Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495420241001Feature representation via graph-regularized entropy-weighted nonnegative matrix factorization289304553510.22060/ajmc.2024.23353.1252ENHazhirSohrabiDepartment of Applied Mathematics, University of Kurdistan, Sanandaj, IranShahrokhEsmaeiliDepartment of Applied Mathematics, University of Kurdistan, Sanandaj, Iran0000-0002-0584-6094ParhamMoradiDepartment of Computer Engineering, University of Kurdistan, Sanandaj, IranSchool of Engineering, RMIT University, Melbourne, AustraliaJournal Article20240717Feature extraction plays a crucial role in dimensionality reduction in machine learning applications. Nonnegative Matrix Factorization (NMF) has emerged as a powerful technique for dimensionality reduction; however, its equal treatment of all features may limit accuracy. To address this challenge, this paper introduces Graph-Regularized Entropy-Weighted Nonnegative Matrix Factorization (GEWNMF) for enhanced feature representation. The proposed method improves feature extraction through two key innovations: optimizable feature weights and graph regularization. GEWNMF uses optimizable weights to prioritize the extraction of crucial features that best describe the underlying data structure. These weights, determined using entropy measures, ensure a diverse selection of features, thereby enhancing the fidelity of the data representation. This adaptive weighting not only improves interpretability but also strengthens the model against noisy or outlier-prone datasets. Furthermore, GEWNMF integrates robust graph regularization techniques to preserve local data relationships. By constructing an adjacency graph that captures these relationships, the method enhances its ability to discern meaningful patterns amid noise and variability. This regularization not only stabilizes the method but also ensures that nearby data points appropriately influence feature extraction. Thus, GEWNMF produces representations that capture both global trends and local nuances, making it applicable across various domains. Extensive experiments on four widely used datasets validate the efficacy of GEWNMF compared to existing methods, demonstrating its superior performance in capturing meaningful data patterns and enhancing interpretability.https://ajmc.aut.ac.ir/article_5535_3112c9212ca8838f81402e7dd4358c84.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495420241001Generalized Lorentzian Ricci solitons on 3-dimensional Lie groups associated to the Bott Connection305319519510.22060/ajmc.2023.22329.1153ENGhodratallahFasihi RamandiDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranShahroudAzamiDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranVahidPirhadiDepartment of Pure Mathematics, Faculty of mathematics, University of Kashan, Kashan, IranJournal Article20230411In this paper, we investigate which one of the non-isometric left-invariant Lorentz metrics $g$ on $3$-dimensional Lie groups satisfies the generalized Ricci soliton equation $a{\rm Ric}^B [g] + \dfrac{b}{2}{\cal L}_{ X}^B g +cX^\flat\otimes X^\flat = \lambda g$ associated to the Bott connection $\nabla^B$, here ${X}$ is a vector field and $\lambda , a, b, c$ are real constants such that $c\neq 0$. A complete classification of this structure on $3$-dimensional Lorentzian Lie groups will be presented.https://ajmc.aut.ac.ir/article_5195_b34a3973e7012a6572e01bf73f68e064.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495420241001Composition operators from Zygmund spaces into Besov Zygmund-type spaces321327521110.22060/ajmc.2023.22144.1137ENHamidVaeziDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran000000017797512xSimaHoudfarDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, IranJournal Article20230130In this paper first, the boundedness and compactness of a composition operator from Zygmund space to Besov Zygmund-type space are studied. Then we study this concepts for this operator by using the hyperbolic-type analytic Besov Zygmund-type class. Finally, we show the relation between the hyperbolic-type analytic Besov Zygmund-type class and the meromorphic (or spherical) Besov Zygmund-type class.https://ajmc.aut.ac.ir/article_5211_39af308f07155209f63417ed1a0ba7c6.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495420241001$K$-contact generalized square Finsler manifolds329336525710.22060/ajmc.2023.22528.1166ENHannanehFarajiDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranBehzadNajafi SaghezchiDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranTayebehTabatabaeifarDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranJournal Article20230704We study almost contact generalized square Finsler manifolds and introduce the notion of $K$-contact Finsler structures. Then, we characterize generalized square $K$-contact almost contact manifolds. As an application, we show that every $3$-dimensional Lie group admits a left-invariant generalized square Finsler structure.https://ajmc.aut.ac.ir/article_5257_d6b3494666c9c69fb4c021888afdbd41.