Search

In this paper, the problem of clustering data points that lie near or on a union of independent low‐dimensional subspaces is addressed. To this end, the popular spectral clustering‐based algorithms usually follow a two‐stage strategy that initially builds an affinity matrix and then applies spectral clustering. However, an inappropriate affinity matrix that does not sufficiently connect data points lying on the same subspace will easily lead to the issue of over‐segmentation. To alleviate this issue, building the affinity matrix based on subspace hypotheses generated by an iterative sampling operation according to the Random Cluster Model under the framework of energy minimisation is proposed. Specifically, each hypothesis is generated from a large number of data points by sampling a component in a K‐nearest neighbour graph. Extensive experiments on synthetic data and real‐world datasets show that the proposed method can improve the connectivity of the affinity matrix and provide competitive results against state‐of‐the‐art methods. [ABSTRACT FROM AUTHOR]

Sorted QR decomposition (SQRD) has been extensively adopted for various multiple‐input‐multiple‐output (MIMO) detectors, in which the sorting process incurs severe latency when it comes to larger‐scale MIMO situations. This paper proposes a group‐SQRD (GSQRD) algorithm to alleviate the latency problem of general SQRD architectures for larger‐scale MIMO systems. Via predictively sorting a group of 4 columns at one stage, the GSQRD could eliminate the processing latency by 41% for decomposing 16×16 complex‐valued matrices. Additionally, this percentage even rises up to 68% for decomposing 128×128 matrices. To analyse the side effects, the GSQRD is applied in various MIMO detectors in a simulation link, which exhibits a negligible performance degradation for MIMO detection. Moreover, GSQRD is a hardware‐friendly algorithm because the division and square root operations in GSQRD are converted to multiplications for simplifying the hardware implementation. Based on this algorithm, two corresponding hardware architectures, which contains 2 and 4 columns respectively in a sorting group, are also implemented with 65‐nm CMOS technology. These architectures can work at 513 MHz to decompose 16×16 complex‐valued matrices. The processing latencies are respectively 0.32 and 0.26 μs, superior to the state‐of‐art designs. [ABSTRACT FROM AUTHOR]

Copyright of Papers in Regional Science is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An interference leakage minimisation transceiver design for multiple‐input multiple‐output Interference Channel networks is proposed by making use of the full rank constraint of the desired signal, the low rank constraint and low power constraint of the interference signal. The objective is to suppress interference leakage caused by not only the signal from other users, but also the other streams from the same user. To do so, the transmit precoding matrix and the receive filtering matrix are iteratively optimised through convex optimisation tools at stream level. Furthermore, a Min–Max interference leakage algorithm is also proposed to suppress the maximum interference from user, with the purpose of guaranteeing the fairness among users. Simulation results demonstrate that taking inter‐stream interference into consideration can significantly improve the effectiveness of multiple‐input multiple‐output Interference Channel networks, while the Min–Max method can slightly increase the system capacity under certain conditions. It can be also confirmed that the trade‐off among effectiveness, fairness and robustness exists in the transceiver optimisation of multiple‐input multiple‐output Interference Channel networks. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new approach to multicriteria decision analysis. They were named as processing technique of ratings for ranking of alternatives (PROTERRA). The consecutive steps of the process include normalization of the ratings, calculating of the ratings ratios within each pair of the alternatives, creating a component matrix for each of the criteria, and creating a total matrix that is the sum of the weighted component matrices. Aggregated ratings of individual alternatives result from the sums of all the values of the corresponding rows and columns of the total matrix elements. A practical application of the PROTERRA has been illustrated with an example of a decision problem concerning the choice of a shopping centre location. The analysis results of the PROTERRA are compared with other results obtained using the most popular methods, that is, analytic hierarchy process, preference ranking organization method for enrichment of evaluations, and technique for order performance by similarity to ideal solution. In order to assess the stability of the ranking order obtained by the PROTERRA algorithm, the influence of weights variations on the final ranking results were tested. The sensitivity analysis was also carried out for the other methods, that is, preference ranking organization method for enrichment of evaluations, analytic hierarchy process, and technique for order performance by similarity to ideal solution. On this basis, a stability of rankings resulting from all analysed methods were compared. [ABSTRACT FROM AUTHOR]

