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In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M-1), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible. [ABSTRACT FROM AUTHOR]

This paper is concerned with an important matrix condition in compressed sensing known as the restricted isometry property (RIP). We demonstrate that testing whether a matrix satisfies RIP is \ssr NP-hard. As a consequence of our result, it is impossible to efficiently test for RIP provided \ssr P\ne\ssr NP. [ABSTRACT FROM PUBLISHER]

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]

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]

This paper focuses on the behavior similarity of workflow nets (WF-nets). The similarity of two WF-nets reflects their consistent degree in behaviors. It explores the behavioral relations of subsets of transitions based on the interleaving semantics, and more accurate relations are defined than the existing work. Therefore, a more accurate similarity of two WF-nets (in their behaviors) can be obtained than that in the existing work that usually do not consider the loop and complex correspondence. By refining the interleaving relation in a behavioral profile into six types, this paper proposes the notion of a relation profile based on behavioral profile. Based on the relation profile of a WF-net, behavioral relation matrix can be constructed. Additionally, we refine the complex correspondence and generate a group of behavioral relation submatrices from the behavioral relation matrix. By using them we present a new formula to measure the behavior similarity of two WF-nets. Finally, examples illustrate that our method can measure the similarity degree more accurately. [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]

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]

This paper is concerned with quasi-synchronization of delayed memristive neural networks (MNNs) with switching jumps mismatches via aperiodically intermittent control. The issue is presented for three reasons: 1) the existing controllers for synchronization may be too complicated and not economical; 2) under the influence of switching jumps mismatches, synchronization of MNNs may fail to achieve; and 3) matrix measure method is less conservative but cannot be applied directly to synchronization of MNNs. To overcome these difficulties, the concept of asynchronously switching time interval is proposed to describe the phenomenon when the drive-response MNNs switch their connection weights asynchronously. Then, aperiodically intermittent control is designed and quasi-synchronization analysis is carried out based on a combined method that compromises the merits of interval matrix method and matrix measure method. A quasi-synchronization criterion, expressed in terms of the mixture of ${p}$ -norm and matrix measure of the memristive connection weights, is established. Meanwhile, the fundamental reason for the failure of complete synchronization is revealed. Moreover, an explicit expression of the error level is obtained and the design of the controller under a predetermined error level is presented. The obtained results in this paper reduce the conservativeness and provide a novel insight into the research of synchronization of MNNs. [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]

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]

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]

Recommender systems (RSs) commonly adopt a user-item rating matrix to describe users’ preferences on items. With users and items exploding, such a matrix is usually high-dimensional and sparse (HiDS). Recently, the idea of deep learning has been applied to RSs. However, current deep-structured RSs suffer from high computational complexity. Enlightened by the idea of deep forest, this paper proposes a deep latent factor model (DLFM) for building a deep-structured RS on an HiDS matrix efficiently. Its main idea is to construct a deep-structured model by sequentially connecting multiple latent factor (LF) models instead of multilayered neural networks through a nonlinear activation function. Thus, the computational complexity grows linearly with its layer count, which is easy to resolve in practice. The experimental results on four HiDS matrices from industrial RSs demonstrate that when compared with state-of-the-art LF models and deep-structured RSs, DLFM can well balance the prediction accuracy and computational efficiency, which well fits the desire of industrial RSs for fast and right recommendations. [ABSTRACT FROM AUTHOR]

