Electrical Data Matrix Decomposition in Smart Grid

As the development of smart grid and energy internet, this leads to a significantincrease in the amount of data transmitted in real time. Due to the mismatch withcommunication networks that were not designed to carry high-speed and real time data,data losses and data quality degradation may happen constantly. For this problem,according to the strong spatial and temporal correlation of electricity data which isgenerated by human’s actions and feelings, we build a low-rank electricity data matrixwhere the row is time and the column is user. Inspired by matrix decomposition, we dividethe low-rank electricity data matrix into the multiply of two small matrices and use theknown data to approximate the low-rank electricity data matrix and recover the missedelectrical data. Based on the real electricity data, we analyze the low-rankness of theelectricity data matrix and perform the Matrix Decomposition-based method on the realdata. The experimental results verify the efficiency and efficiency of the proposed scheme.

Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli

We apply the local method of fundamental solutions(LMFS)to boundary value problems(BVPs)for the Laplace and homogeneous biharmonic equations in annuli.By appropriately choosing the collocation points,the LMFS discretization yields sparse block circulant system matrices.As a result,matrix decomposition algorithms(MDAs)and fast Fourier transforms(FFTs)can be used for the solution of the systems resulting in considerable savings in both computational time and storage requirements.The accuracy of the method and its ability to solve large scale problems are demonstrated by applying it to several numerical experiments.

A Unified Co-Processor Architecture for Matrix Decomposition

QR and LU decompositions are the most important matrix decomposition algorithms. Many studies work on accelerating these algorithms by FPGA or ASIC in a case by case style. In this paper, we propose a unified framework for the matrix decomposition algorithms, combining three QR decomposition algorithms and LU algorithm with pivoting into a unified linear array structure. The QR and LU decomposition algorithms exhibit the same two-level loop structure and the same data dependency. Utilizing the similarities in loop structure and data dependency of matrix decomposition, we unify a fine-grained algorithm for all four matrix decomposition algorithms. Furthermore, we present a unified co-processor structure with a scalable linear array of processing elements （PEs）, in which four types of PEs are same in the structure of memory channels and PE connections, but the only difference exists in the internal structure of data path. Our unified co-processor, which is IEEE 32-bit floating-point precision, is implemented and mapped onto a Xilinx Virtex5 FPGA chip. Experimental results show that our co-processors can achieve speedup of 2.3 to 14.9 factors compared to a Pentium Dual CPU with double SSE threads.

Modeling mechanism of a novel fractional grey mode based on matrix analysis

To fully display the modeling mechanism of the novelfractional order grey model （FGM （q,1））, this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and the raw data matrix, whichare consistent with the fractional order accumulative grey model（FAGM （1,1））. Following this, this paper decomposes the accumulativedata difference matrix into the accumulative generationmatrix, the q-order reductive accumulative matrix and the rawdata matrix, and then combines the least square method, findingthat the differential order affects the model parameters only byaffecting the formation of differential sequences. This paper thensummarizes matrix decomposition of some special sequences,such as the sequence generated by the strengthening and weakeningoperators, the jumping sequence, and the non-equidistancesequence. Finally, this paper expresses the influences of the rawdata transformation, the accumulation sequence transformation,and the differential matrix transformation on the model parametersas matrices, and takes the non-equidistance sequence as an exampleto show the modeling mechanism.

Mobility and equilibrium stability analysis of pin-jointed mechanisms with equilibrium matrix SVD

Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equilibrium stability of mechanisms according to the effects of the external loads. The first and second variations of the potential energy function of mechanisms under conservative force field are analyzed. Based on the singular value decomposition (SVD) method, a new crite- rion for the mobility and equilibrium stability of mechanisms can be concluded by analyzing the equilibrium matrix. The mobility and stability of mechanisms can be classified by unified matrix formulae. A number of examples are given to demonstrate the proposed criterion. In the end, criteria are summarized in a table.

