Principal Component Analysis and Randomness Test for Big Data Analysis

The book "Principal Component Analysis and Randomness Test for Big Data Analysis" offers an innovative approach to analyzing large, rectangular numerical datasets known as Big Data. The focus is on capturing the significance of the data immediately, without getting lost in the details of individual data points. Unlike traditional methods of principal component analysis, randomness tests, and visualization techniques, the proposed approach is characterized by its universality and simplicity, regardless of data types, structures, or specific scientific disciplines. The mathematical foundation is thoroughly addressed, with RMT-PCA and the RMT test utilizing the cross-correlation matrix of time series. This methodology is also applied to high-frequency stock prices in the Japanese and American markets to demonstrate its effectiveness in identifying trending business areas in the financial market.