New approach for the identification of power system economic dispatch parameters

It is well known that the coefficients of the input-output characteristics of the thermal steam-turbine model as well as the network model parameters have a great effect on the optimal economic operation of all thermal-electric power systems. Until today, these coefficients, the loss formula coefficients, theB-coefficients, and the active-reactive power loss models have been estimated using the well-known least-square estimation algorithm.In this paper, we present a new algorithm to estimate the power system parameters for economic dispatch calculation (EDC); this algorithm is based on the least absolute-value approximation (LAV)l ₁-norm. We compare the results obtained using the proposed algorithms with those obtained using the least-square error algorithm (LS). Optimal costs as well as overall network performance resulting from the implementation of each technique provide the basis of our conclusion.This work was supported by the Natural Science and Engineering Research Council of Canada, Grant No. A4146.     

Ridgelet bi-frame

This article introduces a new bi-frame called ridgelet bi-frame. The ridgelet bi-frame consists of two ridgelet frames that are dual to each other. The construction of the ridgelet bi-frame starts with a bi-frame built on a biorthogonal wavelet system in the Radon domain. The image of the resulting bi-frame under an isometric map from the Radon domain to L²(R²) is also a bi-frame, which we refer to as the ridgelet bi-frame. The ridgelet bi-frame can be thought of as an extension of the notion of the orthonormal ridgelet, which provides a more flexible and effective tool for image analysis and processing applications. An algorithm for image denoising based on the new bi-frame is developed. Experimental examples have demonstrated that the excellent performance can be achieved when using the ridgelet bi-frame for image denoising.     

A splitting primal-dual proximity algorithm for solving composite optimization problems

Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is associated with many interesting challenges encountered in the image restoration and image reconstruction fields. We developed a splitting primal-dual proximity algorithm to solve this problem. Furthermore, we propose a preconditioned method, of which the iterative parameters are obtained without the need to know some particular operator norm in advance. Theoretical convergence theorems are presented. We then apply the proposed methods to solve a total variation regularization model, in which the L2 data error function is added to the L1 data error function. The main advantageous feature of this model is its capability to combine different loss functions. The numerical results obtained for computed tomography (CT) image reconstruction demonstrated the ability of the proposed algorithm to reconstruct an image with few and sparse projection views while maintaining the image quality.     

Application of the cross-entropy method to clustering and vector quantization

We apply the cross-entropy (CE) method to problems in clustering and vector quantization. The CE algorithm for clustering involves the following iterative steps: (a) generate random clusters according to a specified parametric probability distribution, (b) update the parameters of this distribution according to the Kullback–Leibler cross-entropy. Through various numerical experiments, we demonstrate the high accuracy of the CE algorithm and show that it can generate near-optimal clusters for fairly large data sets. We compare the CE method with well-known clustering and vector quantization methods such as K-means, fuzzy K-means and linear vector quantization, and apply each method to benchmark and image analysis data.     

Dependence of locally linear embedding on the regularization parameter

This paper deals with a method, called locally linear embedding (LLE). It is a nonlinear dimensionality reduction technique that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional data and attempts to discover a nonlinear structure (including manifolds) in high-dimensional data. In practice, the nonlinear manifold learning methods are applied in image processing, text mining, etc. The implementation of the LLE algorithm is fairly straightforward, because the algorithm has only two control parameters: the number of neighbors of each data point and the regularization parameter. The mapping quality is quite sensitive to these parameters. In this paper, we propose a new way of selecting a regularization parameter of a local Gram matrix.     

Multi-Label Markov Random Fields as an Efficient and Effective Tool for Image Segmentation,Total Variations and Regularization

One of the classical optimization models for image segmentation is the well known Markov Random Fields (MRF) model. This model is a discrete optimization problem, which is shown here to formulate many continuous models used in image segmentation. In spite of the presence of MRF in the literature, the dominant perception has been that the model is not effective for image segmentation. We show here that the reason for the non-effectiveness is due to the lack of access to the optimal solution. Instead of solving optimally, heuristics have been engaged. Those heuristic methods cannot guarantee the quality of the solution nor the running time of the algorithm. Worse still, heuristics do not link directly the input functions and parameters to the output thus obscuring what would be ideal choices of parameters and functions which are to be selected by users in each particular application context.We describe here how MRF can model and solve efficiently several known continuous models for image segmentation and describe briefly a very efficient polynomial time algorithm, which is provably fastest possible, to solve optimally the MRF problem. The MRF algorithm is enhanced here compared to the algorithm in Hochbaum (2001) by allowing the set of assigned labels to be any discrete set. Other enhancements include dynamic features that permit adjustments to the input parameters and solves optimally for these changes with minimal computation time. Several new theoretical results on the properties of the algorithm are proved here and are demonstrated for images in the context of medical and biological imaging. An interactive implementation tool for MRF is described, and its performance and flexibility in practice are demonstrated via computational experiments.We conclude that many continuous models common in image segmentation have discrete analogs to various special cases of MRF and as such are solved optimally and efficiently, rather than with the use of continuous techniques, such as PDE methods, which restrict the type of functions used and furthermore, can only guarantee convergence to a local minimum.     

