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Principal Component Analysis and Randomness Test for Big Data Analysis : Prac...

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Specificaties

Objectstaat
Vrijwel nieuw: Een boek dat er als nieuw uitziet, maar al wel is gelezen. De kaft is niet zichtbaar ...
Book Title
Principal Component Analysis and Randomness Test for Big Data Ana
ISBN
9789811939662
Subject Area
Computers, Business & Economics, Mathematics
Publication Name
Principal Component Analysis and Randomness Tests for Big Data Analysis
Item Length
9.3 in
Publisher
Springer
Subject
Probability & Statistics / General, General, Databases / General, Economics / Theory
Publication Year
2023
Series
Evolutionary Economics and Social Complexity Science Ser.
Type
Textbook
Format
Hardcover
Language
English
Author
Yumihiko Ikura, Mieko Tanaka-Yamawaki
Item Width
6.1 in
Item Weight
14.5 Oz
Number of Pages
VII, 152 Pages

Over dit product

Product Information

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.

Product Identifiers

Publisher
Springer
ISBN-10
9811939667
ISBN-13
9789811939662
eBay Product ID (ePID)
28057293814

Product Key Features

Author
Yumihiko Ikura, Mieko Tanaka-Yamawaki
Publication Name
Principal Component Analysis and Randomness Tests for Big Data Analysis
Format
Hardcover
Language
English
Subject
Probability & Statistics / General, General, Databases / General, Economics / Theory
Publication Year
2023
Series
Evolutionary Economics and Social Complexity Science Ser.
Type
Textbook
Subject Area
Computers, Business & Economics, Mathematics
Number of Pages
VII, 152 Pages

Dimensions

Item Length
9.3 in
Item Width
6.1 in
Item Weight
14.5 Oz

Additional Product Features

Series Volume Number
25
Number of Volumes
1 Vol.
Lc Classification Number
Hb90-99.722
Table of Content
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: Jacobi's 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.
Copyright Date
2023
Dewey Decimal
005.7
Dewey Edition
23
Illustrated
Yes

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