Optimal Quantification and Symmetry (Behaviormetrics: Quantitative Approaches to Human Behavior, 12)

Nishisato, Shizuhiko

ISBN 10: 981169169X / ISBN 13: 9789811691690

Published by Springer, 2022

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Bibliographic Details

• Title: Optimal Quantification and Symmetry (Behaviormetrics: Quantitative Approaches to Human Behavior, 12)
• Publisher: Springer
• Publication Date: 2022
• Language: English
• ISBN 10: 981169169X
• ISBN 13: 9789811691690
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.

About the Author

Shizuhiko Nishisato, Professor Emeritus, University of Toronto.