Parameters Compressing in Deep Learning

With the popularity of deep learning tools in image decomposition and natural language processing,how to support and store a large number of parameters required by deep learning algorithms has become an urgent problem to be solved.These parameters are huge and can be as many as millions.At present,a feasible direction is to use the sparse representation technique to compress the parameter matrix to achieve the purpose of reducing parameters and reducing the storage pressure.These methods include matrix decomposition and tensor decomposition.To let vector take advance of the compressing performance of matrix decomposition and tensor decomposition,we use reshaping and unfolding to let vector be the input and output of Tensor-Factorized Neural Networks.We analyze how reshaping can get the best compress ratio.According to the relationship between the shape of tensor and the number of parameters,we get a lower bound of the number of parameters.We take some data sets to verify the lower bound.

A multiscale Galerkin method for the hypersingular integral equation reduced by the harmonic equation

The aim of this paper is to investigate the numerical solution of the hypersingular integral equation reduced by the harmonic equation. First, we transform the hypersingular integral equation into 2π-periodic hypersingular integral equation with the map x=cot（θ/2）. Second, we initiate the study of the multiscale Galerkin method for the 2π-periodic hypersingular integral equation. The trigonometric wavelets are used as trial functions. Consequently, the 2j＋1 × 2j＋1 stiffness matrix Kj can be partitioned j×j block matrices. Furthermore, these block matrices are zeros except main diagonal block matrices. These main diagonal block matrices are symmetrical and circulant matrices, and hence the solution of the associated linear algebraic system can be solved with the fast Fourier transform and the inverse fast Fourier transform instead of the inverse matrix. Finally, we provide several numerical examples to demonstrate our method has good accuracy even though the exact solutions are multi-peak and almost singular.

Note on Implementation of Three-Qubit SWAP Gate

In this paper, the synthesis and implementation of three-qubit SWAP gate is discussed. The three-qubit SWAP gate can be decomposed into product of 2 two-qubit SWAP gates, and it can be realized by 6 CNOT gates. Research illustrated that although the result is very simple, the current methods of matrix decomposition for multi-qubit gate can not get that. Then the implementation of three-qubit SWAP gate in the three spin system with Ising interaction is investigated and the sequence of control pulse and drift process to implement the gate is given. It needs 23 control pulses and 12 drift processes. Since the interaction can not be switched on and off at will, the realization of three-qubit SWAP gate in specific quantum system also can not simply come down to 2 two-qubit SWAP gates.

COMPARISON OF OPTICAL POLARIMETRY AND DIFFUSION TENSOR MR IMAGING FOR ASSESSING MYOCARDIAL ANISOTROPY

We have recently proposed an optical method for assessing heart structure that uses polarized light measurement of birefringence as an indicator of tissue anisotropy.The highly aligned nature of healthy cardiac muscle tissue has a detectable effect on the polarization of light,resulting in a measurable phase shift(“retardance”).When this organized tissue structure is perturbed,for example after cardiac infarction(heart attack),scar tissue containing disorganized collagen is formed,causing a decrease in the measured retardance values.However,these are dependent not only on tissue anisotropy,but also on the angle between the tissue’s optical anisotropy direction and the beam interrogating the sample.To remove this experimental ambiguity,we present a method that interrogates the sample at two different incident beam angles,thus yielding enough information to uniquely determine the true magnitude and orientation of the tissue optical anisotropy.We use an infarcted porcine heart model to compare these polarimetryderived anisotropy metrics with those obtained with diffusion tensor magnetic resonance imaging(DT-MRI).The latter yields the anisotropy and the direction of tissue water diffusivity,providing an independent measure of tissue anisotropy.The optical and MR results are thus directly compared in a common ex vivo biological model of interest,yielding reasonable agreement but also highlighting some technique-specific differences.

The G^3 spline basis functions

The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equations for constructing G3 splines can be presented independently of geometric shape parameters＇ values. It makes the equation＇s solving easier. It is also known that the general form of the G3spline basis function is given in the first time. Its geometric construction method is presented.

