Pub Date : 2024-07-29DOI: 10.1007/s00500-024-09918-2
Ferdinando Auricchio, Maria Roberta Belardo, Francesco Calabrò, Gianluca Fabiani, Ariel F. Pascaner
Artificial Neural Networks (ANNs) are a tool in approximation theory widely used to solve interpolation problems. In fact, ANNs can be assimilated to functions since they take an input and return an output. The structure of the specifically adopted network determines the underlying approximation space, while the form of the function is selected by fixing the parameters of the network. In the present paper, we consider one-hidden layer ANNs with a feedforward architecture, also referred to as shallow or two-layer networks, so that the structure is determined by the number and types of neurons. The determination of the parameters that define the function, called training, is done via the resolution of the approximation problem, so by imposing the interpolation through a set of specific nodes. We present the case where the parameters are trained using a procedure that is referred to as Extreme Learning Machine (ELM) that leads to a linear interpolation problem. In such hypotheses, the existence of an ANN interpolating function is guaranteed. Given that the ANN is interpolating, the error incurred occurs outside the sampling interpolation nodes provided by the user. In this study, various choices of nodes are analyzed: equispaced, Chebychev, and randomly selected ones. Then, the focus is on regular target functions, for which it is known that interpolation can lead to spurious oscillations, a phenomenon that in the ANN literature is referred to as overfitting. We obtain good accuracy of the ANN interpolating function in all tested cases using these different types of interpolating nodes and different types of neurons. The following study is conducted starting from the well-known bell-shaped Runge example, which makes it clear that the construction of a global interpolating polynomial is accurate only if trained on suitably chosen nodes, ad example the Chebychev ones. In order to evaluate the behavior when the number of interpolation nodes increases, we increase the number of neurons in our network and compare it with the interpolating polynomial. We test using Runge’s function and other well-known examples with different regularities. As expected, the accuracy of the approximation with a global polynomial increases only if the Chebychev nodes are considered. Instead, the error for the ANN interpolating function always decays, and in most cases we observe that the convergence follows what is observed in the polynomial case on Chebychev nodes, despite the set of nodes used for training. Then we can conclude that the use of such an ANN defeats the Runge phenomenon. Our results show the power of ANNs to achieve excellent approximations when interpolating regular functions also starting from uniform and random nodes, particularly for Runge’s function.
人工神经网络(ANN)是近似理论中的一种工具,广泛用于解决插值问题。事实上,人工神经网络可以与函数等价,因为它们接受输入并返回输出。具体采用的网络结构决定了基本的近似空间,而函数的形式则通过固定网络参数来选择。在本文中,我们考虑的是具有前馈结构的单隐层 ANN,也称为浅层或双层网络,因此其结构由神经元的数量和类型决定。定义函数的参数的确定(称为训练)是通过近似问题的解决来完成的,即通过一组特定节点进行插值。我们介绍的情况是,使用一种被称为极限学习机(ELM)的程序来训练参数,从而解决线性插值问题。在这种假设中,ANN 插值函数的存在是有保证的。鉴于 ANN 正在进行插值,所产生的误差发生在用户提供的采样插值节点之外。本研究分析了各种节点选择:等距节点、切比切夫节点和随机选择的节点。然后,重点放在规则目标函数上,众所周知,插值会导致虚假振荡,这种现象在 ANN 文献中被称为过拟合。我们使用这些不同类型的插值节点和不同类型的神经元,在所有测试案例中都获得了良好的 ANN 插值函数精度。下面的研究将从著名的钟形 Runge 例子开始,该例子清楚地表明,只有在适当选择节点(例如切比切夫节点)的情况下,全局内插多项式的构建才会准确。为了评估插值节点数量增加时的行为,我们增加了网络中神经元的数量,并与插值多项式进行比较。我们使用 Runge 函数和其他具有不同规则性的著名例子进行了测试。不出所料,只有在考虑到切比切夫节点的情况下,全局多项式的近似精度才会提高。相反,ANN 插值函数的误差总是在减小,而且在大多数情况下,尽管使用了一组节点进行训练,但我们观察到其收敛性与在切比切夫节点上的多项式情况下观察到的收敛性相同。因此,我们可以得出这样的结论:使用这种 ANN 可以消除 Runge 现象。我们的研究结果表明,在对规则函数进行插值时,ANN 也能从均匀节点和随机节点出发,实现出色的近似,尤其是对 Runge 函数。
