given frequency band, which can be arbitrarily large. The proposed approach provides a way to understand electromagnetics, where a full-wave coupling matrix allows the description of electromagnetics in a band of interest as a simple physically insightful circuit, and not the other way around. Finally, several real-life microwave circuits, such as a dual-mode filter and diplexer, will illustrate the capabilities and efficiency of the proposed approach.

Deformation of Gels with Spherical Auxetic Inclusions.

Auxetic metamaterials possess unnatural properties, such as a negative Poisson's ratio, which offers interesting features when combined with traditional materials. This paper describes the deformation behavior of a gel consisting of spherical auxetic inclusions when embedded in a conventional matrix. The auxetic inclusions and conventional matrix were modeled as spherical objects with a controlled pore shape. The auxetic particle had a reentrant honeycomb, and the conventional phase contained honeycomb-shaped pores. The deformation behavior was simulated using various existing models based on continuum mechanics. For the continuum mechanics models-the simplest of which are the Mori-Tanaka theory and self-consistent field mechanics models-the auxetic particle was homogenized as a solid element with Young's modulus and Poisson's ratio and compared with the common composite gel filled with rigid spheres. The finite element analysis simulations using these models were performed for two cases: (1) a detailed model of one particle and its surroundings in which the structure included the design of both the reentrant and conventional honeycombs; and (2) a multiparticle face-centered cubic lattice where both the classic matrix and auxetic particle were homogenized. Our results suggest that auxetic inclusion-filled gels provide an unsurpassed balance of low density and enhanced stiffness.

On the eigenvectors of large-dimensional sample spatial sign covariance matrices

To investigate the limiting behavior of eigenvectors of the sample spatial sign covariance matrix (SSCM), the eigenvector empirical spectral distribution (VESD) is defined with weights depending on the eigenvectors. In this paper, we first show that the VESD of a large-dimensional sample SSCM converges to a generalized Marčenko–Pastur distribution when both the dimension p of observations and the sample size n tend to infinity proportionally. Further, the central limit theorem of linear spectral statistics of VESD is established, which suggests that the eigenmatrix of sample SSCM and the classical sample covariance matrix are asymptotically the same.

BCB-Based Thin-Film Ka-Band Quarter-Mode SIW Packaged Filters With Ultrawide Stopband and Independently Controlled TZs

In this article, quarter-mode substrate-integrated waveguide (QMSIW) filters featuring ultrawide stopband and flexibly allocated transmission zeros (TZs) are proposed. Eight higher modes with resonant frequencies up to 4.7 times of the fundamental mode are highly suppressed. It is realized by the combination of three approaches without extra circuit areas. First, a slot is cut in the first and last QMSIW resonators to make their resonant frequencies of higher modes different from those of other resonators. Second, avoid exciting the specific higher modes by setting the feed point in the area where the electric field strength of the higher modes is weak. Third, mismatch the higher modes when matching the passband. It is realized by using a stripline impedance transformer with its main body not exceeding the area of QMSIW resonators. Furthermore, except for the TZs derived by the classical cross-coupling matrix, two more independently controlled TZs are generated. The packaged filter is fabricated by using a benzocyclobutene (BCB)-based microelectromechanical systems (MEMS) process, which is suitable for millimeter-wave 3-D system-on-package (SOP) applications. The fabricated thin-film filter is measured with an insertion loss of 2.96 dB at 29.4 GHz and a fractional bandwidth (BW) of 17%. Higher mode suppressions up to 138.3 GHz are achieved.

On the eigenstructure of rotations and poses: commonalities and peculiarities

Locating vehicles, targets and objects in three-dimensional space is key to many fields of science and engineering such as robotics, aerospace, computer vision and graphics. Rotations and poses (position plus orientation) of bodies can be expressed in a variety of ways. Rotation matrices constitute one of the classic matrix Lie groups, the special orthogonal group— SO ( 3 ) . Poses can likewise be represented by matrices. One such representation is embodied in a 4 × 4 matrix establishing another famous matrix Lie group, the special Euclidean group— SE ( 3 ) . An alternative representation of pose uses 6 × 6 matrices and is referred to as the group of pose adjoints— Ad ( SE ( 3 ) ) . The eigenstructures of these representations reveal much about them from Euler’s theorem for rotations to the Mozzi–Chasles theorem for the general displacement of a rigid body. While the eigenstructure of SO ( 3 ) has been extensively studied, those of SE ( 3 ) and Ad ( SE ( 3 ) ) have hardly received the same scrutiny yet their structure is much richer. Motivated by their importance in kinematics and dynamics, we provide here a complete characterization of rotations and poses in terms of the eigenstructure of their matrix Lie group representations. An eigendecomposition of pose matrices reveals that they can be cast into a form similar to that of rotations although the structure of the former can vary depending on the nature of the pose involved. In particular, the pose matrices of SE ( 3 ) and Ad ( SE ( 3 ) ) cannot generally be diagonalized as can rotation matrices but they of course do yield to a Jordan normal form, from which we can identify a principal-axis pose in much the same manner that we can a principal-axis rotation. We also address the minimal polynomials for poses and derive a novel expression for the Jacobian in Ad ( SE ( 3 ) ) . Finally, we argue that the true counterpart to SO ( 3 ) for poses is not SE ( 3 ) but Ad ( SE ( 3 ) ) .

Discrete matrix hypergeometric functions

We generalize the scalar discrete hypergeometric series to allow for matrix parameters. We show their connection to classical matrix hypergeometric series, derive conditions for convergence on the boundary disk, show criteria for divergence, derive integral representations, and establish some difference equations they solve. We also highlight the special case of discrete matrix Bessel functions, whose scalar analogue has proved useful in applications.

Classical group matrix models and universal criticality

We study generalizations of the Gross-Witten-Wadia unitary matrix model for the special orthogonal and symplectic groups. We show using a standard Coulomb gas treatment — employing a path integral formalism for the ungapped phase and resolvent techniques for the gapped phase with one coupling constant — that in the large N limit, the free energy normalized modulo the square of the gauge group rank is twice the value for the unitary case. Using generalized Cauchy identities for character polynomials, we then demonstrate the universality of this phase transition for an arbitrary number of coupling constants by linking this model to the random partition based on the Schur measure.