Nonparametric Regression on a Graph

The ‘Signal plus Noise’ model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a graph to measure roughness in penalized regression. Distance between estimate and observation is measured at every vertex in the L₂ norm, and roughness is penalized on every edge in the L₁ norm. Thus the ideas of total variation penalization can be extended to a graph. The resulting minimization problem presents special computational challenges, so we describe a new and fast algorithm and demonstrate its use with examples.

The examples include image analysis, a simulation applicable to discrete spatial variation, and classification. In our examples, penalized regression improves upon kernel smoothing in terms of identifying local extreme values on planar graphs. In all examples we use fully automatic procedures for setting the smoothing parameters. Supplemental materials are available online.     

Non-convex and non-smooth variational decomposition for image restoration

The variational image decomposition model decomposes an image into a structural and an oscillatory component by regularization technique and functional minimization. It is an important task in various image processing methods, such as image restoration, image segmentation, and object recognition. In this paper, we propose a non-convex and non-smooth variational decomposition model for image restoration that uses non-convex and non-smooth total variation (TV) to measure the structure component and the negative Sobolev space $H^{-1}$ to model the oscillatory component. The new model combines the advantages of non-convex regularization and weaker-norm texture modeling, and it can well remove the noises while preserving the valuable edges and contours of the image. The iteratively reweighted l¹ (IRL1) algorithm is employed to solve the proposed non-convex minimization problem. For each subproblem, we use the alternating direction method of multipliers (ADMM) algorithm to solve it. Numerical results validate the effectiveness of the proposed model for both synthetic and real images in terms of peak signal-to-noise ratio (PSNR) and mean structural similarity index (MSSIM).     

On the Brown–Proschan model when repair effects are unknown

A device is repaired after failure. The Brown–Proschan (BP) model assumes that the repair is perfect with probability p and minimal with probability (1−p). Theoretical results usually suppose that each repair effect (perfect or minimal repair) is known. However, this is not generally the case in practice. In this paper, we study the behavior of the BP model when repair effects are unknown. In this context, the main features of the failure process are derived: distribution functions of times between failures, failure intensity, likelihood function, etc. We propose to estimate the repair efficiency parameter p and the parameters of the first time to failure distribution with the likelihood function or equivalently the EM algorithm. We also propose to combine a moment estimation of the scale parameter and a maximum likelihood estimation of other parameters. Copyright © 2010 John Wiley & Sons, Ltd.     

A new multi-threshold image segmentation approach using state transition algorithm

Thresholding plays an important role in image segmentation and image analysis. In this paper, the normalized histogram of an image is fitted by a linear combined normal distribution functions and each normal distribution function represents a class of pixels, whereas the parameters like the mean, the variance and the weights in the fitting function are undetermined. By transforming the fitting problem into a nonlinear and non-convex optimization problem, the state transition algorithm (STA) which is a new global optimization method is used to choose the optimal parameters of the fitting function. The effectiveness of proposed approach in multilevel thresholding problems is tested by several experimental results. By comparing with OTSU, particle swarm optimization (PSO), genetic algorithm (GA) and differential evolution (DE) algorithm, it has shown that STA has competitive performance in terms of both optimization results and thresholding segmentation.     

Structured FISTA for image restoration

In this paper, we propose an efficient numerical scheme for solving some large‐scale ill‐posed linear inverse problems arising from image restoration. In order to accelerate the computation, two different hidden structures are exploited. First, the coefficient matrix is approximated as the sum of a small number of Kronecker products. This procedure not only introduces one more level of parallelism into the computation but also enables the usage of computationally intensive matrix–matrix multiplications in the subsequent optimization procedure. We then derive the corresponding Tikhonov regularized minimization model and extend the fast iterative shrinkage‐thresholding algorithm (FISTA) to solve the resulting optimization problem. Because the matrices appearing in the Kronecker product approximation are all structured matrices (Toeplitz, Hankel, etc.), we can further exploit their fast matrix–vector multiplication algorithms at each iteration. The proposed algorithm is thus called structured FISTA (sFISTA). In particular, we show that the approximation error introduced by sFISTA is well under control and sFISTA can reach the same image restoration accuracy level as FISTA. Finally, both the theoretical complexity analysis and some numerical results are provided to demonstrate the efficiency of sFISTA.     

