Related papers: Summary and Distance between Sets of Texts based o…
Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar…
This research introduces a novel psychometric method for analyzing textual data using large language models. By leveraging contextual embeddings to create contextual scores, we transform textual data into response data suitable for…
There are different ways of measuring diversity in complex systems. In particular, in language, lexical diversity is characterized in terms of the type-token ratio and the word entropy. We here investigate both diversity metrics in six…
Data engineering pipelines are essential - albeit costly - components of predictive analytics frameworks requiring significant engineering time and domain expertise for carrying out tasks such as data ingestion, preprocessing, feature…
Classification in the sense of similarity is an important issue. In this paper, we study similarity classification in Topological Data Analysis. We define a pseudometric $d_{S}^{(p)}$ to measure the distance between barcodes generated by…
We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order…
Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust, multiscale, and interpretable features from complex molecular data for artificial intelligence (AI) modeling and topological deep learning (TDL).…
We study two aspects of information semantics: (i) the collection of all relationships, (ii) tracking and spotting anomaly and change. The first is implemented by endowing all relevant information spaces with a Euclidean metric in a common…
The main approach of traditional information retrieval (IR) is to examine how many words from a query appear in a document. A drawback of this approach, however, is that it may fail to detect relevant documents where no or only few words…
A novel sentence embedding method built upon semantic subspace analysis, called semantic subspace sentence embedding (S3E), is proposed in this work. Given the fact that word embeddings can capture semantic relationship while semantically…
The semantic similarity between documents of a text corpus can be visualized using map-like metaphors based on two-dimensional scatterplot layouts. These layouts result from a dimensionality reduction on the document-term matrix or a…
Feature tracking in time-varying scalar fields is a fundamental task in scientific computing. Topological descriptors, which summarize important features of data, have proved to be viable tools to facilitate this task. The merge tree is a…
Word embeddings represent a transformative technology for analyzing text data in social work research, offering sophisticated tools for understanding case notes, policy documents, research literature, and other text-based materials. This…
We explore the role of torsion in hybrid deep learning models that incorporate topological data analysis, focusing on autoencoders. While most TDA tools use field coefficients, this conceals torsional features present in integer homology.…
In this work, we introduce and study what we believe is an intriguing and, to the best of our knowledge, previously unknown connection between two areas in computational topology, topological data analysis (TDA) and knot theory. Given a…
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…
The advancements in deep learning, particularly the introduction of transformers, have been pivotal in enhancing various natural language processing (NLP) tasks. These include text-to-text applications such as machine translation, text…
Since information in electronic form is already a standard, and that the variety and the quantity of information become increasingly large, the methods of summarizing or automatic condensation of texts is a critical phase of the analysis of…
Persistent homology is a way of determining the topological properties of a data set. It is well known that each persistence module admits the structure of a representation of a finite totally ordered set. In previous work, the authors…
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…