{"title":"On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenon","authors":"Ferdinando Auricchio, Maria Roberta Belardo, Francesco Calabrò, Gianluca Fabiani, Ariel F. Pascaner","doi":"10.1007/s00500-024-09918-2","DOIUrl":"https://doi.org/10.1007/s00500-024-09918-2","url":null,"abstract":"<p>Artificial Neural Networks (ANNs) are a tool in approximation theory widely used to solve interpolation problems. In fact, ANNs can be assimilated to functions since they take an input and return an output. The structure of the specifically adopted network determines the underlying approximation space, while the form of the function is selected by fixing the parameters of the network. In the present paper, we consider one-hidden layer ANNs with a feedforward architecture, also referred to as shallow or two-layer networks, so that the structure is determined by the number and types of neurons. The determination of the parameters that define the function, called training, is done via the resolution of the approximation problem, so by imposing the interpolation through a set of specific nodes. We present the case where the parameters are trained using a procedure that is referred to as Extreme Learning Machine (ELM) that leads to a linear interpolation problem. In such hypotheses, the existence of an ANN interpolating function is guaranteed. Given that the ANN is interpolating, the error incurred occurs outside the sampling interpolation nodes provided by the user. In this study, various choices of nodes are analyzed: equispaced, Chebychev, and randomly selected ones. Then, the focus is on regular target functions, for which it is known that interpolation can lead to spurious oscillations, a phenomenon that in the ANN literature is referred to as overfitting. We obtain good accuracy of the ANN interpolating function in all tested cases using these different types of interpolating nodes and different types of neurons. The following study is conducted starting from the well-known bell-shaped Runge example, which makes it clear that the construction of a global interpolating polynomial is accurate only if trained on suitably chosen nodes, ad example the Chebychev ones. In order to evaluate the behavior when the number of interpolation nodes increases, we increase the number of neurons in our network and compare it with the interpolating polynomial. We test using Runge’s function and other well-known examples with different regularities. As expected, the accuracy of the approximation with a global polynomial increases only if the Chebychev nodes are considered. Instead, the error for the ANN interpolating function always decays, and in most cases we observe that the convergence follows what is observed in the polynomial case on Chebychev nodes, despite the set of nodes used for training. Then we can conclude that the use of such an ANN defeats the Runge phenomenon. Our results show the power of ANNs to achieve excellent approximations when interpolating regular functions also starting from uniform and random nodes, particularly for Runge’s function.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"33 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-29DOI: 10.1007/s00500-024-09667-2
Enrico Ciavolino, Mario Angelelli, Giovanna Alessia Sternativo, Elisa De carlo, Alessia Anna Catalano, Emanuela Ingusci
In recent years, global events have redefined working life, stimulating new organizational models. This work focuses on job crafting, which is considered the way to improve the relationship between some organizational variables and other individual variables such as organizational identification and satisfaction with communication, both of which are crucial to achieving sustainable levels of well-being. The study examines the role of latent constructs that can promote adaptive responses as well as their relations. In particular, we focus on organizational identification in promoting adaptive responses, including the increase in structural resources, the increase in challenging demands, and the increase in social resources as adaptive strategies to improve satisfaction with communication. The analysis is carried out using robust statistical techniques that are suited to the study of causal relations between abstract constructs. Specifically, after Confirmatory Composite Analysis (CCA-PLS) to evaluate the quality of the data collected, a higher order mediation model, based on partial least squares structural equation modeling (PLS-SEM), was performed to test the mediation role of the job crafting. In addition, we prioritize such latent constructs using importance–performance map analysis (IPMA) to evaluate the relevance and performance of each construct of this model. The results show a relationship between organizational identification, corresponding to a high sense of belonging, and communication satisfaction at all levels through the mediation of job crafting.
