Visual Explanation of Eigenvalues and Math Process in Latent Semantic Analysis

Abstract

Latent Semantic Analysis (LSA) is a widely used method in text mining fields to extract the latent concept. 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 another teaching method to explain the eigenvalues and eigenvectors to our students. In the paper, we shall illustrates the way. As the main part of the paper, we have proposed a visualization of the mathematical process behind LSA to make it easily understandable to 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.