Visual Explanation of Eigenvalues and Math Process in Latent Semantic Analysis

Yukari Shirota; Basabi Chakraborty

doi:10.52731/iee.v2.i1.70

Yukari Shirota Gakushuin University
Basabi Chakraborty Iwate Prefectural University

DOI: https://doi.org/10.52731/iee.v2.i1.70

Keywords: LSA, text mining, SVD, visualization, mathematics, multi-variant analysis, eigenvalue

Abstract

Latent Semantic Analysis (LSA) is a widely used method in text mining field to extract the underlying concepts in the text document. The mathematical technique behind LSA is Singular Value Decomposition (SVD) in which the key concept is the eigenvalues. It is difficult to understand the underlying mathematics for general people, not proficient in mathematics. One reason might be that the linear algebra textbooks available in the market are not written for non– mathematics majors such as economics students. We believe that there is better teaching method to explain the eigenvalues and eigenvectors to our students. In this paper, we would like to illustrate the method. In the main part of the paper, we have proposed a visualization of the mathematical process behind LSA to make it easily understandable to general people, novice in mathematics. In addition, to understand the SVD process more deeply, another example which is a time series data analysis by SVD is also presented.

Author Biographies

Yukari Shirota, Gakushuin University

DSc. Prof. of Faculty of Economics, Gakushuin University. Research fields are visualization of data on the web. web data visualization, social media analysis, and visual education methods for business mathematics. For over 17 years, she has developed visual teaching materials for business mathematics and statistics. In VINCI 2015, the tutorial titled “Visually Do Statistics for Business Persons: Visual Materials from Regression to Black-Sholes Model” she talked. Various visual teaching material sites have been published on the web which are freely available as follows:

http://www.gakushuin.ac.jp/univ/eco/english/teacher/sirota.html

http://www-cc.gakushuin.ac.jp/~20010570/VDStat/

http://www-cc.gakushuin.ac.jp/~20010570/mathABC/ABC/

Basabi Chakraborty, Iwate Prefectural University

She received B.Tech, M.Tech and Ph. D degrees in Radio Physics and Electronics from Calcutta University, India and worked in Indian Statistical Institute, Calcutta, India until 1990. She received another Ph. D in Information Science from Tohoku University, Japan in 1996. Currently she is a full professor in Software and Information Science department of Iwate Prefectural University, Japan. Her main research interests are in the area of Pattern Recognition, Machine Learning, Soft Computing Techniques, Data mining and Online Social media mining. She is a senior member of IEEE, member of ACM, INNS and Japanese Society of Artificial Intelligence.

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