In this paper, we propose CodedSketch, as a distributed straggler-resistant scheme to compute an approximation of the multiplication of two massive matrices. The objective is to reduce the recovery threshold, defined as the total number of worker nodes that the master node needs to wait for to be able to recover the final result. To exploit the fact that only an approximated result is required, in reducing the recovery threshold, some sorts of pre-compression are required. However, compression inherently involves some randomness that would lose the structure of the matrices. On the other hand, considering the structure of the matrices is crucial to reduce the recovery threshold. In CodedSketch, we use count–sketch, as a hash-based compression scheme, on the rows of the first and columns of the second matrix, and a structured polynomial code on the columns of the first and rows of the second matrix. This arrangement allows us to exploit the gain of both in reducing the recovery threshold. To increase the accuracy of computation, multiple independent count–sketches are needed. This independency allows us to theoretically characterize the accuracy of the result and establish the recovery threshold achieved by the proposed scheme. To guarantee the independency of resulting count–sketches in the output, while keeping its cost on the recovery threshold minimum, we use another layer of structured codes. The proposed scheme provides an upper-bound on the recovery threshold as a function of the required accuracy of computation and the probability that the required accuracy can be violated. In addition, it provides an upper-bound on the recovery threshold for the case that the result of the multiplication is sparse, and the exact result is required. [ABSTRACT FROM AUTHOR]

Developing resource allocation algorithms for the uplink sparse code multiple access (SCMA) scheme to satisfy multiple objectives is challenging, especially where users are randomly distributed. In this paper, we aim to address this challenge by developing a joint resource allocation method as a multi-objective optimization (MO) problem to maximize the average sum rate and fairness among users as key and sub-key objectives, respectively. For this purpose, the exact analytical expressions for the average sum rate and users’ individual rate are extracted based on an adaptive weighted graph matrix (AWGM). An AWGM matrix beneficially replaces the factor graph and the power allocation matrices to simplify the MO problem based on the asymmetric modified bipartite matching (AMBM) algorithm. The power allocation strategy is utilized during the optimal resource assignment process using the AMBM algorithm. After the AMBM process, we propose a low-complexity four-step algorithm to obtain the AWGM. The simulation results show that our proposed method can compromise and improve the multiple objectives’ performance and guarantees a stable range of network performance at different times. [ABSTRACT FROM AUTHOR]

The construction of a quasi-cyclic low density parity-check (QC-LDPC) matrix is usually carried out in two steps. In the first step, a prototype matrix is defined according to certain criteria (size, girth, check and variable node degrees, and so on). The second step involves the expansion of the prototype matrix. During this last phase, an integer value is assigned to each non-null position in the prototype matrix corresponding to the right-rotation of the identity matrix. The problem of determining these integer values is complex. The state-of-the-art solutions use either some mathematical constructions to guarantee a given girth of the final QC-LDPC code, or a random search of values until the target girth is satisfied. In this paper, we propose an alternative/complementary method that reduces the search space by defining large equivalence classes of topologically identical matrices through row and column permutations using additive, structural, and multiplicative transformations. Selecting only a single element per equivalence class can reduce the search space by a few orders of magnitude. Then, we use the formalism of constraint programming to list the exhaustive sets of solutions for a given girth and a given expansion factor. An example is presented in all sections of the paper to illustrate the methodology. [ABSTRACT FROM AUTHOR]

In 2010, Silva et al. studied certain classes of finite-field matrix channels in order to model random linear network coding where exactly $t$ random errors are introduced. In this paper, we consider a generalization of these matrix channels where the number of errors is not required to be constant, indeed the number of errors may follow any distribution. We show that a capacity-achieving input distribution can always be taken to have a very restricted form (the distribution should be uniform given the rank of the input matrix). This result complements, and is inspired by a paper of Nobrega et al., which establishes a similar result for a class of matrix channels that model network coding with link erasures. Our result shows that the capacity of our channels can be expressed as maximization over probability distributions on the set of possible ranks of input matrices: a set of linear rather than exponential size. [ABSTRACT FROM AUTHOR]