A local f-x Cadzow method for noise reduction of seismic data obtained in complex formations

A noise-reduction method with sliding called the local f-x Cadzow noise-reduction method, windows in the frequency-space （f-x） domain, is presented in this paper. This method is based on the assumption that the signal in each window is linearly predictable in the spatial direction while the random noise is not. For each Toeplitz matrix constructed by constant frequency slice, a singular value decomposition （SVD） is applied to separate signal from noise. To avoid edge artifacts caused by zero percent overlap between windows and to remove more noise, an appropriate overlap is adopted. Besides flat and dipping events, this method can enhance curved and conflicting events. However, it is not suitable for seismic data that contains big spikes or null traces. It is also compared with the SVD, f-x deconvolution, and Cadzow method without windows. The comparison results show that the local Cadzow method performs well in removing random noise and preserving signal. In addition, a real data example proves that it is a potential noise-reduction technique for seismic data obtained in areas of complex formations.

An iterative algorithm for solving ill-conditioned linear least squares problems

Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.

A Geometric View on Inner Transformation between the Variables of a Linear Regression Model

In the teaching and researching of linear regression analysis, it is interesting and enlightening to explore how the dependent variable vector can be inner-transformed into regression coefficient estimator vector from a visible geometrical view. As an example, the roadmap of such inner transformation is presented based on a simple multiple linear regression model in this work. By applying the matrix algorithms like singular value decomposition (SVD) and Moore-Penrose generalized matrix inverse, the dependent variable vector lands into the right space of the independent variable matrix and is metamorphosed into regression coefficient estimator vector through the three-step of inner transformation. This work explores the geometrical relationship between the dependent variable vector and regression coefficient estimator vector as well as presents a new approach for vector rotating.

Research and Implementation of Task Management Model in Product Development Process Management

The implementation of product development process management (PDPM) is an effective means of developing products with higher quality in shorter lead time. It is argued in this paper that product, data, person and activity are basic factors in PDPM With detailed analysis of these basic factors and their relations in product developmed process, all product development activities are considered as tasks and the management of product development process is regarded as the management of task execution A task decomposition based product development model is proposed with methods of constructing task relation matrix from layer model and constraint model resulted from task decomposition. An algorithm for constructing directed task graph is given and is used in the management of tasks. Finally, the usage and limitation of the proposed PDPM model is given with further work proposed.

Cryptanalysis of Schemes Based on Pseudoinverse Matrix

Advances in quantum computation threaten to break public key eryptosystems that are based on the difficulty of fac- torization or the difficulty of discrete logariths, although , no quantum algorithms have been found to be able to solve certain mathematical problems on non-commutative algebraic structures up to now. The proposed new quasi-inverse based cryptography scheme is vulnerable to a linear algebra attack based on the probable occurrence of weak keys in the generation process. In this paper, we illustrate that two of the quasi-inverse based cryptography are vulnerable to a structural attack and that it only requires polynomial time to obtain the equivalent keys for some given public keys. In addition, we conduct a detailed analysis on attack methods and provide some improved suggestions on these two schemes.

Unified calculation of eigen-solutions in power systems based on matrix perturbation theory

Calculation of eigen-solutions plays an important role in the small signal stability analysis of power systems.In this paper,a novel approach based on matrix perturbation theory is proposed for the calculation of eigen-solutions in a perturbed system.Rigorous theoretical analysis is conducted on the solution of distinct,multiple,and close eigen-solutions,respectively,under perturbations of parameters.The computational flowchart of the unified solution of eigen-solutions is then proposed,aimed toward obtaining eigen-solutions of a perturbed system directly with algebraic formulas without solving an eigenvalue problem repeatedly.Finally,the effectiveness of the matrix perturbation based approach for eigen-solutions’calculation in power systems is verified by numerical examples on a two-area four-machine system.

