Related papers: Topological Data Analysis for Speech Processing

The role of the attention mechanism in encoding linguistic knowledge has received special interest in NLP. However, the ability of the attention heads to judge the grammatical acceptability of a sentence has been underexplored. This paper…

Topological Data Analysis (TDA) is a novel new and fast growing field of data science providing a set of new topological and geometric tools to derive relevant features out of complex high-dimensional data. In this paper we apply two of…

Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in complex datasets. The main workhorse is persistent homology,…

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…

A primary hypothesis that drives scientific and engineering studies is that data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments, correlation functions) and signal processing (e.g.,…

While the strength of Topological Data Analysis has been explored in many studies on high dimensional numeric data, it is still a challenging task to apply it to text. As the primary goal in topological data analysis is to define and…

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…

Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is…

Topological Data Analysis (TDA) is a rigorous framework that borrows techniques from geometric and algebraic topology, category theory, and combinatorics in order to study the "shape" of such complex high-dimensional data. Research in this…

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such…

In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…

Topological data analysis (TDA) has become a powerful approach over the last twenty years, mainly due to its ability to capture the shape and the geometry inherent in the data. Persistence homology, which is a particular tool in TDA, has…

Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…

Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural…

This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors…

Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…

Developing reliable methods to discriminate different transient brain states that change over time is a key neuroscientific challenge in brain imaging studies. Topological data analysis (TDA), a novel framework based on algebraic topology,…

The impressive capabilities of recent generative models to create texts that are challenging to distinguish from the human-written ones can be misused for generating fake news, product reviews, and even abusive content. Despite the…

Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…

Timbre allows us to distinguish between sounds even when they share the same pitch and loudness, playing an important role in music, instrument recognition, and speech. Traditional approaches, such as frequency analysis or machine learning,…