9789811939693 - principal component analysis and randomness test for big data analysis: practical applications of rmt-based technique (evolutionary economics and social complexity science, 25, band 25) von tanaka-yamawaki, mieko; ikura, yumihiko (2 Ergebnisse)
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Sprache: Englisch
Verlag: Springer, 2024
Serie: Buch 31 von 32 - Evolutionary Economics and Social Complexity Science
- Softcover
Anbieter: preigu, Osnabrück, Deutschlandpreigu
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Taschenbuch. Zustand: Neu. Principal Component Analysis and Randomness Test for Big Data Analysis | Practical Applications of RMT-Based Technique | Mieko Tanaka-Yamawaki (u. a.) | Taschenbuch | Evolutionary Economics and Social Complexity Science | vii | Englisch | 2024 | Springer | EAN 9789811939693 | Verantwortliche Person für… die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
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Sprache: Englisch
Verlag: Springer, 2024
Serie: Buch 31 von 32 - Evolutionary Economics and Social Complexity Science
- Softcover
Anbieter: AHA-BUCH GmbH, Einbeck, DeutschlandAHA-BUCH GmbH
Verkäufer/-in kontaktierenVerkäufer/-in mit 5 SternenZustand: Neu
EUR 117,69
EUR 61,27 VersandVersand von Deutschland nach USAAnzahl: 1 verfügbar
Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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, whereXrepresents a rectangular matrix ofNrows andLcolumns andXTrepresents the transverse matrix ofX. BecauseCis symmetric, namely,C=CT, it can be converted to a diagonal matrix of eigenvalues by a similarity transformationSCS-1=SCSTusing an orthogonal matrixS. WhenNis 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,Xconsists ofNstock- prices of lengthL, and the correlation matrixCis anNbyNsquare matrix, whose element at thei-th row andj-th column is the inner product of the price time series of the lengthLof thei-th stock and thej-th stock of the equal lengthL. 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.