An Augmented ADMM Algorithm With Application to the Generalized Lasso Problem

In this article, we present a fast and stable algorithm for solving a class of optimization problems that arise in many statistical estimation procedures, such as sparse fused lasso over a graph, convex clustering, and trend filtering, among others. We propose a so-called augmented alternating direction methods of multipliers (ADMM) algorithm to solve this class of problems. Compared to a standard ADMM algorithm, our proposal significantly reduces the computational cost at each iteration while maintaining roughly the same overall convergence speed. We also consider a new varying penalty scheme for the ADMM algorithm, which could further accelerate the convergence, especially when solving a sequence of problems with tuning parameters of different scales. Extensive numerical experiments on the sparse fused lasso problem show that the proposed algorithm is more efficient than the standard ADMM and two other existing state-of-the-art specialized algorithms. Finally, we discuss a possible extension and some interesting connections to two well-known algorithms. Supplementary materials for the article are available online.     

Integer extended ABS algorithms and possible control of intermediate results for linear Diophantine systems

We present a new class of integer extended ABS algorithms for solving linear Diophantine systems. The proposed class contains the integer ABS (the so-called EMAS and our proposed MEMAS) algorithms and the generalized Rosser’s algorithm as its members. After an application of each member of the class a particular solution of the system and an integer basis for the null space of the coefficient matrix are at hand. We show that effective algorithms exist within this class by appropriately setting the parameters of the members of the new class to control the growth of intermediate results. Finally, we propose two effective heuristic rules for selecting certain parameters in the new class of integer extended ABS algorithms.      

Near-perfect token distribution

Suppose that n tokens are arbitrarily placed on the n nodes of a graph. At each parallel step one token may be moved from each node to an adjacent node. An algorithm for the near-perfect token distribution problem redistributes the tokens in a finite number of steps, so that, at the end, no more than O(1) tokens reside at each node. (In perfect distribution, at the end, exactly one token resides at each node.) In this paper we present a simple algorithm that works for all extrovert graphs, a new property which we define and study. In terms of connectivity requirements, extrovert graphs are roughly in-between expanders and compressors. Our results lead to an optimal solution for the near-perfect token distribution problem on almost all cubic graphs. The new solution is conceptually simpler than previous algorithms, and applies to graphs of minimum possible degree. © 1994 John Wiley & Sons, Inc.     

Clustering Multivariate Longitudinal Observations: The Contaminated Gaussian Hidden Markov Model

The Gaussian hidden Markov model (HMM) is widely considered for the analysis of heterogenous continuous multivariate longitudinal data. To robustify this approach with respect to possible elliptical heavy-tailed departures from normality, due to the presence of outliers, spurious points, or noise (collectively referred to as bad points herein), the contaminated Gaussian HMM is here introduced. The contaminated Gaussian distribution represents an elliptical generalization of the Gaussian distribution and allows for automatic detection of bad points in the same natural way as observations are typically assigned to the latent states in the HMM context. Once the model is fitted, each observation has a posterior probability of belonging to a particular state and, inside each state, of being a bad point or not. In addition to the parameters of the classical Gaussian HMM, for each state we have two more parameters, both with a specific and useful interpretation: one controls the proportion of bad points and one specifies their degree of atypicality. A sufficient condition for the identifiability of the model is given, an expectation-conditional maximization algorithm is outlined for parameter estimation and various operational issues are discussed. Using a large-scale simulation study, but also an illustrative artificial dataset, we demonstrate the effectiveness of the proposed model in comparison with HMMs of different elliptical distributions, and we also evaluate the performance of some well-known information criteria in selecting the true number of latent states. The model is finally used to fit data on criminal activities in Italian provinces. Supplementary materials for this article are available online     

Contrast enhancement for image by WNN and GA combining PSNR with information entropy

