Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems

The aim of this paper is to extend the applicability of an algorithm for solving inconsistent linear systems to the rank-deficient case, by employing incomplete projections onto the set of solutions of the augmented system Ax-r = b. The extended algorithm converges to the unique minimal norm solution of the least squares solutions. For that purpose, incomplete oblique projections are used, defined by means of matrices that penalize the norm of the residuals. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known projection methods.Facultad de Ciencias ExactasFacultad de Ingenierí

Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems

The aim of this paper is to extend the applicability of an algorithm for solving inconsistent linear systems to the rank-deficient case, by employing incomplete projections onto the set of solutions of the augmented system Ax-r = b. The extended algorithm converges to the unique minimal norm solution of the least squares solutions. For that purpose, incomplete oblique projections are used, defined by means of matrices that penalize the norm of the residuals. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known projection methods.Facultad de Ciencias ExactasFacultad de Ingenierí

Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems

The aim of this paper is to extend the applicability of an algorithm for solving inconsistent linear systems to the rank-deficient case, by employing incomplete projections onto the set of solutions of the augmented system Ax-r = b. The extended algorithm converges to the unique minimal norm solution of the least squares solutions. For that purpose, incomplete oblique projections are used, defined by means of matrices that penalize the norm of the residuals. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known projection methods.Facultad de Ciencias ExactasFacultad de Ingenierí

Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction

In this paper we improve on the incomplete oblique projections (IOP) method introduced previously by the authors for solving inconsistent linear systems, when applied to image reconstruction problems. That method uses IOP onto the set of solutions of the augmented system Ax - r = b, and converges to a weighted least-squares solution of the system Ax=b. In image reconstruction problems, systems are usually inconsistent and very often rank-deficient because of the underlying discretized model. Here we have considered a regularized least-squares objective function that can be used in many ways such as incorporating blobs or nearest-neighbor interactions among adjacent pixels, aiming at smoothing the image. Thus, the oblique incomplete projections algorithm has been modified for solving this regularized model. The theoretical properties of the new algorithm are analyzed and numerical experiments are presented showing that the new approach improves the quality of the reconstructed images.Material digitalizado en SEDICI gracias a la Biblioteca de la Facultad de Ingeniería (UNLP).Facultad de Ciencias Exacta

On the incomplete oblique projections method for solving box constrained least squares problems

The aim of this paper is to extend the applicability of the incomplete oblique projections method (IOP) previously introduced by the authors for solving inconsistent linear systems to the box constrained case. The new algorithm employs incomplete projections onto the set of solutions of the augmented system Ax − r = b, together with the box constraints, based on a scheme similar to the one of IOP, adding the conditions for accepting an approximate solution in the box. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known methods.Facultad de IngenieríaFacultad de Ciencias Exacta

Projection pursuit random forest using discriminant feature analysis model for churners prediction in telecom industry

A major and demanding issue in the telecommunications industry is the prediction of churn customers. Churn describes the customer who is attrite from one Telecom service provider to competitors searching for better services offers. Companies from the Telco sector frequently have customer relationship management offices it is the main objective in how to win back defecting clients because preserve long-term customers can be much more beneficial to a company than gain newly recruited customers. Researchers and practitioners are paying great attention and investing more in developing a robust customer churn prediction model, especially in the telecommunication business by proposed numerous machine learning approaches. Many approaches of Classification are established, but the most effective in recent times is a tree-based method. The main contribution of this research is to predict churners/non-churners in the Telecom sector based on project pursuit Random Forest (PPForest) that uses discriminant feature analysis as a novelty extension of the conventional Random Forest approach for learning oblique Project Pursuit tree (PPtree). The proposed methodology leverages the advantage of two discriminant analysis methods to calculate the project index used in the construction of PPtree. The first method used Support Vector Machines (SVM) as a classifier in the construction of PPForest to differentiate between churners and non-churners customers. The second method is a Linear Discriminant Analysis (LDA) to achieve linear splitting of variables node during oblique PPtree construction to produce individual classifiers that are robust and more diverse than classical Random Forest. It found that the proposed methods enjoy the best performance measurements e.g. Accuracy, hit rate, ROC curve, Gini coefficient, Kolmogorov-Smirnov statistic and lift coefficient, H-measure, AUC. Moreover, PPForest based on direct applied of LDA on the raw data delivers an effective evaluator for the customer churn prediction model