We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisher's Z‐transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n × n correlation matrix from any vector in Rn(n−1)/2 is provided, and we derive its numerical complexity. [ABSTRACT FROM AUTHOR]

The study addresses the consensus problem of linear time invariant (LTI) multi-agent systems with constant input delay and matched external disturbances by using relative output information. First, distributed disturbance observers are constructed to estimate the disturbances generated by linear exosystems with unknown initial conditions. Next, a disturbance observer-based predictor feedback control law is developed for each agent to realise consensus disturbance rejection in the presence of input delay. Then, a linear matrix inequality-based control design algorithm is given to determine the satisfactory control parameters. It is proved that state consensus can be achieved for both leaderless and leader--follower networks in the presence of large input delay and matched disturbances under the control scheme. Finally, a simulation example is provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

Two multi-parametric iterative algorithms are developed to solve the forward discrete periodic Lyapunov matrix equation associated with discrete-time linear periodic systems. An important feature of one of the proposed algorithms is that the information in the current and the last steps is used to update the iterative sequence. Necessary and sufficient conditions for these two algorithms to be convergent are provided in terms of the roots of a set of polynomial equations. Based on these conditions, a two-dimensional section method is established to search suboptimal tuning parameters for these two algorithms. In addition, convergence properties are also analysed for some special cases of the obtained algorithms. Finally, numerical examples are provided to illustrate the effectiveness of the proposed algorithms. It can be found that the presented algorithms have better convergence performance than some existing iterative algorithms by choosing proper tuning parameters. [ABSTRACT FROM AUTHOR]

According to the structural characteristics of non-uniform dual circular array (NDCA), a new method is proposed to solve the problem of mutual coupling error. In this algorithm, solving the mutual coupling problem of NDCA can be equivalent to solving that of non-uniform linear array (NLA). Firstly, the mutual coupling matrix is divided into several blocks. Then, each sub-block can be decomposed into the sum of several matrices with special characteristics by matrix addition method. As a result, the signal angles and mutual coupling coefficients can be conveniently decoupled. Compared with the iterative self-calibration algorithm, the proposed algorithm has a small amount of calculation. Moreover, it neither requires any prior information nor has problem of local convergence. The new method can accurately estimate the signal directions and mutual coupling coefficients. [ABSTRACT FROM AUTHOR]

According to compressive sensing (CS) technique, the smaller the mutual coherence between CS matrix and transformer matrix (Φ and Ψ), the better the performance of CS matrix to reduce the reconstruction error. Generating CS matrix from any distribution may achieve low but not minimum mutual coherence. In this study, using Chicken Swarm Optimisation (CSO), we propose a new efficient CS matrix optimisation algorithm (CSMO-CSO) to optimise CS matrix by minimising the mutual coherence between Φ and Ψ. The proposed CSMO-CSO succeeds to minimise the coherence between CS matrix and transformer matrix which improves the CS matrix, and thereby minimise the reconstruction error. The simulation results show that the performance of proposed algorithm exceeds the baseline existing algorithm in terms of mutual coherence reduction and normalised mean square error reduction. [ABSTRACT FROM AUTHOR]

This paper is addressing problems related to the construction of classifiers based on the Similarity Discriminant Function (SDF), in which the traditional vector representation of a pattern is replaced with matrix data. We introduce potential modifications of the matrix data structure and propose new variants of the SDF. The algorithms that we present were tested on images of handwritten digits and on photographs of human faces, taken from the ORL and CMU-PIE databases. The results of experiments show that our modifications significantly improved the performance of the original SDF classifier. [ABSTRACT FROM AUTHOR]