{"title":"A higher-order job crafting mediation model with PLS-SEM: relationship between organizational identification and communication satisfaction","authors":"Enrico Ciavolino, Mario Angelelli, Giovanna Alessia Sternativo, Elisa De carlo, Alessia Anna Catalano, Emanuela Ingusci","doi":"10.1007/s00500-024-09667-2","DOIUrl":"https://doi.org/10.1007/s00500-024-09667-2","url":null,"abstract":"<p>In recent years, global events have redefined working life, stimulating new organizational models. This work focuses on job crafting, which is considered the way to improve the relationship between some organizational variables and other individual variables such as organizational identification and satisfaction with communication, both of which are crucial to achieving sustainable levels of well-being. The study examines the role of latent constructs that can promote adaptive responses as well as their relations. In particular, we focus on organizational identification in promoting adaptive responses, including the increase in structural resources, the increase in challenging demands, and the increase in social resources as adaptive strategies to improve satisfaction with communication. The analysis is carried out using robust statistical techniques that are suited to the study of causal relations between abstract constructs. Specifically, after Confirmatory Composite Analysis (CCA-PLS) to evaluate the quality of the data collected, a higher order mediation model, based on partial least squares structural equation modeling (PLS-SEM), was performed to test the mediation role of the job crafting. In addition, we prioritize such latent constructs using importance–performance map analysis (IPMA) to evaluate the relevance and performance of each construct of this model. The results show a relationship between organizational identification, corresponding to a high sense of belonging, and communication satisfaction at all levels through the mediation of job crafting.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"46 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-29DOI: 10.1007/s00500-024-09927-1
Supeng Wu, Hui Liu, Jiang Yang
Firstly, a topology is constructed by nuclei and upsets in residuated lattices and it is shown that a residuated lattice endowed with this topology becomes a topological space. Furthermore, some properties of the topological space are investigated such as compactness and connectedness. Moreover, we study continuities of all the operations with respect to the topology in a residuated lattice. Finally, the relationships are revealed between the two topologies on quotient residuated lattices.
{"title":"A topology based on nuclei and upsets in residuated lattices","authors":"Supeng Wu, Hui Liu, Jiang Yang","doi":"10.1007/s00500-024-09927-1","DOIUrl":"https://doi.org/10.1007/s00500-024-09927-1","url":null,"abstract":"<p>Firstly, a topology is constructed by nuclei and upsets in residuated lattices and it is shown that a residuated lattice endowed with this topology becomes a topological space. Furthermore, some properties of the topological space are investigated such as compactness and connectedness. Moreover, we study continuities of all the operations with respect to the topology in a residuated lattice. Finally, the relationships are revealed between the two topologies on quotient residuated lattices.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"74 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-29DOI: 10.1007/s00500-024-09949-9
G. Nivedhitha, P. Kalpana, A. Sheik Sidthik, V. Anusha Rani, Ajith B. Singh, R. Rajagopal
This work presents an essential module for the Transfer Learning approach's classification of melanoma skin lesions. Melanoma, a highly lethal form of skin cancer, poses a significant health threat globally. Image analysis plays a crucial role in enhancing the accuracy of malignant skin lesion classification. Although neural networks trained on extensive datasets have emerged as the latest solution, their scalability remains a challenge. This study proposes an efficient method for classifying skin lesions utilizing labelled data from open sources, leveraging EfficientNet as the foundational model to robustly capture discriminative features from diverse visual perspectives. Validation of the proposed algorithms relies on the classifier's capacity to distinguish between classes is measured by the Area Under the Receiver Operating Characteristic (AUC-ROC) curve. AUC-ROC score greater than zero denotes better classification performance. Our proposed model achieves an impressive score of 98.65%. In contrast to existing approaches, our method demonstrates swift and accurate identification and segmentation of melanoma skin lesions, showcasing its efficacy in advancing the field of skin lesion classification.
{"title":"Skin lesion classification using transfer learning","authors":"G. Nivedhitha, P. Kalpana, A. Sheik Sidthik, V. Anusha Rani, Ajith B. Singh, R. Rajagopal","doi":"10.1007/s00500-024-09949-9","DOIUrl":"https://doi.org/10.1007/s00500-024-09949-9","url":null,"abstract":"<p>This work presents an essential module for the Transfer Learning approach's classification of melanoma skin lesions. Melanoma, a highly lethal form of skin cancer, poses a significant health threat globally. Image analysis plays a crucial role in enhancing the accuracy of malignant skin lesion classification. Although neural networks trained on extensive datasets have emerged as the latest solution, their scalability remains a challenge. This study proposes an efficient method for classifying skin lesions utilizing labelled data from open sources, leveraging EfficientNet as the foundational model to robustly capture discriminative features from diverse visual perspectives. Validation of the proposed algorithms relies on the classifier's capacity to distinguish between classes is measured by the Area Under the Receiver Operating Characteristic (AUC-ROC) curve. AUC-ROC score greater than zero denotes better classification performance. Our proposed model achieves an impressive score of 98.65%. In contrast to existing approaches, our method demonstrates swift and accurate identification and segmentation of melanoma skin lesions, showcasing its efficacy in advancing the field of skin lesion classification.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"10 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Crop diseases adversely affect agricultural productivity and quality. The primary cause of these diseases is the presence of biotic stresses such as fungi, viruses, and bacteria. Detecting these causes at early stages requires constant monitoring by domain experts. Technological advancements in machine learning and deep learning methods have enabled the automated identification of leaf disease-specific symptoms through image analysis. This paper proposes image-based detection of leaf diseases using various deep learning-based models. The experiment was conducted on the PlantVillage dataset, which consists of 54,305 colour leaf images (healthy and diseased) belonging to 11 crop species categorized into 38 classes. The Inception-ResNet-V2-based model achieved a 10-fold cross-validation accuracy of (0.9991 pm 0.002) outperforming the other deep neural architectures and surpassing the performance of existing models in recent state-of-the-art works. Each underlined model is validated on an independent cohort. The Inception-ResNet-V2-based model achieved the best 10-fold cross-validation accuracy of (0.9535 pm 0.041) and was found statistically significant among other deep learning-based models. However, these deep learning models are considered a black box as their leaf disease predictions are opaque to end users. To address this issue, a local interpretable framework is proposed to mark the superpixels that contribute to identifying leaf disease. These superpixels closely confirmed the annotations of the human expert.
