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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]

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]

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]

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]