Principal Component Analysis and Randomness Test for Big Data Analysis : Practical Applications of RMT-Based Technique

Mieko Tanaka-Yamawaki

ISBN 10: 9811939667 / ISBN 13: 9789811939662

Edité par Springer, Springer Nature Singapore, 2023

A propos de cet article

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.

N° de réf. du vendeur 9789811939662

Détails bibliographiques

• Titre: Principal Component Analysis and Randomness Test for Big Data Analysis : Practical Applications of RMT-Based Technique
• Éditeur: Springer, Springer Nature Singapore
• Date de parution: 2023
• Langue: anglais
• ISBN à 10 chiffres: 9811939667
• ISBN à 13 chiffres: 9789811939662
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 15 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 15 millimètres de profondeur
• Poids: 412 grammes

A propos de ce titre

Synopsis

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 = XX^T, where X represents a rectangular matrix of N rows and L columns and X^T represents the transverse matrix of X. Because C is symmetric, namely, C = C^T, it can be converted to a diagonal matrix of eigenvalues by a similarity transformation SCS^-1 = SCS^T 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.

À propos de l?auteur

Mieko Tanaka-Yamawaki, former professor, Tottori University
Yumihiko Ikura, Meiji University