Principal component analysis and randomness test for big data analysis : practical applications of RMT-based technique / Mieko Tanaka-Yamawaki, Yumihiko Ikura.
Tanaka-Yamawaki, Mieko.; Ikura, Yumihiko.
2023
QA76.9.B45
Available Online

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Title Principal component analysis and randomness test for big data analysis : practical applications of RMT-based technique / Mieko Tanaka-Yamawaki, Yumihiko Ikura.
Author Tanaka-Yamawaki, Mieko.
ISBN 9789811939679 (electronic bk.)
9811939675 (electronic bk.)
9811939667
9789811939662
DOI https://doi.org/10.1007/978-981-19-3967-9
Publication Details Singapore : Springer, 2023.
Language English
Description 1 online resource (153 p.).
Item Number 10.1007/978-981-19-3967-9 doi
Call Number QA76.9.B45
Dewey Decimal Classification 005.7
Summary This book presents the novel approach of analyzing large-sized rectangular-shaped numerical data (so-called big data). The essence of this approach is to grasp the "meaning" of the data instantly, without getting into the details of individual data. Unlike conventional approaches of principal component analysis, randomness tests, and visualization methods, the authors' approach has the benefits of universality and simplicity of data analysis, regardless of data types, structures, or specific field of science. First, mathematical preparation is described. The RMT-PCA and the RMT-test utilize the cross-correlation matrix of time series, C = XXT, where X represents a rectangular matrix of N rows and L columns and XT represents the transverse matrix of X. Because C is symmetric, namely, C = CT, it can be converted to a diagonal matrix of eigenvalues by a similarity transformation SCS-1 = SCST using an orthogonal matrix S. When N is significantly large, the histogram of the eigenvalue distribution can be compared to the theoretical formula derived in the context of the random matrix theory (RMT, in abbreviation). Then the RMT-PCA applied to high-frequency stock prices in Japanese and American markets is dealt with. This approach proves its effectiveness in extracting "trendy" business sectors of the financial market over the prescribed time scale. In this case, X consists of N stock- prices of length L, and the correlation matrix C is an N by N square matrix, whose element at the i-th row and j-th column is the inner product of the price time series of the length L of the i-th stock and the j-th stock of the equal length L. Next, the RMT-test is applied to measure randomness of various random number generators, including algorithmically generated random numbers and physically generated random numbers. The book concludes by demonstrating two applications of the RMT-test: (1) a comparison of hash functions, and (2) stock prediction by means of randomness, including a new index of off-randomness related to market decline.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed June 5, 2023).
Added Author Ikura, Yumihiko.
Series Evolutionary economics and social complexity science ; v.25.
Available in Other Form Principal Component Analysis and Randomness Test for Big Data Analysis
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Big Data Analysis by Means of RMT-Oriented Methodologies
Formulation of the RMT-PCA
RMT-PCA and Stock Markets
The RMT-test: New Tool to Measure the Randomness of a Given Sequence
Application of the RMT-test
Conclusion
Appendix I: Introduction to vector, inner product, correlation matrix
Appendix II: Jacobis rotation algorithm
Appendix III: Program for the RMT-test
Appendix IV: RMT-test applied on TOIPXcore30 index time series in 2014
Appendix V: RMT-test applied on TOIPX index time series in 2011-2014.

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