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In the field of frontier research, information security has received a lot of interest, but in the field of information security algorithm, the introduction of decimals makes it impossible to bypass the topic of calculation accuracy. This article creatively proposes the definition and related proofs of double parameters fractal sorting matrix (DPFSM). As a new matrix classification with fractal properties, DPFSM contains self-similar structures in the ordering of both elements and sub-blocks in the matrix. These two self-similar structures are determined by two different parameters. To verify the theory, this paper presents a type of $2\times 2$ DPFSM iterative generation method, as well as the theory, steps, and examples of the iteration. DPFSM is a space position transformation matrix, which has a better periodic law than a single parameter fractal sorting matrix (FSM). The proposal of DPFSM expands the fractal theory and solves the limitation of calculation accuracy on information security. The image encryption algorithm based on DPFSM is proposed, and the security analysis demonstrates the security. DPFSM has good application value in the field of information security. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has been successfully applied in several data mining tasks. Recently, there is an increasing interest in the acceleration of NMF, due to its high cost on large matrices. On the other hand, the privacy issue of NMF over federated data is worthy of attention, since NMF is prevalently applied in image and text analysis which may involve leveraging privacy data (e.g, medical image and record) across several parties (e.g., hospitals). In this paper, we study the acceleration and security problems of distributed NMF. First, we propose a distributed sketched alternating nonnegative least squares(DSANLS) framework for NMF, which utilizes a matrix sketching technique to reduce the size of nonnegative least squares subproblems with a convergence guarantee. For the second problem, we show that DSANLS with modification can be adapted to the security setting, but only for one or limited iterations. Consequently, we propose four efficient distributed NMF methods in both synchronous and asynchronous settings with a security guarantee. We conduct extensive experiments on several real datasets to show the superiority of our proposed methods. The implementation of our methods is available at https://github.com/qianyuqiu79/DSANLS. [ABSTRACT FROM AUTHOR]

Risk management is considered as a vital process contributing to the successful outcome of a complex construction project in terms of achieving the associated project objectives. The widely used industrial practice in managing construction project risks is to assign probability and impact values to each risk and to map risks on a risk matrix. The main criticism of this practice relates to ignoring complex interdependencies between risks and using point estimates for probability and impact values. Furthermore, risks mapped on a matrix are deemed to influence a specific objective and there is a challenge involved in aggregating the impact of risks across multiple (conflicting) project objectives. Utilizing a data-driven Bayesian Belief Network methodology, in this paper we introduce a new process where the risks mapped on a risk matrix corresponding to each project objective are aggregated and modeled as a risk network, and a holistic impact of each risk is captured across the network by means of new risk metrics. The proposed methodology is demonstrated through a real application. The results specific to the two ranking schemes (assuming independence/interdependence of risks) are found to be negatively correlated, which substantiates the importance of utilizing an interdependency-based risk management process. [ABSTRACT FROM AUTHOR]

White-box block cipher (WBC) has been proposed by Chow et al. to prevent the secret key to be extracted from its implementation in an untrusted context. A pivotal technique behind WBC is to convert the iterated round functions into a series of look-up tables (LUTs) with encodings. The construction of encoded LUTs consists of matrix operations, such as multiplication and inversion. The widely-used matrix libraries in applications, such as open-source NTL and M4RI, are primarily designed for large dimensional matrix operations. Therefore, they might not be suitable for WBC implementations which are mainly based on small-scale matrices and vectors. In this paper, we propose a new matrix library named WBMatrix for the optimization of WBC implementations. WBMatrix reduces the operating steps of multiplication and simultaneously generates pairwise invertible matrices as encodings. The performance comparison supports that WBMatrix improves the table construction and encryption phases on Intel x86 and ARMv8 platforms. Moreover, WBMatrix also boosts the initialization and encryption phases of LowMC/LowMC-M block ciphers and enhances the performance for the generation of key-dependent Sbox. [ABSTRACT FROM AUTHOR]

Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated heterogeneous variance structure. We propose a sequential test which utilizes the edge singular values (i.e., the largest few singular values) of the data matrix. It also naturally leads to a consistent sequential testing estimate of the number of signals. We describe the asymptotic distribution of the test statistic in terms of the Tracy-Widom distribution. The test is shown to be accurate and have full power against the alternative, both theoretically and numerically. The theoretical analysis relies on establishing the Tracy-Widom law for a large class of Gram type random matrices with non-zero means and completely arbitrary variance profiles, which can be of independent interest. [ABSTRACT FROM AUTHOR]

