Topological Signature of 19th Century Novelists: Persistent Homology in 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 textual document may reveal some additive information regarding the document that is not reflected in any other features from conventional 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 textual 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.

Topological Data Analysis for Discourse Semantics?

“…We show that topological information, extracted from the relationships between sentences, can be used in inference, namely it can be applied to the very difficult legal entailment problem given in the COLIEE 2018 data set. Previous results of Doshi and Zadrozny (2018) and Gholizadeh et al (2018) show that topological features are useful for classification. The applications of computational topology to entailment are novel, and in our view provide a new set of tools for discourse semantics: computational topology can perhaps provide a bridge between the brittleness of logic and the regression of neural networks.…”

“…Gholizadeh et al (2018) applied a different method for computing homological persistence to the task of authorship attribution, which is also a classification task, showing that the patterns of how authors introduce characters in novels can be captured to large extent using topological descriptors. Interestingly, neither of these works uses topological features to augments the usual tf/idf representations of documents: Doshi and Zadrozny (2018) use counts of words (from a previously identified vocabularies) to form a matrix which is the only input to topological persistence, and then they make a rule based decision based only on the presence of barcodes; and Gholizadeh et al (2018) use time series. To use topological data analysis (TDA), Zhu (2013) assumes that text is implicitly coherent (SIFTS method), and so do Doshi and Zadrozny (2018).…”

Classification Of Skin Lesions By Topological Data Analysis Alongside With Neural Network

“…Some visualization tools such as "Persistent Diagram", "Barcode" and " Persistent Landscape" are invented to indicate the main topological features of data. Persistent homology has been previously used in brain [6], image analysis [4] and data mining [5].…”

Proceedings of the 13th International Conference on Computational Semantics - Student Papers

“…Gholizadeh et al (2018) applied a different method for computing homological persistence to the task of authorship attribution, which is also a classification task, showing that the patterns of how authors introduce characters in novels can be captured to large extent using topological descriptors. Interestingly, neither of these works uses topological features to augments the usual tf/idf representations of documents: Doshi and Zadrozny (2018) use counts of words (from a previously identified vocabularies) to form a matrix which is the only input to topological persistence, and then they make a rule based decision based only on the presence of barcodes; and Gholizadeh et al (2018) use time series. To use topological data analysis (TDA), Zhu (2013) assumes that text is implicitly coherent (SIFTS method), and so do Doshi and Zadrozny (2018).…”