The problem of partitioning dense matrices into sets of sub-matrices has received increased attention recently and is crucial when considering dense linear algebra and kernels with similar communication patterns on heterogeneous platforms. The problem of load balancing and minimizing communication is traditionally reducible to an optimization problem that involves partitioning a square into rectangles. This problem has been proven to be NP-Complete for an arbitrary number of partitions. In this paper, we present recent approaches that relax the restriction that all partitions be rectangles. The first approach uses an original mathematical technique to find the exact optimal partitioning. Due to the complexity of the technique, it has been developed for a small number of partitions only. However, even at a small scale, the optimal partitions found by this approach are often non-rectangular and sometimes non-intuitive. The second approach is the study of approximate partitioning methods utilizing recursive partitioning algorithms. In particular we use the work on optimal partitioning to improve pre-existing algorithms. In this paper we discuss the different perspectives this approach opens and present two algorithms, SNRPP which is a $\sqrt{\frac{3}{2}}$ approximation, and NRPP which is a $\frac{2}{\sqrt{3}}$ approximation. While sub-optimal, the NRRP approach works for an arbitrary number of partitions. We use the first exact approach to analyse how close to the known optimal solutions the NRRP algorithm is for small numbers of partitions. [ABSTRACT FROM AUTHOR]

Fully polarimetric model-based decompositions are developed by accounting for the physical scattering model and experimental polarimetric SAR data acquisition processes. These decompositions offer the promising straightforward interpretation and highly improved inversion models for visualizing images of scattering scenarios optimally. However, the attempts in existing decompositions to implement the split real and imaginary components of the $T_{13}$ element of the coherency matrix have been hampered by the absence of physical models to fit the coherency matrix. In this paper, two additional physical scattering submodels are derived. The real and imaginary parts of $T_{13}$ are accounted for by implementing two newly developed physical scattering models. (One is for oriented dipole scattering and the other is for oriented quarter-wave reflection.) Furthermore, this paper is extended by implementing these physical models into a six-component scattering power model-based decomposition. To this date, the developed novel decompositions account for the maximum elements of the coherency matrix in a physical manner compared to the existing model-based decompositions. The proposed novel decomposition is tested on L-band and X-band fully polarimetric SAR data sets of the Advanced Land Observing Satellite-2/Phased Array L-band Synthetic Aperture Radar-2 and the X-band TerraSAR-X, respectively. This new decomposition produces additional two scattering submatrix components. Such scattering components are prevalent in vegetation and urban areas and even dominant over highly oriented urban scenarios. The new method enhances the truly existing double-bounce scattering contributions and reduces the overrated volume scattering from double-bounce scatterers. By comparing the results, it is found that the proposed decomposition considerably enhances the SAR image quality and its more correct visualizing presentation compared to existing decompositions. It is also found to be more robust over the oriented urban areas than the existing decompositions, resulting from the utilization of both the real and imaginary components of $T_{13}$ polarimetric information in a physical scattering manner. [ABSTRACT FROM AUTHOR]

This paper investigates the situation awareness issue of power system with massive measured data. To address this issue, first, a graph-theory-based network partitioning algorithm is proposed to realize decentralized detection in a faster response speed, while using power flow characteristics highlights the independency of different groups. Further, a hierarchical event detection method is proposed to judge voltage change and locate event position according to spectral distribution change of established multidimensional matrix. With the proposed method, the system situation can be assessed and the knowledge of the system model is not required. In addition, the accurate result of weak event happened in system could also be obtained. The simulation results are presented to illustrate the effectiveness of the proposed detection method. [ABSTRACT FROM AUTHOR]

