Wataru Souma

By Wataru Souma and Mari Jibu

A number of citations have been used to measure the value of paper. However, recently, Google’s PageRank is also extensively applied to quantify the worth of papers. In this chapter, we summarize the recent progress of studies on citations and PageRank. We also show our latest investigations of the citation network consisting of 34,666,719 articles and 591,321,826 citations. We propose the generalized beta distribution of the second kind to explain the distribution of citation and introduce the stochastic model with aging effect and super preferential attachment. Furthermore, we clarify the positive linear relation between citations and Google’s PageRank. By using this relationship as the benchmark to classify papers, we extract extremely prestigious papers, popular papers, and rising papers.

Part of the book: Scientometrics

By Wataru Souma

Conventional principal component analysis operates using a correlation matrix that is defined in the space of real numbers. This study introduces a novel method—complex Hilbert principal component analysis—which analyzes data using a correlation matrix defined in the space of complex numbers. As a practical application, we examine 10 major categories from the Japanese Family Income and Expenditure Survey for the period between January 1, 2000 and June 30, 2023, paying special attention to the time periods preceding and following the onset of the novel coronavirus disease 2019 pandemic. By analyzing the mode signal’s peaks, we identify specific days that exhibit characteristics that are consistent with the events occurring before and after the pandemic.

Part of the book: New Insights on Principal Component Analysis