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Author: Shizuhiko Nishisato
Publisher: Springer Nature
ISBN: 9811691703
Category : Mathematics
Languages : en
Pages : 199
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Book Description
This book offers a unique new look at the familiar quantification theory from the point of view of mathematical symmetry and spatial symmetry. Symmetry exists in many aspects of our life—for instance, in the arts and biology as an ingredient of beauty and equilibrium, and more importantly, for data analysis as an indispensable representation of functional optimality. This unique focus on symmetry clarifies the objectives of quantification theory and the demarcation of quantification space, something that has never caught the attention of researchers. Mathematical symmetry is well known, as can be inferred from Hirschfeld’s simultaneous linear regressions, but spatial symmetry has not been discussed before, except for what one may infer from Nishisato’s dual scaling. The focus on symmetry here clarifies the demarcation of quantification analysis and makes it easier to understand such a perennial problem as that of joint graphical display in quantification theory. The new framework will help advance the frontier of further developments of quantification theory. Many numerical examples are included to clarify the details of quantification theory, with a focus on symmetry as its operational principle. In this way, the book is useful not only for graduate students but also for researchers in diverse areas of data analysis.
Author: Shizuhiko Nishisato
Publisher: Springer Nature
ISBN: 9811691703
Category : Mathematics
Languages : en
Pages : 199
Get Book
Book Description
This book offers a unique new look at the familiar quantification theory from the point of view of mathematical symmetry and spatial symmetry. Symmetry exists in many aspects of our life—for instance, in the arts and biology as an ingredient of beauty and equilibrium, and more importantly, for data analysis as an indispensable representation of functional optimality. This unique focus on symmetry clarifies the objectives of quantification theory and the demarcation of quantification space, something that has never caught the attention of researchers. Mathematical symmetry is well known, as can be inferred from Hirschfeld’s simultaneous linear regressions, but spatial symmetry has not been discussed before, except for what one may infer from Nishisato’s dual scaling. The focus on symmetry here clarifies the demarcation of quantification analysis and makes it easier to understand such a perennial problem as that of joint graphical display in quantification theory. The new framework will help advance the frontier of further developments of quantification theory. Many numerical examples are included to clarify the details of quantification theory, with a focus on symmetry as its operational principle. In this way, the book is useful not only for graduate students but also for researchers in diverse areas of data analysis.
Author: Ali Kaveh
Publisher: Springer Science & Business Media
ISBN: 3709115655
Category : Science
Languages : en
Pages : 473
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Book Description
Optimal analysis is defined as an analysis that creates and uses sparse, well-structured and well-conditioned matrices. The focus is on efficient methods for eigensolution of matrices involved in static, dynamic and stability analyses of symmetric and regular structures, or those general structures containing such components. Powerful tools are also developed for configuration processing, which is an important issue in the analysis and design of space structures and finite element models. Different mathematical concepts are combined to make the optimal analysis of structures feasible. Canonical forms from matrix algebra, product graphs from graph theory and symmetry groups from group theory are some of the concepts involved in the variety of efficient methods and algorithms presented. The algorithms elucidated in this book enable analysts to handle large-scale structural systems by lowering their computational cost, thus fulfilling the requirement for faster analysis and design of future complex systems. The value of the presented methods becomes all the more evident in cases where the analysis needs to be repeated hundreds or even thousands of times, as for the optimal design of structures by different metaheuristic algorithms. The book is of interest to anyone engaged in computer-aided analysis and design and software developers in this field. Though the methods are demonstrated mainly through skeletal structures, continuum models have also been added to show the generality of the methods. The concepts presented are not only applicable to different types of structures but can also be used for the analysis of other systems such as hydraulic and electrical networks.