{"title":"Explaining deep learning-based leaf disease identification","authors":"Ankit Rajpal, Rashmi Mishra, Sheetal Rajpal, Kavita, Varnika Bhatia, Naveen Kumar","doi":"10.1007/s00500-024-09939-x","DOIUrl":"https://doi.org/10.1007/s00500-024-09939-x","url":null,"abstract":"<p>Crop diseases adversely affect agricultural productivity and quality. The primary cause of these diseases is the presence of biotic stresses such as fungi, viruses, and bacteria. Detecting these causes at early stages requires constant monitoring by domain experts. Technological advancements in machine learning and deep learning methods have enabled the automated identification of leaf disease-specific symptoms through image analysis. This paper proposes image-based detection of leaf diseases using various deep learning-based models. The experiment was conducted on the PlantVillage dataset, which consists of 54,305 colour leaf images (healthy and diseased) belonging to 11 crop species categorized into 38 classes. The Inception-ResNet-V2-based model achieved a 10-fold cross-validation accuracy of <span>(0.9991 pm 0.002)</span> outperforming the other deep neural architectures and surpassing the performance of existing models in recent state-of-the-art works. Each underlined model is validated on an independent cohort. The Inception-ResNet-V2-based model achieved the best 10-fold cross-validation accuracy of <span>(0.9535 pm 0.041)</span> and was found statistically significant among other deep learning-based models. However, these deep learning models are considered a black box as their leaf disease predictions are opaque to end users. To address this issue, a local interpretable framework is proposed to mark the superpixels that contribute to identifying leaf disease. These superpixels closely confirmed the annotations of the human expert.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"38 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-27DOI: 10.1007/s00500-024-09817-6
Satabdi Ray, Birojit Das, Baby Bhattacharya, Ómer Kişi, Carlos Granados
The central objective of this treatise is to introduce the concept ((j,k)^*_gamma )–operation in fuzzy bitopological spaces. The same operation is applied to study the concept of ((j,k)^*)-fuzzy open sets in a given fuzzy bitopological space. Existence of all the conceptions are shown by considering different operations. Various properties of the newly introduced notion are presented and justifications are provided by placing suitable examples. Furthermore, minimality of fuzzy open sets are also being studied up to some extent. Finally, results on locally finiteness of a given fuzzy bitopological space are established via operation approach.
{"title":"Application of operation approach in fuzzy bitopological spaces","authors":"Satabdi Ray, Birojit Das, Baby Bhattacharya, Ómer Kişi, Carlos Granados","doi":"10.1007/s00500-024-09817-6","DOIUrl":"https://doi.org/10.1007/s00500-024-09817-6","url":null,"abstract":"<p>The central objective of this treatise is to introduce the concept <span>((j,k)^*_gamma )</span>–operation in fuzzy bitopological spaces. The same operation is applied to study the concept of <span>((j,k)^*)</span>-fuzzy open sets in a given fuzzy bitopological space. Existence of all the conceptions are shown by considering different operations. Various properties of the newly introduced notion are presented and justifications are provided by placing suitable examples. Furthermore, minimality of fuzzy open sets are also being studied up to some extent. Finally, results on locally finiteness of a given fuzzy bitopological space are established via operation approach.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"11 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Generating uniform design tables (UDTs) is the first step to experimenting efficiently and effectively, and is also one of the most critical steps. Thus, the construction of uniform design tables has received much attention over the past decades. This paper presents a new algorithm for constructing uniform design tables: restart discrete dynamical evolutionary algorithm (RDDE). This algorithm is based on a well-designed dynamical evolutionary algorithm and utilizes discrete rounding technology to convert continuous variables into discrete variables. Considering the optimization of UDT is a multi-objective optimization problem, RDDE uses Friedman rank to select the optimal solution with better comprehensive comparison ranking. RDDE also utilizes a simulated annealing-based restart technology to select control parameters, thereby increasing the algorithm's ability to jump out of local optima. Comparisons with state-of-the-art UDTs and two practical engineering examples are presented to verify the uniformity of the design table constructed by RDDE. Numerical results indicate that RDDE can indeed construct UDTs with excellent uniformity at different levels, factors, and runs. Especially, RDDE can flexibly construct UDTs with unequal intervals of factors that cannot be directly processed by other designs of experiment.