Representations in the form of Symmetric Positive Definite (SPD) matrices have been popularized in a variety of visual learning applications due to their demonstrated ability to capture rich second-order statistics of visual data. There exist several similarity measures for comparing SPD matrices with documented benefits. However, selecting an appropriate measure for a given problem remains a challenge and in most cases, is the result of a trial-and-error process. In this paper, we propose to learn similarity measures in a data-driven manner. To this end, we capitalize on the $\alpha \beta$ α β -log-det divergence, which is a meta-divergence parametrized by scalars $\alpha$ α and $\beta$ β , subsuming a wide family of popular information divergences on SPD matrices for distinct and discrete values of these parameters. Our key idea is to cast these parameters in a continuum and learn them from data. We systematically extend this idea to learn vector-valued parameters, thereby increasing the expressiveness of the underlying non-linear measure. We conjoin the divergence learning problem with several standard tasks in machine learning, including supervised discriminative dictionary learning and unsupervised SPD matrix clustering. We present Riemannian gradient descent schemes for optimizing our formulations efficiently, and show the usefulness of our method on eight standard computer vision tasks. [ABSTRACT FROM AUTHOR]

Massive multiple-input multiple-output (MIMO) is considered as a critical technique in 5 G New Radio (NR), due to its capability to significantly improve data rate and link reliability for the radio link. To make it a reality, it is essential to evaluate massive MIMO performance in realistic spatial fading channel conditions. Specifically, dynamic spatial channel emulation is crucial to evaluate the massive MIMO beam operations. Due to the high cost associated with both the traditional conduced testing method and the standardized multi-probe anechoic chamber (MPAC) based Over-the-Air (OTA) testing setup for massive MIMO performance testing, fading channel emulation for massive MIMO testing using a conductive phase matrix setup has been proposed in the literature. However, it is still a challenging problem to emulate dynamic spatial channels in a cost-effective and efficient manner for the conductive phase matrix setup, since traditional algorithms suffer from high computational complexity and system cost. This paper proposes a fast and accurate framework to emulate dynamic spatial channels in the phase matrix setup, where the basic idea is to mimic a virtual MPAC setup. By doing so, we can mimic MPAC setup with flexible probe configurations. Furthermore, a novel successive cancellation strategy and a closed-form algorithm are proposed to determine the probe locations and probe weights, respectively, which can significantly reduce the computational complexity associated with dynamic channel emulation. Simulation results show that the proposed algorithm is highly accurate and computationally efficient, compared to state-of-art solutions. Further, we apply our developed algorithm to emulate measured non-stationary channels and excellent emulation accuracy can be achieved. The proposed method can be employed for emulating dynamic spatial channels, which is of great importance for massive MIMO performance testing. [ABSTRACT FROM AUTHOR]

As a multivariate data analysis tool, canonical correlation analysis (CCA) has been widely used in computer vision and pattern recognition. However, CCA uses Euclidean distance as a metric, which is sensitive to noise or outliers in the data. Furthermore, CCA demands that the two training sets must have the same number of training samples, which limits the performance of CCA-based methods. To overcome these limitations of CCA, two novel canonical correlation learning methods based on low-rank learning are proposed in this paper for image representation, named robust canonical correlation analysis (robust-CCA) and low-rank representation canonical correlation analysis (LRR-CCA). By introducing two regular matrices, the training sample numbers of the two training datasets can be set as any values without any limitation in the two proposed methods. Specifically, robust-CCA uses low-rank learning to remove the noise in the data and extracts the maximization correlation features from the two learned clean data matrices. The nuclear norm and $L_{1}$ -norm are used as constraints for the learned clean matrices and noise matrices, respectively. LRR-CCA introduces low-rank representation into CCA to ensure that the correlative features can be obtained in low-rank representation. To verify the performance of the proposed methods, five publicly image databases are used to conduct extensive experiments. The experimental results demonstrate the proposed methods outperform state-of-the-art CCA-based and low-rank learning methods. [ABSTRACT FROM AUTHOR]

A fundamental technique in machine learning called “embedding” has made significant impact on data representation. Some examples of embedding include word embedding, image embedding and audio embedding. With the embedding techniques, many real-world objects can be represented using matrices. For example, a document can be represented by a matrix, where each row of the matrix represents a word. On the other hand, we have witnessed that many applications continuously generate new data represented by matrices and require real-time query answering on the data. These continuously generated matrices need to be well managed for efficient retrieval. In this paper, we propose a high-performance index for real-time matrix retrieval. Besides fast query response, the index also supports real-time insertion by exploiting the log-structured merge-tree (LSM-tree). Since the index is built for matrices, it consumes much more memory and requires much more time to search than the traditional index for information retrieval. To tackle the challenges, we propose an index with precise and fuzzy inverted lists, and design a series of novel techniques to improve the memory consumption and the search efficiency of the index. The proposed techniques include vector signature, vector residual sorting, hashing based lookup, and dictionary initialization to guarantee the index quality. Comprehensive experimental results show that our proposed index can support real-time search on matrices, and is more time and memory efficient than the state-of-the-art method. [ABSTRACT FROM AUTHOR]