It is known that prices only cannot usually be utilized to coordinate a linear economic system. This paper considers a linear economic system. formally represented as a linear programming model which is interpreted as a resource-allocation problem. An algorithm founded on the idea of associating with each resource a linearly increasing price schedule rather than a constant price is developed. The paper hence demonstrates that a mechanism rather similar to a pure price mechanism can be used both to find and sustain an optimal allocation of resources in a linear economic system. [ABSTRACT FROM AUTHOR]

Torrance [4] has proposed a "new" approach to finding an initial solution of a linear programming problem for use in conjunction with the dual simplex algorithm. The purpose of this note is to comment on two aspects of that paper. Firstly, Torrance's method is not new at all, but !`as proposed in 1958 by Wagner. Secondly, the method can be implemented much more efficiently than Torrance suggests. [ABSTRACT FROM AUTHOR]

Multiple twinning in cubic crystals is represented geometrically by a three-dimensional fractal and algebraically by a groupoid. In this groupoid, the variant crystals are the objects, the misorientations between the variants are the operations, and the Σ3 n operators are the different types of operations (expressed by sets of equivalent operations). A general formula gives the number of variants and the number of Σ3 n operators for any twinning order. Different substructures of this groupoid (free group, semigroup) can be equivalently introduced to encode the operations with strings. For any coding substructure, the operators are expressed by sets of equivalent strings. The composition of two operators is determined without any matrix calculation by string concatenations. It is multivalued due to the groupoid structure. The composition table of the operators is used to identify the Σ3 n grain boundaries and to reconstruct the twin related domains in the electron back-scattered diffraction maps. [ABSTRACT FROM AUTHOR]

The Lemke-Howson algorithm is the classical method for finding one Nash equilibrium of a bimatrix game. This paper presents a class of square bimatrix games for which this algorithm takes, even in the best case, an exponential number of steps in the dimension d of the game. Using polytope theory, the games are constructed using pairs of dual cyclic polytopes with 2d suitably labeled facets in rf-space. The construction is extended to nonsquare games where, in addition to exponentially long Lemke-Howson computations, finding an equilibrium by support enumeration takes on average exponential time. [ABSTRACT FROM AUTHOR]

This paper presents the necessary and sufficient conditions for determining the signs of the solution variables of a system of linear equations based only upon a knowledge of the signs of the coefficient matrix and the signs of the "right hand side" variables. This problem was initially formulated in economics due to the idea that the signs of an equation's derivatives might have a stronger empirical basis than that of a particular functional form. A new interest in qualitative problems has arisen in connection with the need to develop analytic measures in order to better manage the understanding and use of large, computer-based mathematical systems. The conditions for the qualitative determinancy of nonhomogeneous systems are developed in terms of a small number of necessary conditions which are jointly sufficient. Algorithmic approaches are given for testing a given system for qualitative determinancy. For nonhomogeneous systems algorithms are given for constructing all possible qualitatively determinate systems of a given size. For the homogeneous case conditions are also given for the qualitative invertibility of the (irreducible) coefficient matrix. These conditions are then related to the problem of partially qualitatively determinate systems and the signs in the qualitative inverse of a matrix. [ABSTRACT FROM AUTHOR]

This paper demonstrates how a two or three component error structure can be used with seemingly unrelated regressions. Its application may be particularly useful with large panel data sets when the researcher wishes to estimate several equations simultaneously and believes that errors both between and within equations are correlated over time and across units. Relatively simple algorithms are presented for estimation of the error covariance matrix and generalized least squares coefficients. [ABSTRACT FROM AUTHOR]

In a very interesting recent paper, the authors proposed a least support denoising-orthogonal matching pursuit (LSD-OMP) algorithm and gave a sufficient condition for LSD-OMP algorithm in terms of restricted isometry constant of the measurement matrix. According to Dai and Milenkovic (2009), Wang et al. (2012) and Needell and Tropp (2009), this comment will point out that there are some errors in Tawfic and Kayhan (2015). [ABSTRACT FROM AUTHOR]