{"title":"Constructing uniform design tables based on restart discrete dynamical evolutionary algorithm","authors":"Yuelin Zhao, Feng Wu, Yuxiang Yang, Xindi Wei, Zhaohui Hu, Jun Yan, Wanxie Zhong","doi":"10.1007/s00500-024-09890-x","DOIUrl":"https://doi.org/10.1007/s00500-024-09890-x","url":null,"abstract":"<p>Generating uniform design tables (UDTs) is the first step to experimenting efficiently and effectively, and is also one of the most critical steps. Thus, the construction of uniform design tables has received much attention over the past decades. This paper presents a new algorithm for constructing uniform design tables: restart discrete dynamical evolutionary algorithm (RDDE). This algorithm is based on a well-designed dynamical evolutionary algorithm and utilizes discrete rounding technology to convert continuous variables into discrete variables. Considering the optimization of UDT is a multi-objective optimization problem, RDDE uses Friedman rank to select the optimal solution with better comprehensive comparison ranking. RDDE also utilizes a simulated annealing-based restart technology to select control parameters, thereby increasing the algorithm's ability to jump out of local optima. Comparisons with state-of-the-art UDTs and two practical engineering examples are presented to verify the uniformity of the design table constructed by RDDE. Numerical results indicate that RDDE can indeed construct UDTs with excellent uniformity at different levels, factors, and runs. Especially, RDDE can flexibly construct UDTs with unequal intervals of factors that cannot be directly processed by other designs of experiment.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"21 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-26DOI: 10.1007/s00500-024-09885-8
Pradip Roul, Vikas Rohil
This article aims to develop an optimal superconvergent numerical method for approximating the solution of the nonlinear time-fractional generalized Fisher’s (TFGF) equation. The time-fractional derivative in the model problem is considered in the sense of Caputo and is approximated using the (L2-1_{sigma }) scheme. Spatial discretization is performed using an optimal superconvergent quintic B-spline (OSQB) technique. To derive the method, a high-order perturbation of the semi-discretized equation of the original problem is generated using spline alternate relations. Convergence and stability of the method are analyzed, demonstrating that the method converges with (O(Delta t^{2}+Delta x^6)), where (Delta x) and (Delta t) are step sizes in space and time, respectively. Three numerical examples are provided to demonstrate the robustness of the proposed method. Our method is compared with an existing method in the literature and the elapsed computational time for the present scheme is provided.
{"title":"An accurate numerical method and its analysis for time-fractional Fisher’s equation","authors":"Pradip Roul, Vikas Rohil","doi":"10.1007/s00500-024-09885-8","DOIUrl":"https://doi.org/10.1007/s00500-024-09885-8","url":null,"abstract":"<p>This article aims to develop an optimal superconvergent numerical method for approximating the solution of the nonlinear time-fractional generalized Fisher’s (TFGF) equation. The time-fractional derivative in the model problem is considered in the sense of Caputo and is approximated using the <span>(L2-1_{sigma })</span> scheme. Spatial discretization is performed using an optimal superconvergent quintic B-spline (OSQB) technique. To derive the method, a high-order perturbation of the semi-discretized equation of the original problem is generated using spline alternate relations. Convergence and stability of the method are analyzed, demonstrating that the method converges with <span>(O(Delta t^{2}+Delta x^6))</span>, where <span>(Delta x)</span> and <span>(Delta t)</span> are step sizes in space and time, respectively. Three numerical examples are provided to demonstrate the robustness of the proposed method. Our method is compared with an existing method in the literature and the elapsed computational time for the present scheme is provided.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"16 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-26DOI: 10.1007/s00500-024-09889-4
Ihab Abusaif, Coşkun Kuş
This paper introduces a novel modification of the negative binomial distribution, which serves as a generalization encompassing both negative binomial and zero-inflated negative binomial distributions. This innovative distribution offers flexibility by accommodating an arbitrary number of inflation points at various locations. The paper explores key distributional properties associated with this modified distribution. Additionally, this study proposes several estimators designed to obtain estimates for the unknown parameters. Furthermore, the paper introduces a new count regression model that utilizes the modified distribution. To assess the performance of the proposed distribution and the count regression model, a comprehensive Monte Carlo simulation study is conducted. In the final stage of the paper, a real-world dataset is scrutinized to ascertain the superiority of the proposed model. This empirical analysis contributes to validating the practical applicability and effectiveness of the newly introduced distribution in comparison to existing models.