In this paper, we design and analyze Mc2g (Matrix Completion with 2 Graphs), an efficient algorithm that performs matrix completion in the presence of social and item similarity graphs. Mc2g runs in quasilinear time and is parameter free. It is based on spectral clustering and local refinement steps. For the matrix completion problem which possesses additional block structures in its rows and columns, we derive the expected number of sampled entries required for Mc2g to succeed, and further show that it matches an information-theoretic lower bound up to a constant factor for a wide range of parameters. We perform extensive experiments on both synthetic datasets and a semi-real dataset inspired by real graphs. The experimental results show that Mc2g outperforms other state-of-the-art matrix completion algorithms. [ABSTRACT FROM AUTHOR]

Low rank matrix factorisation is often used in recommender systems as a way of extracting latent features. When dealing with large and sparse datasets, traditional recommendation algorithms face the problem of acquiring large, unrestrained, fluctuating values over predictions. Imposing bounding constraints has been proven an effective solution. However, existing bounding algorithms can only deal with one pair of fixed bounds, and are very time-consuming when applied on large-scale datasets. In this paper, we propose a novel algorithm named Magnitude Bounded Matrix Factorisation (MBMF), which allows different bounds for individual users/items and performs very quickly on large scale datasets. The key idea of our algorithm is to construct a model by constraining the magnitudes of each individual user/item feature vector. By converting coordinate system with radii set as the corresponding magnitudes, MBMF allows the above constrained optimisation problem to become an unconstrained one, which can be solved by unconstrained optimisation algorithms such as the stochastic gradient descent. We also explore an acceleration approach and the choice of magnitudes are given in detail as well. Experiments on synthetic and real datasets demonstrate that in most cases the proposed MBMF is superior over all existing algorithms in terms of accuracy and time complexity. [ABSTRACT FROM AUTHOR]

The low-rank matrix completion problem is fundamental in both machine learning and computer vision fields with many important applications, such as recommendation system, motion capture, face recognition, and image inpainting. In order to avoid solving the rank minimization problem which is NP-hard, several surrogate functions of the rank have been proposed in the literature. However, the matrix restored from the optimization problem based on the existing surrogate functions seriously deviates from the original one. In this paper, we first design a new non-convex Schatten capped $p$ p norm which generalizes several existing non-convex matrix norms and balances between the rank and the nuclear norm of the matrix. Then, a matrix completion method based on the Schatten capped $p$ p norm is proposed by exploiting the framework of the alternating direction method of multipliers. Meanwhile, the Schatten capped $p$ p norm regularized least squares subproblem is analyzed in detail and is solved explicitly. Finally, we evaluate the performance of the proposed matrix completion method based on extensive experiments in the field of image inpainting. All the experimental results demonstrate that the proposed method can indeed improve the accuracy of matrix completion compared with the existing methods. [ABSTRACT FROM AUTHOR]

Agnostic matrix phase retrieval (AMPR) is a general low-rank matrix recovery problem given a set of noisy high-dimensional data samples. To be specific, AMPR is targeting at recovering an $r$ -rank matrix $\mathbf {M}^*\in \mathbb {R}^{d_1\times d_2}$ as the parametric component from $n$ instantiations/samples of a semi-parametric model $y=f(\langle \mathbf {M}^*, \mathbf {X}\rangle, \epsilon)$ , where the predictor matrix is denoted as $\mathbf {X}\in \mathbb {R}^{d_1\times d_2}$ , link function $f(\cdot, \epsilon)$ is agnostic under some mild distribution assumptions on $\mathbf {X}$ , and $\epsilon$ represents the noise. In this paper, we formulate AMPR as a rank-restricted largest eigenvalue problem by applying the second-order Stein's identity and propose a new spectrum truncation power iteration (STPower) method to obtain the desired matrix efficiently. Also, we show a favorable rank recovery result by adopting the STPower method, i.e., a near-optimal statistical convergence rate under some relatively general model assumption from a wide range of applications. Extensive simulations verify our theoretical analysis and showcase the strength of STPower compared with the other existing counterparts. [ABSTRACT FROM AUTHOR]

