Abstract: A method for performing data recovering operation by an electronic device is provided. The method includes: receiving, by a processor of the electronic device, object data, wherein the object data comprises an incomplete matrix; identifying, by the processor, a plurality of first entries (xi,j) of the incomplete matrix according to the object data; inputting, by the processor, the first entries (xi,j) and a preset maximum loop count (Kmax) into an executed analysis model using Bi-Branch Neural Network (BiBNN) Algorithm; and obtaining, by the processor, a plurality of second entries (mi,j) of a recovered complete matrix corresponding to the incomplete matrix from the analysis model, wherein values of the second entries are determined as original values of the first entries of the incomplete matrix, such that incorrect data in the incomplete matrix is recovered.

Abstract: A computer-implemented method for simulating a market index is provided. The method includes: receiving object data from a data source; receiving control data from an input operation applied to the analysis server; identifying one or more first values and one or more second values from the object data, and identifying a first parameter, a second parameter and a third parameter from the control data; inputting the first values, the second values, the first parameter, the second parameter and the third parameter into an executed analysis model; and obtaining an optimized weight vector corresponding to the component stocks from the analysis model, so as to simulate the market index by the weight vector and the prices of the component stocks, wherein the weight vector comprising weight percentages respectively corresponding to the component stocks, and the sum of the weight percentages is equal to one.

Abstract: A method for performing data recovering operation is provided. The method includes: identifying a plurality of first values and a plurality of first indexes of a plurality of first entries of an incomplete matrix in a received object data, and one or more second values and one or more second indexes of one or more second entries of the incomplete matrix; inputting the first values, the first indexes, a preset first parameter, a preset second parameter and a preset third parameter into an analysis model using Adaptive Rank-One Matrix Completion (AROMC) algorithm; and obtaining a recovered complete matrix corresponding to the incomplete matrix from the analysis model, so as to obtain optimized one or more second values of the second entries, wherein the optimized one or more second values are determined as original values of the second entries, such that the incomplete matrix is recovered to the recovered complete matrix.

Abstract: A wireless communication system and a precoder device for use in such system. The precoder device includes a delay element arranged to introduce a delay to a plurality of sub-channels of a signal at a transmitter end of the communication system; wherein the delay in a plurality of sub-channels are associated with a process time of a receiver component at a receiver end of the communication system.

Abstract: A method for processing electronic data includes the steps of transforming the electronic data to a matrix representation including a plurality of matrices; decomposing the matrix representation into a series of matrix approximations; and processing, with an approximation process, the plurality of matrices thereby obtaining a low-rank approximation of the plurality of matrices.

Abstract: A wireless communication system and a precoder device for use in such system. The precoder device includes a delay element arranged to introduce a delay to a plurality of sub-channels of a signal at a transmitter end of the communication system; wherein the delay in a plurality of sub-channels are associated with a process time of a receiver component at a receiver end of the communication system.

Abstract: A method for processing electronic data includes the steps of transforming the electronic data to a matrix representation including a plurality of matrices; decomposing the matrix representation into a series of matrix approximations; and processing, with an approximation process, the plurality of matrices thereby obtaining a low-rank approximation of the plurality of matrices.

Abstract: A method for processing electronic data includes the steps of transforming the electronic data to a matrix representation including a plurality of matrices; decomposing the matrix representation into a series of matrix approximations; and processing, with an approximation process, the plurality of matrices thereby obtaining a low-rank approximation of the plurality of matrices.

Abstract: A method for processing electronic data includes the steps of transforming the electronic data to a matrix representation including a plurality of matrices; decomposing the matrix representation into a series of matrix approximations; and processing, with an approximation process, the plurality of matrices thereby obtaining a low-rank approximation of the plurality of matrices.

Abstract: The present disclosure relates to methods and systems for signal processing using coordinate descent technique for solving technical implementation problems that are expressed as unit-modulus least squares (UMLS) and unit-modulus quadratic program (UMQP) problems. Embodiments provide for iteratively minimizing an objective function of a signal vector associated with a UMLS/UMQP problem expression over a set of coordinates of the signal vector to a convergence point. The objective function is minimized with respect to a vector element corresponding to a selected coordinate index, while other vector elements that do not correspond to the selected coordinate index are fixed. Accordingly, at each iteration, minimizing the objective function involves a solution to a one-dimensional univariate quadratic minimization. Embodiments also provide various coordinate index selection rules that include a cyclic CD rule (CCD), a randomized CD rule (RCD), randomly permuted CD rule (RPCD), and a greedy CD rule (CCD).