Author: A. Kaveh
Publisher: Springer
ISBN: 9783709115664
Category : Science
Languages : en
Pages : 463
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Book Description
Optimal analysis is defined as an analysis that creates and uses sparse, well-structured and well-conditioned matrices. The focus is on efficient methods for eigensolution of matrices involved in static, dynamic and stability analyses of symmetric and regular structures, or those general structures containing such components. Powerful tools are also developed for configuration processing, which is an important issue in the analysis and design of space structures and finite element models. Different mathematical concepts are combined to make the optimal analysis of structures feasible. Canonical forms from matrix algebra, product graphs from graph theory and symmetry groups from group theory are some of the concepts involved in the variety of efficient methods and algorithms presented. The algorithms elucidated in this book enable analysts to handle large-scale structural systems by lowering their computational cost, thus fulfilling the requirement for faster analysis and design of future complex systems. The value of the presented methods becomes all the more evident in cases where the analysis needs to be repeated hundreds or even thousands of times, as for the optimal design of structures by different metaheuristic algorithms. The book is of interest to anyone engaged in computer-aided analysis and design and software developers in this field. Though the methods are demonstrated mainly through skeletal structures, continuum models have also been added to show the generality of the methods. The concepts presented are not only applicable to different types of structures but can also be used for the analysis of other systems such as hydraulic and electrical networks.
Author: Shizuhiko Nishisato
Publisher: Springer Nature
ISBN: 981992295X
Category : Mathematics
Languages : en
Pages : 214
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Book Description
The purpose of this book is to thoroughly prepare diverse areas of researchers in quantification theory. As is well known, quantification theory has attracted the attention of a countless number of researchers, some mathematically oriented and others not, but all of them are experts in their own disciplines. Quantifying non-quantitative (qualitative) data requires a variety of mathematical and statistical strategies, some of which are quite complicated. Unlike many books on quantification theory, the current book places more emphasis on preliminary requisites of mathematical tools than on details of quantification theory. As such, the book is primarily intended for readers whose specialty is outside mathematical sciences. The book was designed to offer non-mathematicians a variety of mathematical tools used in quantification theory in simple terms. Once all the preliminaries are fully discussed, quantification theory is then introduced in the last section as a simple application of those mathematical procedures fully discussed so far. The book opens up further frontiers of quantification theory as simple applications of basic mathematics.
Author: Shizuhiko Nishisato
Publisher: Springer Nature
ISBN: 9811624704
Category : Social Science
Languages : en
Pages : 231
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Book Description
This book offers a new look at well-established quantification theory for categorical data, referred to by such names as correspondence analysis, dual scaling, optimal scaling, and homogeneity analysis. These multiple identities are a consequence of its large number of properties that allow one to analyze and visualize the strength of variable association in an optimal solution. The book contains modern quantification theory for analyzing the association between two and more categorical variables in a variety of applicative frameworks. Visualization has attracted much attention over the past decades and given rise to controversial opinions. One may consider variations of plotting systems used in the construction of the classic correspondence plot, the biplot, the Carroll-Green-Schaffer scaling, or a new approach in doubled multidimensional space as presented in the book. There are even arguments for no visualization at all. The purpose of this book therefore is to shed new light on time-honored graphical procedures with critical reviews, new ideas, and future directions as alternatives. This stimulating volume is written with fresh new ideas from the traditional framework and the contemporary points of view. It thus offers readers a deep understanding of the ever-evolving nature of quantification theory and its practice. Part I starts with illustrating contingency table analysis with traditional joint graphical displays (symmetric, non-symmetric) and the CGS scaling and then explores logically correct graphs in doubled Euclidean space for both row and column variables. Part II covers a variety of mathematical approaches to the biplot strategy in graphing a data structure, providing a useful source for this modern approach to graphical display. Part II is also concerned with a number of alternative approaches to the joint graphical display such as bimodal cluster analysis and other statistical problems relevant to quantification theory.