Incomplete multi-view clustering (IMVC) optimally combines multiple pre-specified incomplete views to improve clustering performance. Among various excellent solutions, the recently proposed multiple kernel $k$ k -means with incomplete kernels (MKKM-IK) forms a benchmark, which redefines IMVC as a joint optimization problem where the clustering and kernel matrix imputation tasks are alternately performed until convergence. Though demonstrating promising performance in various applications, we observe that the manner of kernel matrix imputation in MKKM-IK would incur intensive computational and storage complexities, over-complicated optimization and limitedly improved clustering performance. In this paper, we first propose an Efficient and Effective Incomplete Multi-view Clustering (EE-IMVC) algorithm to address these issues. Instead of completing the incomplete kernel matrices, EE-IMVC proposes to impute each incomplete base matrix generated by incomplete views with a learned consensus clustering matrix. Moreover, we further improve this algorithm by incorporating prior knowledge to regularize the learned consensus clustering matrix. Two three-step iterative algorithms are carefully developed to solve the resultant optimization problems with linear computational complexity, and their convergence is theoretically proven. After that, we theoretically study the generalization bound of the proposed algorithms. Furthermore, we conduct comprehensive experiments to study the proposed algorithms in terms of clustering accuracy, evolution of the learned consensus clustering matrix and the convergence. As indicated, our algorithms deliver their effectiveness by significantly and consistently outperforming some state-of-the-art ones. [ABSTRACT FROM AUTHOR]

Compressed sensing is an emerging theory of signal processing and it has wide applications in many frontier fields. The construction of the measurement matrices is still a central problem in compressed sensing. In this paper, two types of deterministic constructions of binary measurement matrices are presented via unitary geometry. Then, the lower bounds of the spark of unitary geometry measurement matrices are theoretically analyzed, and an asymptotic comparison between unitary geometry measurement matrices and projective geometry measurement matrices is given via the worst-case recovery capability. After that, a clipping-embedding operation is proposed for binary matrices to generate measurement matrices with more sizes, which can strongly extend the applicability of the deterministic binary matrices in practice. Finally, simulation results demonstrate that the performance of our measurement matrices is comparable to, sometimes even better than, that of the corresponding Gaussian random matrices under OMP and BP. [ABSTRACT FROM AUTHOR]

Given a convex and differentiable objective $Q({\mathbf M})$ Q (M) for a real symmetric matrix ${\mathbf M}$ M in the positive definite (PD) cone—used to compute Mahalanobis distances—we propose a fast general metric learning framework that is entirely projection-free. We first assume that ${\mathbf M}$ M resides in a space ${\mathcal S}$ S of generalized graph Laplacian matrices corresponding to balanced signed graphs. ${\mathbf M}\in {\mathcal S}$ M ∈ S that is also PD is called a graph metric matrix. Unlike low-rank metric matrices common in the literature, ${\mathcal S}$ S includes the important diagonal-only matrices as a special case. The key theorem to circumvent full eigen-decomposition and enable fast metric matrix optimization is Gershgorin disc perfect alignment (GDPA): given ${\mathbf M}\in {\mathcal S}$ M ∈ S and diagonal matrix ${\mathbf S}$ S , where $S_{ii} = 1/v_i$ S i i = 1 / v i and ${\mathbf v}$ v is the first eigenvector of ${\mathbf M}$ M , we prove that Gershgorin disc left-ends of similarity transform ${\mathbf B}= {\mathbf S}{\mathbf M}{\mathbf S}^{-1}$ B = S M S - 1 are perfectly aligned at the smallest eigenvalue $\lambda _{\min }$ λ min . Using this theorem, we replace the PD cone constraint in the metric learning problem with tightest possible linear constraints per iteration, so that the alternating optimization of the diagonal / off-diagonal terms in ${\mathbf M}$ M can be solved efficiently as linear programs via the Frank-Wolfe method. We update ${\mathbf v}$ v using Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) with warm start as entries in ${\mathbf M}$ M are optimized successively. Experiments show that our graph metric optimization is significantly faster than cone-projection schemes, and produces competitive binary classification performance. [ABSTRACT FROM AUTHOR]

In the phase retrieval problem one seeks to recover an unknown $n$ dimensional signal vector $\mathbf {x}$ from $m$ measurements of the form $y_{i} = |(\mathbf {A} \mathbf {x})_{i}|$ , where $\mathbf {A}$ denotes the sensing matrix. Many algorithms for this problem are based on approximate message passing. For these algorithms, it is known that if the sensing matrix $\mathbf {A}$ is generated by sub-sampling $n$ columns of a uniformly random (i.e., Haar distributed) orthogonal matrix, in the high dimensional asymptotic regime ($m,n \rightarrow \infty, n/m \rightarrow \kappa $), the dynamics of the algorithm are given by a deterministic recursion known as the state evolution. For a special class of linearized message-passing algorithms, we show that the state evolution is universal: it continues to hold even when $\mathbf {A}$ is generated by randomly sub-sampling columns of the Hadamard-Walsh matrix, if the signal is drawn from a Gaussian prior. [ABSTRACT FROM AUTHOR]

