Principal Component Analysis and Randomness Test for Big Data Analysis by Mieko Tanaka-Yamawaki & Yumihiko Ikura

Author:Mieko Tanaka-Yamawaki & Yumihiko Ikura
Language: eng
Format: epub
ISBN: 9789811939679
Publisher: Springer Nature Singapore

(2)

The sequence created in (1) is further shuffled by 1,000,000 times, and the result is written on the file named “the random number sequence of 2,000,000 shuffles.”

By means of repeating this process, 55 samples are created for each of level of randomness. The number 55 is required to apply the NIST test.

Preparing those data sets, we have done the experiments as follows.

First, we confirm that the randomness indeed increases according to the number of shuffles. The result of applying the quantitative evaluation of the RMT-test on the random number sequences created by shuffling 1,000,000–5,000,000 times is summarized in Fig. 4.10, where the vertical axis shows the |Dk| in Eq. (4.28) averaged over 55 samples, for the k-th moments of k = 2, …, 6. The result shows the three facts. (1)

As the number of shuffles increases, the values of |Dk| decrease monotonically before saturation region around T = 1.7 million. This fact confirms that the shuffling indeed helps increasing the randomness of given sequences.

Fig. 4.10The errors (|Dk|, k = 2-6) decrease as T increases until reaching the saturation region

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