Coded caching systems have been widely studied to reduce the data transmission during the peak traffic time. In practice, two important parameters of a coded caching system should be considered, i.e., the transmission rate which is the maximum amount of the data transmission during the peak traffic time, and the subpacketization level, the number of divided packets of each file when we implement a coded caching scheme. Although there exists a tradeoff between transmission rate and subpacketization, we prefer to design a scheme with transmission rate and subpacketization as small as possible since they reflect the transmission efficiency and complexity of the caching scheme, respectively. In this paper, we first characterize a coded caching scheme from the viewpoint of linear algebra and show that designing a linear coded caching scheme is equivalent to constructing three classes of matrices satisfying some rank conditions. Then based on the invariant subspaces in linear algebra and combinatorial design theory, a new class of coded caching schemes over $\mathbb {F}_{2}$ is obtained by constructing these three classes of matrices. It turns out that the transmission rate of our new scheme is the same as the scheme construct by Yan et al. (IEEE Trans. Inf. Theory 63, 5821-5833, 2017), but the subpacketization is significantly reduced. Finally by means of these matrices, we show that the minimum storage regenerating codes can also be used to construct coded caching schemes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a powerful technique based on Leave-One-Out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for iterative stochastic procedures in the presence of probabilistic dependency. We demonstrate the power of this approach in analyzing two of the most important algorithms for matrix completion: (i) the non-convex approach based on Projected Gradient Descent (PGD) for a rank-constrained formulation, also known as the Singular Value Projection algorithm, and (ii) the convex relaxation approach based on nuclear norm minimization (NNM). Using this approach, we establish the first convergence guarantee for the original form of PGD without regularization or sample splitting, and in particular shows that it converges linearly in the infinity norm. For NNM, we use this approach to study a fictitious iterative procedure that arises in the dual analysis. Our results show that NNM recovers an $d$ -by- $d$ rank- $r$ matrix with $\mathcal {O}(\mu r \log (\mu r) d\log d)$ observed entries. This bound has optimal dependence on the matrix dimension and is independent of the condition number. To the best of our knowledge, none of previous sample complexity results for tractable matrix completion algorithms satisfies these two properties simultaneously. [ABSTRACT FROM AUTHOR]

This paper proposes a new coupling matrix synthesis technique called the coupling matrix compression technique, which focuses on reducing the dimension of the $N+2$ coupling matrix. The presented coupling matrices can be compressed, and this technique can be used to design dual-mode resonators for high-isolation dual-band filters. One dual-mode resonator is represented as two closely coupled resonators when using this technique. The formulae for resonant frequencies and $\omega _{m}$ in dual-mode theory are also derived in this paper. A dual-mode embedded hairpin resonator is designed and analyzed using this technique, and a dual-band filter using the proposed resonators is designed and fabricated to validate the proposed technique. [ABSTRACT FROM AUTHOR]

Counting short cycles in bipartite graphs is a fundamental problem of interest in many fields including the analysis and design of low-density parity-check (LDPC) codes. There are two computational approaches to count short cycles (with length smaller than $2g$ , where $g$ is the girth of the graph) in bipartite graphs. The first approach is applicable to a general (irregular) bipartite graph, and uses the spectrum $\{\eta _{i}\}$ of the directed edge matrix of the graph to compute the multiplicity $N_{k}$ of $k$ -cycles with $k < 2g$ through the simple equation $N_{k} = \sum _{i} \eta _{i}^{k}/(2k)$. This approach has a computational complexity $\mathcal {O}(|E|^{3})$ , where $|E|$ is number of edges in the graph. The second approach is only applicable to bi-regular bipartite graphs, and uses the spectrum $\{\lambda _{i}\}$ of the adjacency matrix (graph spectrum) and the degree sequences of the graph to compute $N_{k}$. The complexity of this approach is $\mathcal {O}(|V|^{3})$ , where $|V|$ is number of nodes in the graph. This complexity is less than that of the first approach, but the equations involved in the computations of the second approach are complex and tedious, particularly for $k \geq g+6$. In fact, the computational complexity of the equations increases exponentially with $k$. In this paper, we establish an analytical relationship between the two spectra $\{\eta _{i}\}$ and $\{\lambda _{i}\}$ for bi-regular bipartite graphs. Through this relationship, the former spectrum can be derived from the latter through simple equations with computational complexity constant in $k$. This allows the computation of $N_{k}$ using $N_{k} = \sum _{i} \eta _{i}^{k}/(2k)$ but with a complexity of $\mathcal {O}(|V|^{3})$ rather than $\mathcal {O}(|E|^{3})$. [ABSTRACT FROM AUTHOR]

