Understanding latent semantic indexing: A topological structure analysis using Q‐analysis

Abstract The method of latent semantic indexing (LSI) is well‐known for tackling the synonymy and polysemy problems in information retrieval; however, its performance can be very different for various datasets, and the questions of what characteristics of a dataset and why these characteristics contribute to this difference have not been fully understood. In this article, we propose that the mathematical structure of simplexes can be attached to a term‐document matrix in the vector space model (VSM) for information retrieval. The Q‐analysis devised by R.H. Atkin ( 1974 ) may then be applied to effect an analysis of the topological structure of the simplexes and their corresponding dataset. Experimental results of this analysis reveal that there is a correlation between the effectiveness of LSI and the topological structure of the dataset. By using the information obtained from the topological analysis, we develop a new method to explore the semantic information in a dataset. Experimental results show that our method can enhance the performance of VSM for datasets over which LSI is not effective.