A new contrast enhancement algorithm for image is proposed combining genetic algorithm (GA) with wavelet neural network (WNN). In-complete Beta transform (IBT) is used to obtain non-linear gray transform curve so as to enhance global contrast for an image. GA determines optimal gray transform parameters. In order to avoid the expensive time for traditional contrast enhancement algorithms, which search optimal gray transform parameters in the whole parameters space, based on gray distribution of an image, a classification criterion is proposed. Contrast type for original image is determined by the new criterion. Parameters space is, respectively, determined according to different contrast types, which greatly shrink parameters space. Thus searching direction of GA is guided by the new parameter space. Considering the drawback of traditional histogram equalization that it reduces the information and enlarges noise and background blur in the processed image, a synthetic objective function is used as fitness function of GA combining peak signal-noise-ratio (PSNR) and information entropy. In order to calculate IBT in the whole image, WNN is used to approximate the IBT. In order to enhance the local contrast for image, discrete stationary wavelet transform (DSWT) is used to enhance detail in an image. Having implemented DSWT to an image, detail is enhanced by a non-linear operator in three high frequency sub-bands. The coefficients in the low frequency sub-bands are set as zero. Final enhanced image is obtained by adding the global enhanced image with the local enhanced image. Experimental results show that the new algorithm is able to well enhance the global and local contrast for image while keeping the noise and background blur from being greatly enlarged.     

Parameter estimation for von Mises–Fisher distributions

When analyzing high-dimensional data, it is often appropriate to pay attention only to the direction of each datum, disregarding its norm. The von Mises–Fisher (vMF) distribution is a natural probability distribution for such data. When we estimate the parameters of vMF distributions, parameter κ which corresponds to the degree of concentration is difficult to obtain, and some approximations are necessary. In this article, we propose an iterative algorithm using fixed points to obtain the maximum likelihood estimate (m.l.e.) for κ. We prove that there is a unique local maximum for κ. Besides, using a specific function to calculate the m.l.e., we obtain the upper and lower bounds of the interval in which the exact m.l.e. exists. In addition, based on these bounds, a new and good approximation is derived. The results of numerical experiments demonstrate the new approximation exhibits higher precision than traditional ones.     

A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising

The total variation model proposed by Rudin, Osher and Fatemi performs very well for removing noise while preserving edges. However, it favors a piecewise constant solution in BV space which often leads to the staircase effect, and small details such as textures are often filtered out with noise in the process of denoising. To preserve the textures and eliminate the staircase effect, we improve the total variation model in this paper. This is accomplished by the following steps: (1) we define a new space of functions of fractional-order bounded variation called the BV_α space by using the Grünwald–Letnikov definition of fractional-order derivative; (2) we model the structure of the image as a function belonging to the BV_α space, and the textures in different scales as functions belonging to different negative Sobolev spaces. Thus, we propose a class of fractional-order multi-scale variational models for image denoising. (3) We analyze some properties of the fraction-order total variation operator and its conjugate operator. By using these properties, we develop an alternation projection algorithm for the new model and propose an efficient condition of the convergence of the algorithm. The numerical results show that the fractional-order multi-scale variational model can improve the peak signal to noise ratio of image, preserve textures and eliminate the staircase effect efficiently in the process of denoising.     

Automorphic and endomorphic reducibility and primitive endomorphisms of free metabelian groups

Let S be the free metabelian group of rank 2. In this paper we prove the following results:(i) Given a pair of elements g, h of S, there exists an algorithm to decide whether or not g is an automorphic image of h; (ii) If g, h are in the commutator subgroup S′ of S such that each is an endomorphic image of the other then g , h are automorphic; (iii) If an endomorphism of S maps primitive elements of S to primitive elements of S then it defines an automorphism of S. We also include an example to show that, in (ii) above,the requirement that g,h are in S ? can not be relaxed.     

Promoting cooperation in selfish computational grids

In distributed computing, the recent paradigm shift from centrally-owned clusters to organizationally distributed computational grids introduces a number of new challenges in resource management and scheduling. In this work, we study the problem of Selfish Load Balancing which extends the well-known load balancing (LB) problem to scenarios in which each processor is concerned only with the performance of its local jobs. We propose a simple mathematical model for such systems and a novel function for computing the cost of the execution of foreign jobs. Then, we use the game-theoretic framework to analyze the model in order to compute the expected result of LB performed in a grid formed by two clusters. We show that, firstly, LB is a socially-optimal strategy, and secondly, for similarly loaded clusters, it is sufficient to collaborate during longer time periods in order to make LB the dominant strategy for each cluster. However, we show that if we allow clusters to make decisions depending on their current queue length, LB will never be performed. Then, we propose a LB algorithm which balances the load more equitably, even in the presence of overloaded clusters. Our algorithms do not use any external forms of compensation (such as money). The load is balanced only by considering the parameters of execution of jobs. This analysis is assessed experimentally by simulation, involving scenarios with multiple clusters and heterogeneous load.