Modeling the Correlations of Relations for Knowledge Graph Embedding

Knowledge graph embedding, which maps the entities and relations into low-dimensional vector spaces, has demonstrated its effectiveness in many tasks such as link prediction and relation extraction. Typical methods include TransE, TransH, and TransR. All these methods map different relations into the vector space separately and the intrinsic correlations of these relations are ignored. It is obvious that there exist some correlations among relations because different relations may connect to a common entity. For example, the triples （Steve Jobs, PlaceOfBrith, California） and （Apple Inc., Location, California） share the same entity California as their tail entity. We analyze the embedded relation matrices learned by TransE/TransH/TransR, and find that the correlations of relations do exist and they are showed as low-rank structure over the embedded relation matrix. It is natural to ask whether we can leverage these correlations to learn better embeddings for the entities and relations in a knowledge graph. In this paper, we propose to learn the embedded relation matrix by decomposing it as a product of two low-dimensional matrices, for characterizing the low-rank structure. The proposed method, called TransCoRe （Translation-Based Method via Modeling the Correlations of Relations）, learns the embeddings of entities and relations with translation-based framework. Experimental results based on the benchmark datasets of WordNet and Freebase demonstrate that our method outperforms the typical baselines on link prediction and triple classification tasks.

Efficient Preference Clustering via Random Fourier Features

Approximations based on random Fourier features have recently emerged as an efficient and elegant method for designing large-scale machine learning tasks.Unlike approaches using the Nystr?m method,which randomly samples the training examples,we make use of random Fourier features,whose basis functions(i.e.,cosine and sine)are sampled from a distribution independent from the training sample set,to cluster preference data which appears extensively in recommender systems.Firstly,we propose a two-stage preference clustering framework.In this framework,we make use of random Fourier features to map the preference matrix into the feature matrix,soon afterwards,utilize the traditional k-means approach to cluster preference data in the transformed feature space.Compared with traditional preference clustering,our method solves the problem of insufficient memory and greatly improves the efficiency of the operation.Experiments on movie data sets containing 100000 ratings,show that the proposed method is more effective in clustering accuracy than the Nystr?m and k-means,while also achieving better performance than these clustering approaches.

Compositional metric learning for multi-label classification

Multi-label classification aims to assign a set of proper labels for each instance,where distance metric learning can help improve the generalization ability of instance-based multi-label classification models.Existing multi-label metric learning techniques work by utilizing pairwise constraints to enforce that examples with similar label assignments should have close distance in the embedded feature space.In this paper,a novel distance metric learning approach for multi-label classification is proposed by modeling structural interactions between instance space and label space.On one hand,compositional distance metric is employed which adopts the representation of a weighted sum of rank-1 PSD matrices based on com-ponent bases.On the other hand,compositional weights are optimized by exploiting triplet similarity constraints derived from both instance and label spaces.Due to the compositional nature of employed distance metric,the resulting problem admits quadratic programming formulation with linear optimization complexity w.r.t.the number of training examples.We also derive the generalization bound for the proposed approach based on algorithmic robustness analysis of the compositional metric.Extensive experiments on sixteen benchmark data sets clearly validate the usefulness of compositional metric in yielding effective distance metric for multi-label classification.

Psycho-visual modulation based information display:introduction and survey

Industry and academia have been making great efforts in improving refresh rates and resolutions of display devices to meet the ever increasing needs of consumers for better visual quality.As a result,many modem displays have spatial and temporal resolutions far beyond the discern capability of human visual systems.Thus,leading to the possibility of using those display-eye redundancies for innovative usages.Tempo-ral/spatial psycho-visual modulation(TPVM/SPVM)was proposed to exploit those redundancies to generate multiple visual percepts for different viewers or to transmit non-visual data to computing devices without affecting normal viewing.This paper reviews the STPVM technology from both conceptual and algorithmic perspectives,with exemplary applications in multiview display,display with visible light communication,etc.Some possible future research directions are also identified.