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Optimal quantification and symmetry

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Optimal quantification and symmetryby Shizuhiko Nishisato.
出版者:	Singapore :Springer Singapore :2022.
面頁冊數:	xvi, 195 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Predicate calculus.
電子資源:	https://doi.org/10.1007/978-981-16-9170-6
ISBN:	9789811691706$q(electronic bk.)

Optimal quantification and symmetry
Optimal quantification and symmetry[electronic resource] /by Shizuhiko Nishisato. - Singapore :Springer Singapore :2022. - xvi, 195 p. :ill., digital ;24 cm. - Behaviormetrics: quantitative approaches to human behavior,v. 122524-4035 ;. - Behaviormetrics: quantitative approaches to human behavior ;v.5..

Optimality and Symmetry -- Examples of Quantification -- Constraints on Quantification -- Quantification Procedures -- Mathematical Symmetry -- Data Format and Information -- Space Theory and Symmetry.

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.

ISBN: 9789811691706$q(electronic bk.)

Standard No.: 10.1007/978-981-16-9170-6doiSubjects--Topical Terms:

760596
Predicate calculus.

LC Class. No.: QA9.35 / .N57 2022

Dewey Class. No.: 511.3

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490 1 $a Behaviormetrics: quantitative approaches to human behavior, $x 2524-4035 ; $v v. 12
505 0 $a Optimality and Symmetry -- Examples of Quantification -- Constraints on Quantification -- Quantification Procedures -- Mathematical Symmetry -- Data Format and Information -- Space Theory and Symmetry.
520 $a 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.
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