While capacities of discrete memoryless channels are well studied, it is still not possible to obtain a closed-form expression for the capacity of an arbitrary discrete memoryless channel (DMC). In this paper, we study a class of DMCs whose channel matrix is an invertible positive matrix. This class of channel matrices can be used to model many real-world settings. Next, an elementary technique based on Karush-Kuhn-Tucker (KKT) conditions is used to obtain (1) a good upper bound of a discrete memoryless channel having an invertible positive channel matrix and (2) a closed-form expression for the capacity if the channel matrix satisfies certain conditions related to its singular value and its Gershgorin's disk. [ABSTRACT FROM AUTHOR]

The analysis of nonconvex matrix completion has recently attracted much attention in the community of machine learning thanks to its computational convenience. Existing analysis on this problem, however, usually relies on $\ell _{2,\infty }$ projection or regularization that involves unknown model parameters, although they are observed to be unnecessary in numerical simulations. In this paper, we extend the analysis of the vanilla gradient descent for positive semidefinite matrix completion in the literature to the rectangular case, and more significantly, improve the required sampling rate from $O(\mathrm {poly}(\kappa)\mu ^{3}~r^{3} \log ^{3}~n/n)$ to $O(\mu ^{2}~r^{2} \kappa ^{14} \log n/n)$. Our technical ideas and contributions are potentially useful in improving the leave-one-out analysis in other related problems. [ABSTRACT FROM AUTHOR]

Phase retrieval refers to algorithmic methods for recovering a signal from its phaseless measurements. There has been recent interest in understanding the performance of local search algorithms that work directly on the non-convex formulation of the problem. Due to the non-convexity of the problem, the success of these local search algorithms depends heavily on their starting points. The most widely used initialization scheme is the spectral method, in which the leading eigenvector of a data-dependent matrix is used as a starting point. Recently, the performance of the spectral initialization was characterized accurately for measurement matrices with independent and identically distributed entries. This paper aims to obtain the same level of knowledge for isotropically random column-orthogonal matrices, which are substantially better models for practical phase retrieval systems. Towards this goal, we consider the asymptotic setting in which the number of measurements $m$ , and the dimension of the signal, $n$ , diverge to infinity with $m/n = \delta \in (1,\infty)$ , and obtain a simple expression for the overlap between the spectral estimator and the true signal vector. [ABSTRACT FROM AUTHOR]

This paper presents a fast and efficient alternative method to enforce passivity of frequency-dependent network equivalents (FDNE). Based on the eigenvalue perturbation theory, the proposed technique relocates the eigenvalues of the half-size singularity matrix by iteratively perturbing the residues of the FDNE model until the rational function becomes passive. It is demonstrated that the proposed technique achieves significant computational savings compared to traditional techniques. Three illustrative case studies involving different conditions of passivity violations are presented to validate the proposed method. Its effectiveness is demonstrated via comparison with two commonly used techniques, i.e., Fast Residue Perturbation (FRP) and Hamiltonian Matrix Perturbation (HMP). [ABSTRACT FROM AUTHOR]

Multi-view graph-based clustering aims to provide clustering solutions to multi-view data. However, most existing methods do not give sufficient consideration to weights of different views and require an additional clustering step to produce the final clusters. They also usually optimize their objectives based on fixed graph similarity matrices of all views. In this paper, we propose a general Graph-based Multi-view Clustering (GMC) to tackle these problems. GMC takes the data graph matrices of all views and fuses them to generate a unified graph matrix. The unified graph matrix in turn improves the data graph matrix of each view, and also gives the final clusters directly. The key novelty of GMC is its learning method, which can help the learning of each view graph matrix and the learning of the unified graph matrix in a mutual reinforcement manner. A novel multi-view fusion technique can automatically weight each data graph matrix to derive the unified graph matrix. A rank constraint without introducing a tuning parameter is also imposed on the graph Laplacian matrix of the unified matrix, which helps partition the data points naturally into the required number of clusters. An alternating iterative optimization algorithm is presented to optimize the objective function. Experimental results using both toy data and real-world data demonstrate that the proposed method outperforms state-of-the-art baselines markedly. [ABSTRACT FROM AUTHOR]

