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001468507 001__ 1468507
001468507 003__ OCoLC
001468507 005__ 20230707003254.0
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001468507 008__ 230603s2023\\\\si\\\\\\ob\\\\000\0\eng\d
001468507 019__ $$a1380615412
001468507 020__ $$a9789811939679$$q(electronic bk.)
001468507 020__ $$a9811939675$$q(electronic bk.)
001468507 020__ $$z9811939667
001468507 020__ $$z9789811939662
001468507 0247_ $$a10.1007/978-981-19-3967-9$$2doi
001468507 035__ $$aSP(OCoLC)1381096715
001468507 040__ $$aEBLCP$$beng$$cEBLCP$$dGW5XE$$dYDX$$dEBLCP
001468507 049__ $$aISEA
001468507 050_4 $$aQA76.9.B45
001468507 08204 $$a005.7$$223/eng/20230605
001468507 1001_ $$aTanaka-Yamawaki, Mieko.
001468507 24510 $$aPrincipal component analysis and randomness test for big data analysis :$$bpractical applications of RMT-based technique /$$cMieko Tanaka-Yamawaki, Yumihiko Ikura.
001468507 260__ $$aSingapore :$$bSpringer,$$c2023.
001468507 300__ $$a1 online resource (153 p.).
001468507 4901_ $$aEvolutionary Economics and Social Complexity Science ;$$vv.25
001468507 504__ $$aIncludes bibliographical references.
001468507 5050_ $$aBig 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.
001468507 506__ $$aAccess limited to authorized users.
001468507 520__ $$aThis 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.
001468507 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed June 5, 2023).
001468507 650_0 $$aBig data$$xEconomic aspects.
001468507 650_0 $$aPrincipal components analysis.
001468507 655_0 $$aElectronic books.
001468507 7001_ $$aIkura, Yumihiko.
001468507 77608 $$iPrint version:$$aTanaka-Yamawaki, Mieko$$tPrincipal Component Analysis and Randomness Test for Big Data Analysis$$dSingapore : Springer Singapore Pte. Limited,c2023$$z9789811939662
001468507 830_0 $$aEvolutionary economics and social complexity science ;$$vv.25.
001468507 852__ $$bebk
001468507 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-19-3967-9$$zOnline Access$$91397441.1
001468507 909CO $$ooai:library.usi.edu:1468507$$pGLOBAL_SET
001468507 980__ $$aBIB
001468507 980__ $$aEBOOK
001468507 982__ $$aEbook
001468507 983__ $$aOnline
001468507 994__ $$a92$$bISE