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Optimal Quantification and Symmetry - Shizuhiko Nishisato

Optimal Quantification and Symmetry

Buch | Hardcover
195 Seiten
2022 | 1st ed. 2022
Springer Verlag, Singapore
978-981-16-9169-0 (ISBN)
CHF 194,70 inkl. MwSt
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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.

Shizuhiko Nishisato, Professor Emeritus, University of Toronto.

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

Erscheinungsdatum
Reihe/Serie Behaviormetrics: Quantitative Approaches to Human Behavior ; 12
Zusatzinfo 20 Illustrations, color; 3 Illustrations, black and white; XVI, 195 p. 23 illus., 20 illus. in color.
Verlagsort Singapore
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Informatik Datenbanken
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte Correspondence Analysis • Dual Scaling • mathematical symmetry • Multidimensional Nonlinear Analysis • Optimal Analysis of Qualitative Data • Quantification analysis • Spatial Symmetry
ISBN-10 981-16-9169-X / 981169169X
ISBN-13 978-981-16-9169-0 / 9789811691690
Zustand Neuware
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