Gabidulin codes are the first general construction of linear codes that are maximum rank distant (MRD). They have found applications in linear network coding, for example, when the transmitter and receiver are oblivious to the inner workings and topology of the network (the so-called incoherent regime). The reason is that Gabidulin codes can be used to map information to linear subspaces, which in the absence of errors cannot be altered by linear operations, and in the presence of errors can be corrected if the subspace is perturbed by a small rank. Furthermore, in distributed coding and distributed systems, one is led to the design of error correcting codes whose generator matrix must satisfy a given support constraint. In this paper, we give necessary and sufficient conditions on the support of the generator matrix that guarantees the existence of Gabidulin codes and general MRD codes. When the rate of the code is not very high, this is achieved with the same field size necessary for Gabidulin codes with no support constraint. When these conditions are not satisfied, we characterize the largest possible rank distance under the support constraints and show that they can be achieved by subcodes of Gabidulin codes. The necessary and sufficient conditions are identical to those that appear for MDS codes which were recently proven by Yildiz et al. and Lovett in the context of settling the GM-MDS conjecture. [ABSTRACT FROM AUTHOR]

Multiple kernel clustering (MKC) algorithms optimally combine a group of pre-specified base kernel matrices to improve clustering performance. However, existing MKC algorithms cannot efficiently address the situation where some rows and columns of base kernel matrices are absent. This paper proposes two simple yet effective algorithms to address this issue. Different from existing approaches where incomplete kernel matrices are first imputed and a standard MKC algorithm is applied to the imputed kernel matrices, our first algorithm integrates imputation and clustering into a unified learning procedure. Specifically, we perform multiple kernel clustering directly with the presence of incomplete kernel matrices, which are treated as auxiliary variables to be jointly optimized. Our algorithm does not require that there be at least one complete base kernel matrix over all the samples. Also, it adaptively imputes incomplete kernel matrices and combines them to best serve clustering. Moreover, we further improve this algorithm by encouraging these incomplete kernel matrices to mutually complete each other. The three-step iterative algorithm is designed to solve the resultant optimization problems. After that, we theoretically study the generalization bound of the proposed algorithms. Extensive experiments are conducted on 13 benchmark data sets to compare the proposed algorithms with existing imputation-based methods. Our algorithms consistently achieve superior performance and the improvement becomes more significant with increasing missing ratio, verifying the effectiveness and advantages of the proposed joint imputation and clustering. [ABSTRACT FROM AUTHOR]

In the traditional index coding problem, a server employs coding to send messages to a set of clients within the same broadcast domain. Each client already has some messages as side information and requests a particular unknown message from the server. All clients learn the coding matrix so that they can decode and retrieve their requested data. Our starting observation comes from the work by Karmoose et al., which shows that learning the coding matrix can pose privacy concerns: it may enable a client to infer information about the requests and side information of other clients. In this paper, we mitigate this privacy concern by allowing each client to have limited access to the coding matrix. In particular, we design coding matrices so that each client needs only to learn some of (and not all) the rows to decode her requested message. We start by showing that this approach can indeed help mitigate that privacy concern. We do so by considering two different privacy metrics. The first one shows the attained privacy benefits based on a geometric interpretation of the problem. Differently, the second metric, referred to as maximal information leakage, provides upper bounds on: (i) the guessing power of the adversaries (i.e., curious clients) when our proposed approach is employed, and (ii) the effect of decreasing the number of accessible rows on the attained privacy. Then, we propose the use of $k$ -limited-access schemes: given an index coding scheme that employs $T$ transmissions, we create a $k$ -limited-access scheme with $T_{k}\geq T$ transmissions, and with the property that each client needs at most $k$ transmissions to decode her message. We derive upper and lower bounds on $T_{k}$ for all values of $k$ , and develop deterministic designs for these schemes, which are universal, i.e., independent of the coding matrix. We show that our schemes are order-optimal for some parameter regimes, and we propose heuristics that complement the universal schemes for the remaining regimes. [ABSTRACT FROM AUTHOR]