The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completion problem are based on singular value thresholding and nuclear norm minimization. Most of the past works on this subject assume that there is a single number $p$ such that each entry of the matrix is available independently with probability $p$ and missing otherwise. This assumption may not be realistic for many applications. In this work, we replace it with the assumption that the probability that an entry is available is an unknown function $f$ of the entry itself. For example, if the entry is the rating given to a movie by a viewer, then it seems plausible that high value entries have greater probability of being available than low value entries. We propose two new estimators, based on singular value thresholding and nuclear norm minimization, to recover the matrix under this assumption. The estimators involve no tuning parameters, and are shown to be consistent under a low rank assumption. We also provide a consistent estimator of the unknown function $f$. [ABSTRACT FROM AUTHOR]

The matrix-multiply assist (MMA) facility is the latest addition to IBM's power instruction set architecture and first shipped in the recently introduced POWER10 processor. MMA is designed to accelerate matrix–matrix operations, such as matrix multiplication and convolution, using instructions that compute the outer product of vector-register operands. Outer product computations have been used for decades in linear algebra libraries to deliver high-performance implementations of matrix operations. Such libraries use conventional single-instruction–multiple-data (SIMD) instructions to emulate outer product operations. MMA in POWER10 is the first hardware with direct support for outer product operations released in the market. MMA operates with the widest diversity of data types compared to any accelerator design currently announced. Unleashing the high-performance enabled by MMA requires careful code generation. Two key considerations for optimal MMA code performance are 1) the choice of accumulation layout when maximizing the using the accumulators and 2) the selection of matrix access order. This article shows that over 92% of peak performance in POWER10 with MMA can be achieved when the code generation makes the right choices. [ABSTRACT FROM AUTHOR]

Despite the rapidly increasing interest in analog multibeam antennas, there has been a lack of systematic theoretical approaches to synthesizing circuit-type multiple beamforming networks, such as the Blass matrix and the Nolen matrix. To address the issue, this article presents a new concept, the generalized joined coupler (GJC) matrix, which encapsulates both the Blass matrix and the Nolen matrix, as well as their variants, and presents a novel theoretical framework for generating individually and independently controllable multiple beams using the GJC matrix. A GJC matrix has $N $ columns to feed $N $ antenna elements and $M $ rows to feed $M $ beams, and the direction of each individual beam can be controlled by tuning the phase shifters in the associated row of the GJC matrix. In this article, a matrix theory is developed, and an optimization algorithm is proposed to provide a mathematical tool for synthesizing such matrices and, consequently, the multiple beams. Using a particle swarm optimization algorithm, numerical results demonstrate that multibeams with independent control of individual beam directions and sidelobes can, indeed, be synthesized in a systematic manner. Specifically, two GJC matrix variants, the Blass-like matrix and the Nolen-like matrix, are investigated. [ABSTRACT FROM AUTHOR]

In this article, a new approach for solving the power flow (PF) problem of distributed generations (DGs) integrated three-phase distribution networks is proposed that is based on backward-forward sweep, graph theory, and matrix algebra. The key concept is the formation of two matrices, one that depicts the configuration or structure of the distribution system (these matrices are connectivity matrix and bus-branch topology matrix) and the second which is directly involved in computing PF parameters. The major advantage of the architecture is that the size of matrices and sparsity problems can be handled better than contemporary approaches making the approach very robust and efficient. To emulate the feature of DGs modeled as PV bus into the proposed power flow algorithm, a PV injection sensitivity matrix has been developed which facilitates computation of the required reactive power injections to offset the voltage deviation at PV bus. The computed injection is replicated in the PF using PV current beyond the branch matrix and net branch current matrix. Several test analyses have been carried out to validate the viability and efficiency of the proposed PF algorithm. [ABSTRACT FROM AUTHOR]