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495420241001A matrix approach to multi-term fractional differential equations using two new diffusive representations for the Caputo fractional derivative337359553710.22060/ajmc.2024.23042.1222ENHassanKhosravian-ArabDepartment of Applied Mathematics and Computer Science, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran0000-0003-1924-3531MehdiDehghanDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranJournal Article20240307In the last decade, there has been a surge of interest in application of fractional calculus in various areas such as, mathematics, physics, engineering, mechanics and etc. So, numerical methods have rapidly been developed to handle problems containing fractional derivatives (or integrals). Due to the fact that all the operators which appear in fractional calculus are non-local, so, the classical linear multi-step methods have some difficulties from the (time/space) computational complexity point of view. Recently, two new non-classical methods or diffusive based methods have been proposed by the authors to approximate the Caputo fractional derivatives. Here, the main aim of this paper is to use these methods to solve linear multi-term fractional differential equations numerically. To reach our aim, an efficient matrix approach has been provided to solve some well-known multi-term fractional differential equations.https://ajmc.aut.ac.ir/article_5537_5eff5d595f295a9da6f5919d486bff66.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495420241001Lipschitzness effect of a loss function on generalization performance of deep neural networks trained by Adam and AdamW optimizers361375521310.22060/ajmc.2023.22182.1139ENMohammadLashkariDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranAminGheibiDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranJournal Article20230208The generalization performance of deep neural networks with regard to the optimization algorithm is one of the major concerns in machine learning. This performance can be affected by various factors. In this paper, we theoretically prove that the Lipschitz constant of a loss function is an important factor to diminish the generalization error of the output model obtained by Adam or AdamW. The results can be used as a guideline for choosing the loss function when the optimization algorithm is Adam or AdamW. In addition, to evaluate the theoretical bound in a practical setting, we choose the human age estimation problem in computer vision. For assessing the generalization better, the training and test datasets are drawn from different distributions. Our experimental evaluation shows that the loss function with a lower Lipschitz constant and maximum value improves the generalization of the model trained by Adam or AdamW.https://ajmc.aut.ac.ir/article_5213_d2f92dc2f0d589cb0599e1b2588d0643.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495420241001Some results concerning asymptotic distribution of functional linear regression with points of impact377383525510.22060/ajmc.2023.22629.1181ENAlirezaShirvaniDepartment of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, IranOmidKhademnoeDepartment of Statistics, Faculty of Sciences, University of Zanjan, Zanjan, IranMohammadHosseini NasabDepartment of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, IranJournal Article20230826Lately, issues related to functional linear regression models with points of impact have garnered significant interest. While the literature has addressed the estimation of parameters for this model with scalar response, less attention has been paid to the asymptotic distribution of the impact points coefficients estimators. In recent literature, the asymptotic distribution has been pointed out in a particular case, but the demonstration of its validity has not been adequately addressed. By explicating the necessary requirements, we derive an important part of the asymptotic distribution of the impact points coefficients estimators in a general setting. This is a fundamental result for finding the asymptotic distribution of the impact points coefficients estimators. Moreover, we perform a simulation study to exhibit the efficiency of the obtained results.https://ajmc.aut.ac.ir/article_5255_b1098d7a80a82ac84a51b2b4990d0165.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495420241001A survey on usage of smartphone accelerometer sensor in intelligent transportation systems385401523810.22060/ajmc.2023.22592.1179ENHamid RezaEftekhariDepartment of Computer Engineering, Malayer University, Iran0000-0003-4450-1926Journal Article20230802The numerous capabilities of smartphones have made them suitable alternative to expensive tools and methods in intelligent transportation systems. This study surveys the literature on the role of the accelerometer of smartphones in intelligent transportation applications. At first, the opportunities and challenges of using the accelerometer are stated. Then, the architecture of using this sensor including preprocessing, feature extraction, mode detection, reorientation and applications are explained. Finally, different applications that have used the accelerometer of mobile phones in the intelligent transportation systems have been investigated.https://ajmc.aut.ac.ir/article_5238_81ddf3998faee74d1d5babdf5e26830c.pdf