Related papers: Algebraic Topology for Data Analysis

Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise…

The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…

Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics…

Many statistical models are algebraic in that they are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of such models are typically semi-algebraic subsets of the…

Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…

Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological…

Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey…

In the present article we describe and discuss a framework for applying different topological data analysis (TDA) techniques to a music fragment given as a score in traditional Western notation. We first consider different sets of points in…

Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and…

Topological Data Analysis (TDA) has been successfully used for various tasks in signal/image processing, from visualization to supervised/unsupervised classification. Often, topological characteristics are obtained from persistent homology…

We use topological data analysis (TDA) to study how data transforms as it passes through successive layers of a deep neural network (DNN). We compute the persistent homology of the activation data for each layer of the network and summarize…

Topological data analysis (TDA) is a rising field in the intersection of mathematics, statistics, and computer science/data science. The cornerstone of TDA is persistent homology, which produces a summary of topological information called a…

We give a new approach to the study of statistical mechanical systems: algebraic topology is used to investigate the statistical distributions of stochastic currents generated in graphs. In the adiabatic and low temperature limits we will…

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…

Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…

Machine learning (ML) on tabular data is ubiquitous, yet obtaining abundant high-quality tabular data for model training remains a significant obstacle. Numerous works have focused on tabular data augmentation (TDA) to enhance the original…

Unsupervised data representation and visualization using tools from topology is an active and growing field of Topological Data Analysis (TDA) and data science. Its most prominent line of work is based on the so-called Mapper graph, which…

Topological data analysis (TDA) has emerged as an effective approach in data science, with its key technique, persistent homology, rooted in algebraic topology. Although alternative approaches based on differential topology, geometric…

Firm financials are well established as return predictors, being the inspiration for a large set of anomalies in the asset pricing literature. Employing topological data analysis we revisit the question of association between seven of the…

We introduce a very general approach to the analysis of signals from their noisy measurements from the perspective of Topological Data Analysis (TDA). While TDA has emerged as a powerful analytical tool for data with pronounced topological…