For graph-based multi-view clustering, a critical issue is to capture consensus cluster structures via a two-stage learning scheme. Specifically, first learn similarity graph matrices of multiple views and then fuse them into a unified superior graph matrix. Most current methods learn pairwise similarities between data points for each view independently, which is widely used in single view. However, the consensus information contained in multiple views are ignored, and the involved biases lead to an undesirable unified graph matrix. To this end, we propose a bipartite graph based multi-view clustering (BIGMC) approach. The consensus information can be represented by a small number of representative uniform anchor points for different views. A bipartite graph is constructed between data points and the anchor points. BIGMC constructs the bipartite graph matrices of all views and fuses them to produce a unified bipartite graph matrix. The unified bipartite graph matrix in turn improves the bipartite graph similarity matrix of each view and updates the anchor points. The final unified graph matrix forms the final clusters directly. In BIGMC, an adaptive weight is added for each view to avoid outlier views. A low-rank constraint is imposed on the Laplacian matrix of the unified matrix to construct a multi-component unified bipartite graph, where the component number corresponds to the required cluster number. The objective function is optimized in an alternating optimization fashion. Experimental results on synthetic and real-world data sets demonstrate its effectiveness and superiority compared with the state-of-the-art baselines. [ABSTRACT FROM AUTHOR]

We consider the problem of secure distributed matrix computation (SDMC), where a user queries a function of data matrices generated at distributed source nodes. We assume the availability of $N$ honest but curious computation servers, which are connected to the sources, the user, and each other through orthogonal and reliable communication links. Our goal is to minimize the amount of data that must be transmitted from the sources to the servers, called the upload cost, while guaranteeing that no $T$ colluding servers can learn any information about the source matrices, and the user cannot learn any information beyond the computation result. We first focus on secure distributed matrix multiplication (SDMM), considering two matrices, and propose a novel polynomial coding scheme using the properties of finite field discrete Fourier transform, which achieves an upload cost significantly lower than the existing results in the literature. We then generalize the proposed scheme to include straggler mitigation, and to the multiplication of multiple matrices while keeping the input matrices, the intermediate computation results, as well as the final result secure against any $T$ colluding servers. We also consider a special case, called computation with own data, where the data matrices used for computation belong to the user. In this case, we drop the security requirement against the user, and show that the proposed scheme achieves the minimal upload cost. We then propose methods for performing other common matrix computations securely on distributed servers, including changing the parameters of secret sharing, matrix transpose, matrix exponentiation, solving a linear system, and matrix inversion, which are then used to show how arbitrary matrix polynomials can be computed securely on distributed servers using the proposed procedure. [ABSTRACT FROM AUTHOR]

Linear transformations are the dominating computation within many important applications. The natural multiply-and-accumulate feature of memristor crossbar arrays promise unprecedented processing capabilities to resistive dot-product engines (DPEs), which can accelerate approximate matrix–vector multiplication (MVM). Unfortunately, the precision of the analog computation may be degraded by parasitics, nonlinear device characteristics, and variations. In this article, we propose a framework, called XMAP, for mapping an arbitrary matrix into appropriate memristor conductance values (or state variables for nonlinear devices). The specified conductance values are next programmed to the memristor hardware using accurate closed-loop tuning. XMAP is based on formulating the mapping problem as a mathematical optimization problem, which can be elegantly minimized using the concept of representable matrices, i.e., the matrices that can be represented on a crossbar. Compared to the state-of-the-art conversion algorithm, the computational accuracy is improved with up to $3.29 \times $ at the expense of overhead in runtime. The precision improvements translate into noteworthy application-level benefits within signal compression and neural network inference. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surfaces (RIS) have been actively researched as a potential technique for future wireless communications, which intelligently ameliorate the signal propagation environment. In the conventional design, each RIS element configures and reflects its received signal independently of all other RIS elements, which results in a diagonal phase shift matrix. By contrast, we propose a novel RIS architecture, where the incident signal impinging on one element can be reflected from another element after an appropriate phase shift adjustment, which increases the flexibility in the design of RIS phase shifts, hence, potentially improving the system performance. The resultant RIS phase shift matrix also has off-diagonal elements, as opposed to the pure diagonal structure of the conventional design. Compared to the state-of-art fully-connected/group-connected RIS structures, our proposed RIS architecture has lower complexity, while attaining a higher channel gain than the group-connected RIS structure, and approaching that of the fully-connected RIS structure. We formulate and solve the problem of maximizing the achievable rate of our proposed RIS architecture by jointly optimizing the transmit beamforming and the non-diagonal phase shift matrix based on alternating optimization and semi-define relaxation (SDR) methods. Moreover, the closed-form expressions of the channel gain, the outage probability and bit error ratio (BER) are derived. Simulation results demonstrate that our proposed RIS architecture results in an improved performance in terms of the achievable rate compared to the conventional architecture, both in single-user as well as in multi-user scenarios. [ABSTRACT FROM AUTHOR]