Abstract: The present disclosure relates to methods and systems for signal processing using coordinate descent technique for solving technical implementation problems that are expressed as unit-modulus least squares (UMLS) and unit-modulus quadratic program (UMQP) problems. Embodiments provide for iteratively minimizing an objective function of a signal vector associated with a UMLS/UMQP problem expression over a set of coordinates of the signal vector to a convergence point. The objective function is minimized with respect to a vector element corresponding to a selected coordinate index, while other vector elements that do not correspond to the selected coordinate index are fixed. Accordingly, at each iteration, minimizing the objective function involves a solution to a one-dimensional univariate quadratic minimization. Embodiments also provide various coordinate index selection rules that include a cyclic CD rule (CCD), a randomized CD rule (RCD), randomly permuted CD rule (RPCD), and a greedy CD rule (CCD).

Abstract: Coordinate descent is applied to recover a signal-of-interest from only magnitude information. In doing so, a single unknown value is solved at each iteration, while all other variables are held constant. As a result, only minimization of a univariate quartic polynomial is required, which is efficiently achieved by finding the closed-form roots of a cubic polynomial. Cyclic, randomized, and/or a greedy coordinate descent technique can be used. Each coordinate descent technique globally converges to a stationary point of the nonconvex problem, and specifically, the randomized coordinate descent technique locally converges to the global minimum and attains exact recovery of the signal-of-interest at a geometric rate with high probability when the sample size is sufficiently large. The cyclic and randomized coordinate descent techniques can also be modified via minimization of the l1-regularized quartic polynomial for phase retrieval of sparse signals-of-interest, i.e.

Abstract: A system and a method for processing a data structure includes the steps of: providing an incomplete data structure arranged to represent source information; processing the incomplete data structure to determine at least one estimated data element of an output data structure; and transforming the source information to output information associated with the output data structure based on a combination of the incomplete data structure and the at least one estimated data element.

Abstract: Systems and methods which provide robust low-rank matrix approximation using low-rank matrix factorization in the lp-norm space, where p<2 (e.g., 1?p<2), providing a lp-PCA technique are described. For example, embodiments are configured to provide robust low-rank matrix approximation using low-rank matrix factorization in the least absolute deviation (l1-norm) space providing a l1-PCA technique. Embodiments minimize the lp-norm of the residual matrix in the subspace factorization of an observed data matrix, such as to minimize the l1-norm of the residual matrix where p=1. The alternating direction method of multipliers (ADMM) is applied according to embodiments to solve the subspace decomposition of the low-rank matrix factorization with respect to the observed data matrix. Iterations of the ADMM may comprise solving a l2-subspace decomposition and calculating the proximity operator of the l1-norm.

Abstract: Systems and methods which provide robust low-rank matrix approximation using low-rank matrix factorization in the lp-norm space, where p<2 (e.g., 1?p<2), providing a lp-PCA technique are described. For example, embodiments are configured to provide robust low-rank matrix approximation using low-rank matrix factorization in the least absolute deviation (l1-norm) space providing a l1-PCA technique. Embodiments minimize the lp-norm of the residual matrix in the subspace factorization of an observed data matrix, such as to minimize the l1-norm of the residual matrix where p=1. The alternating direction method of multipliers (ADMM) is applied according to embodiments to solve the subspace decomposition of the low-rank matrix factorization with respect to the observed data matrix. Iterations of the ADMM may comprise solving a l2-subspace decomposition and calculating the proximity operator of the l1-norm.

Abstract: A system and a method for processing a data structure includes the steps of: providing an incomplete data structure arranged to represent source information; processing the incomplete data structure to determine at least one estimated data element of an output data structure; and transforming the source information to output information associated with the output data structure based on a combination of the incomplete data structure and the at least one estimated data element.

Abstract: Coordinate descent is applied to recover a signal-of-interest from only magnitude information. In doing so, a single unknown value is solved at each iteration, while all other variables are held constant. As a result, only minimization of a univariate quartic polynomial is required, which is efficiently achieved by finding the closed-form roots of a cubic polynomial. Cyclic, randomized, and/or a greedy coordinate descent technique can be used. Each coordinate descent technique globally converges to a stationary point of the nonconvex problem, and specifically, the randomized coordinate descent technique locally converges to the global minimum and attains exact recovery of the signal-of-interest at a geometric rate with high probability when the sample size is sufficiently large. The cyclic and randomized coordinate descent techniques can also be modified via minimization of the l1-regularized quartic polynomial for phase retrieval of sparse signals-of-interest, i.e.