Topological Signature of 19th Century Novelists: Persistence Homology in Context-Free Text Mining

Abstract

Topological Data Analysis (TDA) refers to a collection of methods that find the structure of shapes in data. Although recently, TDA methods have been used in many areas of data mining, it has not been widely applied to text mining tasks. In most text processing algorithms, the order in which different entities appear or co-appear is being lost. Assuming these lost orders are informative features of the data, TDA may play a significant role in the resulted gap on text processing state of the art. Once provided, the topology of different entities through a textural document may reveal some additive information regarding the document that is not reflected in any other features from traditional text processing methods. In this paper, we introduce a novel approach that hires TDA in text processing in order to capture and use the topology of different same-type entities in textural documents. First, we will show how to extract some topological signatures in the text using persistent homology-i.e., a TDA tool that captures topological signature of data cloud. Then we will show how to utilize these signatures for text classification.

Statistical inference for dependence networks in topological data analysis

“…In TDA applications, Rips-Vietoris filtrations are often applied to multivariate time series data (Umeda, 2017;Gholizadeh and Zadrozny, 2018;El-Yaagoubi et al, 2023). These filtrations are often constructed from clouds of points, or from a weighted network.…”

“…Topological data analysis (TDA) has witnessed many important advances over the last twenty years that aim to unravel and provide insight to the "shape" of the data (Edelsbrunner et al, 2002;Edelsbrunner and Harer, 2008;Wasserman, 2018;Chazal and Michel, 2021). The development of TDA tools such as barcodes and persistence diagrams (Ghrist, 2008;Bubenik, 2015;Adams et al, 2017) have opened many new perspectives for analyzing various types of data (Umeda, 2017;Gholizadeh and Zadrozny, 2018;Motta, 2018;Xu et al, 2021;Leykam and Angelakis, 2023). These tools enable practitioners to grasp the topological characteristics inherent in high-dimensional data, which often remain beyond the reach of classical data analysis methods.…”