Distributed matrix computations over large clusters can suffer from the problem of slow or failed worker nodes (called stragglers) which can dominate the overall job execution time. Coded computation utilizes concepts from erasure coding to mitigate the effect of stragglers by running “coded” copies of tasks comprising a job; stragglers are typically treated as erasures. While this is useful, there are issues with applying, e.g., MDS codes in a straightforward manner. Several practical matrix computation scenarios involve sparse matrices. MDS codes typically require dense linear combinations of submatrices of the original matrices which destroy their inherent sparsity. This is problematic as it results in significantly higher worker computation times. Moreover, treating slow nodes as erasures ignores the potentially useful partial computations performed by them. Furthermore, some MDS techniques also suffer from significant numerical stability issues. In this work we present schemes that allow us to leverage partial computation by stragglers while imposing constraints on the level of coding that is required in generating the encoded submatrices. This significantly reduces the worker computation time as compared to previous approaches and results in improved numerical stability in the decoding process. Exhaustive numerical experiments on Amazon Web Services (AWS) clusters support our findings. [ABSTRACT FROM AUTHOR]

The performance of most clustering methods hinges on the used pairwise affinity, which is usually denoted by a similarity matrix. However, the pairwise similarity is notoriously known for its vulnerability of noise contamination or the imbalance in samples or features, and thus hinders accurate clustering. To tackle this issue, we propose to use information among samples to boost the clustering performance. We proved that a simplified similarity for pairs, denoted by a fourth order tensor, equals to the Kronecker product of pairwise similarity matrices under decomposable assumption, or provide complementary information for which the pairwise similarity missed under indecomposable assumption. Then a high order similarity matrix is obtained from the tensor similarity via eigenvalue decomposition. The high order similarity capturing spatial information serves as a robust complement for the pairwise similarity. It is further integrated with the popular pairwise similarity, named by IPS2, to boost the clustering performance. Extensive experiments demonstrated that the proposed IPS2 significantly outperformed previous similarity-based methods on real-world datasets and it was capable of handling the clustering task over under-sampled and noisy datasets. [ABSTRACT FROM AUTHOR]

We present a condition for 1/2 degree of freedom for each user in constant $K$ -user single-antenna interference channels. This condition is sufficient for all and necessary for almost all channel matrices. Moreover, it applies to all channel topologies, i.e., to fully-connected channels as well as channels that have individual links absent, reflected by corresponding zeros in the channel matrix. Moreover, it captures the essence of interference alignment by virtue of being expressed in terms of a generic injectivity condition that guarantees separability of signal and interference. Finally, we provide codebook constructions achieving 1/2 degree of freedom for each user for all channel matrices satisfying the condition we identified. [ABSTRACT FROM AUTHOR]

This note corrects a few errors in the proof of the main result of the article “Provable Low Rank Phase Retrieval.” The result itself has no change. This article introduced an alternating minimization solution, called AltMinLowRaP, for solving the Low Rank Phase Retrieval (LRPR) problem: recover an $n \times q$ matrix ${{X}^{*}}$ of rank $r$ from ${y}_{k}:= |{A}_{k}'{x}^{*}_{k}|, k=1,2, {\dots }, q$ when the measurement matrices $ {A}_{k}$ are mutually independent. Here $ {y}_{k}$ is an $m$ length vector, $ {A}_{k}$ is an $n \times m$ matrix, and $'$ denotes transpose. [ABSTRACT FROM AUTHOR]

In this work, we propose a method for the compression of the coupling matrix in volume-surface integral equation (VSIE) formulations. VSIE methods are used for electromagnetic (EM) analysis in magnetic resonance imaging (MRI) applications, for which the coupling matrix models the interactions between the coil and the body. We showed that these effects can be represented as independent interactions between remote elements in 3-D tensor formats, and subsequently decomposed with the Tucker model. Our method can work in tandem with the adaptive cross approximation (ACA) technique to provide fast solutions of VSIE problems. We demonstrated that our compression approaches can enable the use of VSIE matrices of prohibitive memory requirements, by allowing the effective use of modern graphical processing units (GPUs) to accelerate the arising matrix-vector products. This is critical to enable numerical MRI simulations at clinical voxel resolutions in a feasible computation time. In this article, we demonstrate that the VSIE matrix-vector products needed to calculate the EM field produced by an MRI coil inside a numerical body model with 1 mm3 voxel resolution, could be performed in ~33 s in a GPU, after compressing the associated coupling matrix from ~80 TB to ~43 MB. [ABSTRACT FROM AUTHOR]

