🍩 Database of Original & Non-Theoretical Uses of Topology

1. The Shape of Word Embeddings: Quantifying Non-Isometry With Topological Data Analysis (2024)

   Ondřej Draganov, Steven Skiena

   Abstract

   Word embeddings represent language vocabularies as clouds of d-dimensional points. We investigate how information is conveyed by the general shape of these clouds, instead of representing the semantic meaning of each token. Specifically, we use the notion of persistent homology from topological data analysis (TDA) to measure the distances between language pairs from the shape of their unlabeled embeddings. These distances quantify the degree of non-isometry of the embeddings. To distinguish whether these differences are random training errors or capture real information about the languages, we use the computed distance matrices to construct language phylogenetic trees over 81 Indo-European languages. Careful evaluation shows that our reconstructed trees exhibit strong and statistically-significant similarities to the reference.

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   • Language
   • linguistics
   • Textual document
   • word embedding
   • Barcode statistics
   • Bottleneck distance
   • Clustering
   • Wasserstein distance
   • persistent homology
   • persistent homology:persistence diagrams
   • persistent homology:persistence images
   • vietoris-rips

2. Towards a Philological Metric Through a Topological Data Analysis Approach (2020)

   Eduardo Paluzo-Hidalgo, Rocio Gonzalez-Diaz, Miguel A. Gutiérrez-Naranjo

   Abstract

   The canon of the baroque Spanish literature has been thoroughly studied with philological techniques. The major representatives of the poetry of this epoch are Francisco de Quevedo and Luis de Góngora y Argote. They are commonly classified by the literary experts in two different streams: Quevedo belongs to the Conceptismo and G\ńgora to the Culteranismo. Besides, traditionally, even if Quevedo is considered the most representative of the Conceptismo, Lope de Vega is also considered to be, at least, closely related to this literary trend. In this paper, we use Topological Data Analysis techniques to provide a first approach to a metric distance between the literary style of these poets. As a consequence, we reach results that are under the literary experts' criteria, locating the literary style of Lope de Vega, closer to the one of Quevedo than to the one of G\'ǵora.

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   • Literature analysis
   • Philology
   • Spanish literature
   • Word embedding
   • Confirm
   • Persistence diagrams
   • Persistent homology