Globally convergent algorithms for solving unconstrained optimization problems

Taheri, Sona; Mammadov, Musa; Seifollahi, Sattar

doi:10.1080/02331934.2012.745529

Cited by 11 publications

(7 citation statements)

References 15 publications

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“…This type approach analyses the relationship among every characteristic and the category for every instance to derive a conditional hazard chance for the relationships between the features utility and the class. At the training stage, the possibility of all magnificence is evaluated by counting how frequently it happens inside the databank which is already trained [25]. NB is speedy, easy to put into effect with the easy shape and fruitful.…”

Section: Nb Classifiermentioning

confidence: 99%

Performance Evaluation of Several Machine Learning Techniques Used in the Diagnosis of Mammograms

Tripathy¹

2019

IJITEE

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Throughout the world breast cancer has become a common disease among the women and it is also a life threatening diseases. Machine learning(ML) approach has been widely used for the diagnosis of benign and malignant masses in the mammogram. In this manuscript, I have represented the theoretical research and practical advances on various machine learning techniques the diagnosis of benign and malignant masses in the mammogram. The objective of this manuscript is to analyze the performance of distinct machine learning techniques used in the diagnosis of the Digital Mammography Image Analysis Society (MIAS) database. In this work I have compared performance of four machine learning approaches i.e. Support Vector, Naive Bayes, K-Nearest Neighbours and Multilayer Perceptron. The above four types of machine learning algorithm are used to categorize mammograms image. The achievements of these four techniques were recognized to discover the most acceptable classifier. On the end of the examine, derived outcomes indicates that support vector is a successful approach compares to other approach.

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Section: Nb Classifiermentioning

confidence: 99%

Performance Evaluation of Several Machine Learning Techniques Used in the Diagnosis of Mammograms

Tripathy¹

2019

IJITEE

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“…In calculations, we take η = 10 −3 , ϑ = 1.1, δ = 10 −3 , ω = 10 −10 , ϖ = 10 10 for the CGN based on [40] and we set µ = 10 3 , ε = 0.1, ρ 0 = 2 10 for the proposed algorithm.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…In this case, we choose an optimal network from all possible combinations of removing some arcs in the existing cycles. In the second case, when we have a large number of cycles, we apply the global optimization algorithm AGOP introduced in [24,25] in conjunction with the recently developed local optimization algorithm CGN [39,40]. AGOP is an efficient algorithm in solving many difficult practical problems where objective functions were discontinuous [19,26] and even piecewise constant [42].…”

Section: Introductionmentioning

confidence: 99%

Structure learning of Bayesian Networks using global optimization with applications in data classification

Taheri

Mammadov

2014

Optim Lett

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Bayesian Networks are increasingly popular methods of modeling uncertainty in artificial intelligence and machine learning. A Bayesian Network consists of a directed acyclic graph in which each node represents a variable and each arc represents probabilistic dependency between two variables. Constructing a Bayesian Network from data is a learning process that consists of two steps: learning structure and learning parameter. Learning a network structure from data is the most difficult task in this process. This paper presents a new algorithm for constructing an optimal structure for Bayesian Networks based on optimization. The algorithm has two major parts. First, we define an optimization model to find the better network graphs. Then, we apply an optimization approach for removing possible cycles from the directed graphs obtained in the first part which is the first of its kind in the literature. The main advantage of the proposed method is that the maximal number of parents for variables is not fixed a priory and it is defined during the optimization procedure. It also considers all networks including cyclic ones and then choose a best structure by applying a global optimization method. To show the efficiency of the algorithm, several closely related algorithms including unrestricted dependency Bayesian Network algorithm, as well as, benchmarks algorithms SVM and C4.5 are employed for comparison. We apply these algorithms on data classification; data sets are taken from the UCI machine learning repository and the LIBSVM. keywordsData Classifi-cationBayesian NetworksGlobal Optimization

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“…Although theoretically, Newton method has a fast convergence rate [8], it is practically also related with the difficulty of finding its second derivative when involving the largescale problems and it has possible failure to converge to the solution of problem (1) from weak initial points. Therefore, in practice, many researchers tend to modify or combine it with another method for solving large-scale unconstrained optimization to make it more computationally efficient and to achieve an accurate solution [9][10][11][12][13][14]. Bouaricha et al in [9] presented a Newton method with trust region for finding (1) min ∈ℝ n f , large-scale unconstrained optimization problems and used two types of an iterative method which are the incomplete Cholesky decomposition and conjugate gradient method to obtain the trust region step instead of using the classical Newton direction.…”

Section: Introductionmentioning

confidence: 99%

“…Next, Grapsa [12] proposed a modified Newton's direction method using a proper gradient's vector modification to have a descent property without a line search technique for solving problems of unconstrained optimization and proved its rate of convergence based on a Dennis modified Newton-Kantorovich theorem. Taheri et al [13] developed a new algorithm for solving unconstrained optimization problems by combining the anti-gradient direction with the Newton direction to improve the convergence rate of Newton's method. Abiodun and Adelabu [14] recently presented two iterative modifications of Newton's method using an updated formula based on the recurrence of matrix factorizations to replaces an inverse matrix and maintains its positive definiteness property.…”

Section: Introductionmentioning

confidence: 99%

Newton-2EGSOR Method for Unconstrained Optimization Problems with a Block Diagonal Hessian

et al. 2019

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We find that finding the unconstrained optimizer for large-scale problems with the Newton method can be very expensive. Therefore, in this paper, we developed a new efficient method for solving large-scale unconstrained optimization problems with block diagonal Hessian matrices to reduce the cost of computing Newton's direction. This method is a combination of the Newton method and the 2-point explicit group successive-over relaxation (2EGSOR) block iterative method. To calculate the performance of the developed method, we used a combination of the Newton method with Gauss-Seidel (Newton-GS) point iteration and the Newton method with successive-over relaxation (Newton-SOR) point iteration as reference methods. The numerical experiment has proven that the developed algorithms generate results that are more efficient compared to the reference methods with less execution time and fewer iterations. Through 90 test cases, we observe that the speedup ratio for our proposed method is up to 659.87 times faster compared to the Newton-SOR method and up to 1963.57 times more rapidly than the Newton-GS method.

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Globally convergent algorithms for solving unconstrained optimization problems

Cited by 11 publications

References 15 publications

Performance Evaluation of Several Machine Learning Techniques Used in the Diagnosis of Mammograms

Performance Evaluation of Several Machine Learning Techniques Used in the Diagnosis of Mammograms

Structure learning of Bayesian Networks using global optimization with applications in data classification

Newton-2EGSOR Method for Unconstrained Optimization Problems with a Block Diagonal Hessian

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