Browsing by Author "T. Som"

Now showing 1 - 11 of 11

An accelerated forward-backward splitting algorithm for solving inclusion problems with applications to regression and link prediction problems
(Biemdas Academic Publishers, 2021) A. Dixit; D.R. Sahu; P. Gautam; T. Som; J.C. Yao
The forward-backward method is a very popular approach to solve composite inclusion problems. In this paper, we propose a novel accelerated forward-backward algorithm to obtain the vanishing point of sum of two operators in which one is maximal monotone and other is M-cocoercive, where M is a linear bounded operator on underlying spaces. Our proposed algorithm is more general than previously known algorithms. We study the convergence behavior of proposed algorithm under mild assumptions in the framework of real Hilbert spaces. We employ our model to solve regression problems and link prediction problems for high dimensional datasets and conduct numerical experiments to support our results. This model improves convergence speed and accuracy in respective problems. We also conduct numerical experiments to support our results. © 2021 Journal of Nonlinear and Variational Analysis
An intuitionistic fuzzy-rough set model and its application to feature selection
(IOS Press, 2019) Anoop Kumar Tiwari; Shivam Shreevastava; Karthikeyan Subbiah; T. Som
Due to the development of modern internet-based technology, the electronically stored information is growing exponentially with time. It is highly challenging to select relevant and non-redundant features of the real-valued high dimensional datasets. Feature selection, a preprocessing technique, refers to the process of reducing the dimension of the input data in order to extract the most meaningful features for processing and analysis. One of the numerous useful applications of rough set theory is the attribute or feature selection, but it has certain limitations as it cannot be applied on real-valued data sets directly because rough set based feature selection can handle discrete data only. In order to deal with real-valued data sets, discretization method is applied to convert dataset from real-valued to discrete, which usually leads to information loss. Fuzzy rough set theory is profitably applied to address this problem and retain the semantics of real-valued datasets. However, intuitionistic fuzzy set can deal with uncertainty in a much better way when compared to fuzzy set theory as it considers membership, non-membership and hesitancy degree of an object simultaneously. In this paper, an intuitionistic fuzzy rough set model is established by combining intuitionistic fuzzy set and rough set. Furthermore, we propose a novel approach of feature selection derived from this model. Moreover, we develop an algorithm based on our proposed concept. Finally, our approach is applied to some benchmark data sets and compared with the existing fuzzy rough set based technique. The performed experiments show the superiority of our approach. © 2019 - IOS Press and the authors.
Application of a new accelerated algorithm to regression problems
(Springer, 2020) Avinash Dixit; D.R. Sahu; Amit Kumar Singh; T. Som
Many iterative algorithms like Picard, Mann, Ishikawa are very useful to solve fixed point problems of nonlinear operators in real Hilbert spaces. The recent trend is to enhance their convergence rate abruptly by using inertial terms. The purpose of this paper is to investigate a new inertial iterative algorithm for finding the fixed points of nonexpansive operators in the framework of Hilbert spaces. We study the weak convergence of the proposed algorithm under mild assumptions. We apply our algorithm to design a new accelerated proximal gradient method. This new proximal gradient technique is applied to regression problems. Numerical experiments have been conducted for regression problems with several publicly available high-dimensional datasets and compare the proposed algorithm with already existing algorithms on the basis of their performance for accuracy and objective function values. Results show that the performance of our proposed algorithm overreaches the other algorithms, while keeping the iteration parameters unchanged. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
Application of new strongly convergent iterative methods to split equality problems
(Springer Science and Business Media Deutschland GmbH, 2020) Pankaj Gautam; Avinash Dixit; D.R. Sahu; T. Som
In this paper, we study the generalized problem of split equality variational inclusion problem. For this purpose, we introduced the problem of finding the zero of a nonnegative lower semicontinuous function over the common solution set of fixed point problem and monotone inclusion problem. We proposed and studied the convergence behaviour of different iterative techniques to solve the generalized problem. Furthermore, we study an inertial form of the proposed algorithm and compare the convergence speed. Numerical experiments have been conducted to compare the convergence speed of the proposed algorithm, its inertial form and already existing algorithms to solve the generalized problem. © 2020, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.
Convergence analysis of two-step inertial Douglas-Rachford algorithm and application
(Springer Science and Business Media Deutschland GmbH, 2022) Avinash Dixit; D.R. Sahu; Pankaj Gautam; T. Som
Monotone inclusion problems are crucial to solve engineering problems and problems arising in different branches of science. In this paper, we propose a novel two-step inertial Douglas-Rachford algorithm to solve the monotone inclusion problem of the sum of two maximally monotone operators based on the normal S-iteration method (Sahu, D.R.: Applications of the S-iteration process to constrained minimization problems and split feasibility problems. Fixed Point Theory 12(1), 187–204 (2011)). We have studied the convergence behavior of the proposed algorithm. Based on the proposed method, we develop an inertial primal-dual algorithm to solve highly structured monotone inclusions containing the mixtures of linearly composed and parallel-sum type operators. Finally, we apply the proposed inertial primal-dual algorithm to solve a highly structured minimization problem. We also perform a numerical experiment to solve the generalized Heron problem and compare the performance of the proposed inertial primal-dual algorithm to already known algorithms. © 2021, Korean Society for Informatics and Computational Applied Mathematics.