Author: Akinori Okada
Publisher: Springer Nature
ISBN: 9819922402
Category : Mathematics
Languages : en
Pages : 335
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Book Description
This edited book is the first one written in English that deals comprehensively with behavior metrics. The term “behaviormetrics” comprehends the research including all sorts of quantitative approaches to disclose human behavior. Researchers in behavior metrics have developed, extended, and improved methods such as multivariate statistical analysis, survey methods, cluster analysis, machine learning, multidimensional scaling, corresponding analysis or quantification theory, network analysis, clustering, factor analysis, test theory, and related factors. In the spirit of behavior metrics, researchers applied these methods to data obtained by surveys, experiments, or websites from a diverse range of fields. The purpose of this book is twofold. One is to represent studies that display how the basic elements of behavior metrics have developed into present-day behavior metrics. The other is to represent studies performed mainly by those who would like to pioneer new fields of behavior metrics and studies that display elements of future behavior metrics. These studies consist of various characteristics such as those dealing with theoretical or conceptual subjects, the algorithm, the model, the method, and the application to a wide variety of fields. This book helps readers to understand the present and future of behavior metrics.
Author: Ali Kaveh
Publisher: Springer Nature
ISBN: 303113429X
Category : Technology & Engineering
Languages : en
Pages : 369
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Book Description
The main purpose of the present book is to develop a general framework for population-based metaheuristics based on some basic concepts of set theory. The idea of the framework is to divide the population of individuals into subpopulations of identical sizes. Therefore, in each iteration of the search process, different subpopulations explore the search space independently but simultaneously. The framework aims to provide a suitable balance between exploration and exploitation during the search process. A few chapters containing algorithm-specific modifications of some state-of-the-art metaheuristics are also included to further enrich the book. The present book is addressed to those scientists, engineers, and students who wish to explore the potentials of newly developed metaheuristics. The proposed metaheuristics are not only applicable to structural optimization problems but can also be used for other engineering optimization applications. The book is likely to be of interest to a wide range of engineers and students who deal with engineering optimization problems.
Author: Ali Kaveh
Publisher: Springer Nature
ISBN: 3030455491
Category : Technology & Engineering
Languages : en
Pages : 311
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Book Description
This book proposes and validates a number of methods and shortcuts for frugal engineers, which will allow them to significantly reduce the computational costs for analysis and reanalysis and, as a result, for structural design processes. The need for accuracy and speed in analyzing structural systems with ever-tighter design tolerances and larger numbers of elements has been relentlessly driving forward research into methods that are capable of analyzing structures at a reasonable computational cost. The methods presented are of particular value in situations where the analysis needs to be repeated hundreds or even thousands of times, as is the case with the optimal design of structures using different metaheuristic algorithms. Featuring methods that are not only applicable to skeletal structures, but by extension also to continuum models, this book will appeal to researchers and engineers involved in the computer-aided analysis and design of structures, and to software developers in this field. It also serves as a complement to previous books on the optimal analysis of large-scale structures utilizing concepts of symmetry and regularity. Further, its novel application of graph-theoretical methods is of interest to mathematicians.
Author: Chu Kiong Loo
Publisher: Springer
ISBN: 3319126431
Category : Computers
Languages : en
Pages : 706
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Book Description
The three volume set LNCS 8834, LNCS 8835, and LNCS 8836 constitutes the proceedings of the 20th International Conference on Neural Information Processing, ICONIP 2014, held in Kuching, Malaysia, in November 2014. The 231 full papers presented were carefully reviewed and selected from 375 submissions. The selected papers cover major topics of theoretical research, empirical study, and applications of neural information processing research. The 3 volumes represent topical sections containing articles on cognitive science, neural networks and learning systems, theory and design, applications, kernel and statistical methods, evolutionary computation and hybrid intelligent systems, signal and image processing, and special sessions intelligent systems for supporting decision, making processes, theories and applications, cognitive robotics, and learning systems for social network and web mining.
Author: A. Kaveh
Publisher: Springer
ISBN: 331948012X
Category : Technology & Engineering
Languages : en
Pages : 373
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Book Description
The book presents recently developed efficient metaheuristic optimization algorithms and their applications for solving various optimization problems in civil engineering. The concepts can also be used for optimizing problems in mechanical and electrical engineering.