Modern computers keep following the traditional model of addressing memory linearly for their main memory and out-of-core storage. While this model allows efficient row access to row-major 2D matrices, it introduces complexity to perform efficient column access. A common strategy to improve these accesses is to transpose or rotate the matrix beforehand, thus the accessing complexity is centralized in one transformation operation. Further column accesses are performed as row accesses to the transposed matrix therefore they are optimized to the memory model. In this article, we propose an efficient solution to perform in-memory or out-of-core rectangular matrix transposition and rotation by using an out-of-place strategy, reading a matrix from an input file and writing the transformed matrix to another (output) file. An originality of our processing algorithm is to rely on an optimized use of the page cache mechanism. It is parallel, optimized by several levels of tiling and independent of any disk block size. We evaluate our approach on five common storage configurations: HDD, hybrid HDD-SSD, SSD, software RAID 0 of several SSDs, and NVMe. We show that it brings significant performance improvement over a hand-tuned optimized reference implementation developed by the Caldera company and we confront it against the baseline speed of a straight file copy. [ABSTRACT FROM AUTHOR]

In this article, a vector control strategy based on indirect rotor field-oriented control (IRFOC) for star-connected three-phase induction motor (SCTPIM) drives under open-phase fault (OPF) using balanced and unbalanced transformation matrices (TMs) is proposed. Most of the current works studying SCTPIM drives under this type of fault are based on using two unbalanced TMs and ignore the leakage inductance in the FOC equations. This article studies a novel control strategy, considering the leakage inductance in the FOC equations of an SCTPIM drive under OPF. It is shown that using an unbalanced TM for stator current components and the conventional balanced TM for stator voltage components, it is possible to control an SCTPIM under OPF using a modified IRFOC system. The proposed vector control scheme is simulated and implemented using MATLAB/M-File software and DSP/TMS320F28335 controller board for a 0.75 kW SCTPIM drive system. Results show that the introduced IRFOC technique can satisfactorily control the SCTPIM under OPF condition. [ABSTRACT FROM AUTHOR]

Distributed matrix computations – matrix-matrix or matrix-vector multiplications – are well-recognized to suffer from the problem of stragglers (slow or failed worker nodes). Much of prior work in this area is (i) either sub-optimal in terms of its straggler resilience, or (ii) suffers from numerical problems, i.e., there is a blow-up of round-off errors in the decoded result owing to the high condition numbers of the corresponding decoding matrices. Our work presents a convolutional coding approach to this problem that removes these limitations. It is optimal in terms of its straggler resilience, and has excellent numerical robustness as long as the workers’ storage capacity is slightly higher than the fundamental lower bound. Moreover, it can be decoded using a fast peeling decoder that only involves add/subtract operations. Our second approach has marginally higher decoding complexity than the first one, but allows us to operate arbitrarily close to the storage capacity lower bound. Its numerical robustness can be theoretically quantified by deriving a computable upper bound on the worst case condition number over all possible decoding matrices by drawing connections with the properties of large block Toeplitz matrices. All above claims are backed up by extensive experiments done on the AWS cloud platform. [ABSTRACT FROM AUTHOR]

Resistive crossbars implement parallel vector-matrix multiplication (VMM) in analog fashion, and thus enable fast and energy-efficient neuromorphic systems. However, interconnect resistance and resistive switching devices form a complex resistance network with sneak paths. It could result in severe distortions on the output currents. When implementing neural networks, current distortions also cause significant accuracy loss. This article proposes an accurate and computationally efficient model of VMM in resistive crossbars, called diagonal matrix regression (DMR), and incorporates the model into the topology of neural networks as DMR layer (DMRL). Given an m × n crossbar, two diagonal matrices are calculated directly according to the resistance network in a time complexity of only O(m2 + n2). No hyper-parameter needs to be determined manually. Modeling of VMM is implemented in a time complexity of only O(mn). DMRL is developed to replace the weight matrix of neural networks so that the effect of interconnect resistance and the sneak path problem are well handled during ex-situ training. Using this technique, for the task of MNIST and fashion-MNIST classification, the accuracy is dramatically restored. [ABSTRACT FROM AUTHOR]

By use of the method of sliding-mode control, the stabilization of the T–S fuzzy stochastic system with time delay is considered in this article. The characteristic of the proposed method is that the input matrices of the fuzzy system are not common. And the proposed control method of this article can resist the disturbance. First, a novel sliding-mode surface is introduced. Using the new surface, the stability of the fuzzy system can be studied even if the input matrices are not common. Second, a new lemma is given to judge if the surface can be utilized in the considered system. Third, a new control law is constructed according to the new sliding-mode surface. The control law is designed to deal with the problems produced by time delay and stochastic systems. At last, two simulations are provided. In this part, the input matrices of fuzzy systems are different from each other and there is a disturbance in this considered system. From the simulations, the results illustrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]