This paper presents a novel combined method for analog circuit fault diagnosis based on dependence matrices and intelligent classifiers (DM–IC). The main purpose of this method is to obtain preliminary ambiguity groups by constructing a dependence matrix, to achieve a more accurate diagnostic result by using several simple intelligent classifiers. Considering the presence of imperfect test points, a new 0-1-X dependence matrix is defined and an expansion–reduction algorithm is proposed to obtain preliminary ambiguity groups. For each of these preliminary ambiguity groups, the algorithm of separability discrimination analysis based on Fisher discriminant analysis is proposed to determine whether an ambiguity group can be further classified and how many classes should be classified. Furthermore, a new test-point optimization algorithm is proposed to simplify the input nodes, and the classifier is constructed for each separable ambiguity group. This combined method can break down a difficult classification problem into several simpler classification problems. In this way, only a small number of classifiers need to be constructed, and at most one classifier is required to participate in the diagnosis process. Our experimental results clearly demonstrate the superiority of the DM–IC method, which has a 100% correct classification of fault classes, fewer ambiguity groups, and smaller ambiguity groups in the sample circuit. [ABSTRACT FROM AUTHOR]

This paper evaluates a design structure matrix (DSM) as a new approach for assessing the system readiness level (SRL) of complex systems. A framework to demonstrate how a current SRL calculation method can be incorporated into the DSM tool is presented to demonstrate the benefits of DSMs for improved confidence in system readiness assessments. A cross-comparison of the modeled system readiness results obtained with a current SRL approach with nesting assumptions and the proposed DSM approach suggests that the DSM approach provides more accurate results and may be more practical for complex system analysis. The application of the DSM approach to a real-world example is also presented to demonstrate how a DSM framework facilitates the decision-making process for system readiness assessment by providing a more evidence-based maturity assessment for complex systems. The DSM approach discussed in this research can be easily adopted by program managers and practitioners for a wide range of complex systems and system architectures with multiple subsystem components. [ABSTRACT FROM AUTHOR]

Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises. Traditional matrix completion algorithms are always based on $l_2$ -norm minimization and are sensitive to non-Gaussian noise with outliers. In this paper, we propose a novel robust and fast matrix completion method based on the maximum correntropy criterion (MCC). The correntropy-based error measure is utilized instead of the $l_2$ -based error norm to improve robustness against noise. By using the half-quadratic optimization technique, the correntropy-based optimization can be transformed into a weighted matrix factorization problem. Two efficient algorithms are then derived: an alternating minimization-based algorithm and an alternating gradient descent-based algorithm. These algorithms do not require the singular value decomposition (SVD) to be calculated for each iteration. Furthermore, an adaptive kernel width selection strategy is proposed to accelerate the convergence speed as well as improve the performance. A comparison with existing robust matrix completion algorithms is provided by simulations and shows that the new methods can achieve better performance than the existing state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel methodology for characterizing the performance of deep learning networks (ResNets and DenseNet) with respect to training convergence and generalization as a function of mini-batch size and learning rate for image classification. This methodology is based on novel measurements derived from the eigenvalues of the approximate Fisher information matrix, which can be efficiently computed even for high capacity deep models. Our proposed measurements can help practitioners to monitor and control the training process (by actively tuning the mini-batch size and learning rate) to allow for good training convergence and generalization. Furthermore, the proposed measurements also allow us to show that it is possible to optimize the training process with a new dynamic sampling training approach that continuously and automatically change the mini-batch size and learning rate during the training process. Finally, we show that the proposed dynamic sampling training approach has a faster training time and a competitive classification accuracy compared to the current state of the art. [ABSTRACT FROM AUTHOR]

This paper treats the recovery of sparse, binary signals through box-constrained basis pursuit using biased measurement matrices. Using a probabilistic model, we provide conditions under which the recovery of both sparse and saturated binary signals is very likely. In fact, we also show that under the same condition, the solution of the boxed-constrained basis pursuit program can be found using boxed-constrained least squares. [ABSTRACT FROM AUTHOR]