Convergence of generalized mann type of iterates to common fixed point
(Springer New York LLC, 2018) T. Som; Amalendu Choudhury; D.R. Sahu; Ajeet Kumar
The present paper deals with the convergence of two modified Mann type of iteration schemes for a single and a finite family of mappings to the fixed and common fixed point, respectively, of a single and a finite family of quasi-nonexpansive mappings on a uniformly convex Banach space. An example is added in support of our main result. The results obtained generalize the earlier results of Rhoades (J Math Anal Appl 56:741–750, [6]), Som et al. (Proc Nat Acad Sci (India) 70(A)(II):185–189, [8]), and others in turn. © Springer Nature Singapore Pte Ltd. 2018.
Different classes ratio and laplace summation operator based intuitionistic fuzzy rough attribute selection
(University of Sistan and Baluchestan, 2021) S. Shreevastava; S. Singh; A.K. Tiwari; T. Som
In real-world data deluge, due to insignificant information and high dimension, irrelevant and redundant attributes reduce the ability of experts both in predictive accuracy and speed, respectively. Attribute selection is the notion of selecting those attributes that are essential as well as enough to specify the target knowledge preferably. Fuzzy rough set-based approaches play a crucial role in selecting relevant and less redundant attributes from a high-dimensional dataset. Intuitionistic fuzzy set-based approaches can handle uncertainty as it gives an additional degree of freedom when compared to fuzzy approaches. So, it has a more flexible and practical ability to deal with vagueness and noise available in the information system. In this paper, we introduce two new robust approaches for attribute selection based on intuitionistic fuzzy rough set theory using the concepts of Different Classes ratio and Laplace Summation operator. Firstly, Different Classes ratio and Laplace Summation operator based lower and upper approximations are established based on intuitionistic fuzzy rough set concept. Moreover, we present algorithms and illustrative examples for a better understanding of our approaches. Finally, experimental analysis is performed on some real-valued datasets for attribute selection and classification accuracies. © 2021, University of Sistan and Baluchestan. All rights reserved.
Multiresolution technique to handwritten English character recognition using learning rule and Euclidean distance metric
(2013) D.K. Patel; T. Som; Manoj Kumar Singh
The present paper deals with the problem of handwritten character recognition of English character. This paper presents a novel method of handwriting character recognition which exploits a compression capability of discrete wavelet transform to enhance the accuracy of recognition at the pixel level, the learning capability of artificial neural network and computational capability of Euclidean distance metric. The problem of handwritten character recognition has been tackled with multiresolution technique using discrete wavelet transform and learning rule through the artificial neural network. Recognition accuracy is improved by Euclidean distance metric along with recognition score in case of misclassification. Features of the handwritten character images are extracted by discrete wavelet transform used with appropriate level of multiresolution. Handwritten characters are classified into 26 pattern classes based on appropriate properties i.e. shape. During preprocessing each character is captured within a rectangular box and then resized to a threshold size. Weight matrix of each class is computed using the learning rule of artificial neural network, and then the unknown input pattern vector is fused with the weight matrices of all the classes to generate the recognition scores. Maximum score corresponds to the recognized input character. Learning rule provides a good recognition accuracy of 88.46%. In case of misclassification, the Euclidean distance metric improves the recognition accuracy to 92.31% and then its product with recognition score further improves the recognition accuracy to 99.23%. The proposed method provides such good recognition accuracy for handwritten characters even with fewer data samples. © 2013 IEEE.
Preface of the proceedings: ICNAAO-2022
(Springer Science and Business Media B.V., 2024) Sorin-Mihai Grad; S. Ponnusamy; D.R. Sahu; T. Som
[No abstract available]
Tikhonov regularized iterative methods for nonlinear problems
(Taylor and Francis Ltd., 2024) Avinash Dixit; D.R. Sahu; Pankaj Gautam; T. Som
We consider the monotone inclusion problems in real Hilbert spaces. Proximal splitting algorithms are very popular technique to solve it and generally achieve weak convergence under mild assumptions. Researchers assume the strong conditions like strong convexity or strong monotonicity on the considered operators to prove strong convergence of the algorithms. Mann iteration method and normal S-iteration method are popular methods to solve fixed point problems. We propose a new common fixed point algorithm based on normal S-iteration method using Tikhonov regularization to find common fixed point of non-expansive operators and prove strong convergence of the generated sequence to the set of common fixed points without assuming strong convexity and strong monotonicity. Based on proposed fixed point algorithm, we propose a forward–backward-type algorithm and a Douglas–Rachford algorithm in connection with Tikhonov regularization to find the solution of monotone inclusion problems. Further, we consider the complexly structured monotone inclusion problems which are very popular these days. We also propose a strongly convergent forward–backward-type primal–dual algorithm and a Douglas–Rachford-type primal–dual algorithm to solve the monotone inclusion problems. Finally, we conduct a numerical experiment to solve image deblurring problems. © 2023 Informa UK Limited, trading as Taylor & Francis Group.
Wavelet-based recognition of handwritten characters using artificial neural network
(IGI Global, 2016) D.K. Patel; T. Som; M.K. Singh
In the present chapter, the widely common problem of handwritten character recognition has been tackled with multiresolution technique using discrete wavelet transform and artificial neural networks. The technique has been tested and found to be more accurate and economic in respect of the recognition process time of the system. Features of the handwritten character images are extracted by discrete wavelet transform used with appropriate level of multiresolution technique, then the artificial neural networks is trained by extracted features. The unknown input handwritten character images are recognized by trained artificial neural networks system. The proposed method provides good recognition accuracy for handwritten characters with less training time, less no. of samples and less no. of iterations. © 2017, IGI Global. All rights reserved.