A scalable method to cluster data sets too large to fit in memory is presented. This method does not depend on random subsampling, but does scan every individual data sample in a deterministic way. The original data are represented in factored form by the product of two matrices, one or both of which is very sparse. This factored form avoids the need to multiply together these two matrices by using a variant of the Principal Direction Divisive Partitioning (PDDP) algorithm which does not depend on computing the distances between the individual samples. The resulting clustering algorithm is Piecemeal PDDP (PMPDDP), in which the original data are broken up into sections which will fit into memory and clustered. The cluster centers are used to create approximations to the original data items, and each original data item is represented by a linear combination of these centers. We evaluate the performance of PMPDDP on three real data sets, and observe that the quality of the clusters of PMPDDP is comparable to PDDP for the data sets examined. [ABSTRACT FROM AUTHOR]

When two structures in close proximity and with different properties (heights, structural systems, materials) are subjected to a strong seismic ground motion there is the possibility that pounding between them may occur. The large impact loads induced by this phenomenon usually lead to catastrophic results. One way to overcome this effect is to couple the structures through elastic or damping elements. This article examines the use of a new variable damping device as a coupling element. The system, which is termed a variable damping semiactive (VDSA) device, consists of two dampers with constant parameters whose lower ends are attached to a common vertical rod whereas the upper ends are attached to the two structures. As the structures vibrate due to the ground motion, the lower end is moved up and down by means of an actuator. By changing the orientation of the dampers, the effective damping in the two structures can be changed in time in an appropriate manner to minimize the response. A new control law is used to calculate the optimal position of the dampers. The algorithm, referred to as Q v, is a variation of the Instantaneous Optimal Control and it is based on the minimization of a performance index J quadratic in the state vector, the control force vector, and a vector of absolute velocities measured at selected points. The algorithm includes a generalized LQR scheme where penalties are imposed on the state vector, on the control vector, and on the absolute velocity vector through three predefined matrices. A numerical simulation is used to verify the performance of the proposed protective system in reducing the seismic response to a series of historic earthquakes. The results show that the proposed device is able not only to eliminate the pounding effects but also to significantly reduce the response of the individual adjacent structures. [ABSTRACT FROM AUTHOR]

Aim The nestedness temperature of presence–absence matrices is currently calculated with the nestedness temperature calculator (NTC). In the algorithm implemented by the NTC: (1) the line of perfect order is not uniquely defined, (2) rows and columns are reordered in such a way that the packed matrix is not the one with the lowest temperature, and (3) the null model used to determine the probabilities of finding random matrices with the same or lower temperature is not adequate for most applications. We develop a new algorithm, BINMATNEST (binary matrix nestedness temperature calculator ), that overcomes these difficulties. Methods BINMATNEST implements a line of perfect order that is uniquely defined, uses genetic algorithms to determine the reordering of rows and columns that leads to minimum matrix temperature, and provides three alternative null models to calculate the statistical significance of matrix temperature. Results The NTC performs poorly when the input matrix has checkerboard patterns. The more efficient packing of BINMATNEST translates into matrix temperatures that are lower than those computed with the NTC. The null model implemented in the NTC is associated with a large frequency of type I error, while the other null models implemented in BINMATNEST (null models 2 and 3) are conservative. Overall, null model 3 provides the best performance. The nestedness temperature of a matrix is affected by its size and fill, but the probability that such a temperature is obtained by chance is not. BINMATNEST reorders the input matrix in such a way that, if fragment size/isolation plays a role in determining community structure, there will be a significant rank correlation between the size/isolation of the fragments and the way that they are ordered in the packed matrix. Main conclusions The nestedness temperature of presence–absence matrices should not be calculated with the NTC. The algorithm implemented by BINMATNEST is more robust, allowing for across-study comparisons of the extent to which the nestedness of communities departs from randomness. The sequence in which BINMATNEST reorders habitat fragments provides information about the causal role of immigration and extinction in shaping the community under study. [ABSTRACT FROM AUTHOR]