{"title":"Multiple arbitrarily inflated negative binomial regression model and its application","authors":"Ihab Abusaif, Coşkun Kuş","doi":"10.1007/s00500-024-09889-4","DOIUrl":"https://doi.org/10.1007/s00500-024-09889-4","url":null,"abstract":"<p>This paper introduces a novel modification of the negative binomial distribution, which serves as a generalization encompassing both negative binomial and zero-inflated negative binomial distributions. This innovative distribution offers flexibility by accommodating an arbitrary number of inflation points at various locations. The paper explores key distributional properties associated with this modified distribution. Additionally, this study proposes several estimators designed to obtain estimates for the unknown parameters. Furthermore, the paper introduces a new count regression model that utilizes the modified distribution. To assess the performance of the proposed distribution and the count regression model, a comprehensive Monte Carlo simulation study is conducted. In the final stage of the paper, a real-world dataset is scrutinized to ascertain the superiority of the proposed model. This empirical analysis contributes to validating the practical applicability and effectiveness of the newly introduced distribution in comparison to existing models.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"16 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-26DOI: 10.1007/s00500-024-09951-1
Amos Bortiew, Swarnajyoti Patra, Lorenzo Bruzzone
Techniques that exploit spectral-spatial information have proven to be very effective in hyperspectral image classification. Joint sparse representation classification (JSRC) is one such technique which has been extensively used for this purpose. However, the use of a single fixed-sized window has limited its ability to incorporate spatial information. Several techniques such as multiscale superpixels based sparse representation classification (MSSRC), multiscale adaptive sparse representation classification (MASRC) and Discriminant Subdictionary Learning (DSDL) have tried to overcome this drawback by fusing information from different scales. However, their inability to simultaneously consider the correlated information at different scales and appropriate spatial neighbourhoods limits their performance. In order to better model contextual information, in this paper, we propose a modified max-tree and modified min-tree to represent the connected components of the image. Then, by exploiting these connected components, adaptive multiscale windows are defined. The potentiality of the proposed technique is validated by performing a comparative analysis with four state-of-the-art sparse representation methods using three real hyperspectral datasets. For a fixed training and test sets of University of Pavia and Indian Pines dataset, our proposed technique provides at least 3% and 2%, respectively higher classification results than the best state-of-the-art method.
{"title":"Component adaptive sparse representation for hyperspectral image classification","authors":"Amos Bortiew, Swarnajyoti Patra, Lorenzo Bruzzone","doi":"10.1007/s00500-024-09951-1","DOIUrl":"https://doi.org/10.1007/s00500-024-09951-1","url":null,"abstract":"<p>Techniques that exploit spectral-spatial information have proven to be very effective in hyperspectral image classification. Joint sparse representation classification (JSRC) is one such technique which has been extensively used for this purpose. However, the use of a single fixed-sized window has limited its ability to incorporate spatial information. Several techniques such as multiscale superpixels based sparse representation classification (MSSRC), multiscale adaptive sparse representation classification (MASRC) and Discriminant Subdictionary Learning (DSDL) have tried to overcome this drawback by fusing information from different scales. However, their inability to simultaneously consider the correlated information at different scales and appropriate spatial neighbourhoods limits their performance. In order to better model contextual information, in this paper, we propose a modified max-tree and modified min-tree to represent the connected components of the image. Then, by exploiting these connected components, adaptive multiscale windows are defined. The potentiality of the proposed technique is validated by performing a comparative analysis with four state-of-the-art sparse representation methods using three real hyperspectral datasets. For a fixed training and test sets of University of Pavia and Indian Pines dataset, our proposed technique provides at least 3% and 2%, respectively higher classification results than the best state-of-the-art method.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"44 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}