Related papers: Algebraic Topology for Data Scientists

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph…

The article is designed to explain to commutative algebraists what spectra (in the sense of algebraic topology) are, why they were originally defined, and how they can be useful for commutative algebra.

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…

We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…

Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…

Topological Data Analysis (TDA), an emerging field in investment sciences, harnesses mathematical methods to extract data features based on shape, offering a promising alternative to classical portfolio selection methodologies. We utilize…

Scientists use a mathematical subject called 'topology' to study the shapes of objects. An important part of topology is counting the numbers of pieces and holes in objects, and people use this information to group objects into different…

This work is devoted to a comprehensive analysis of topological data analysis fortime series classification. Previous works have significant shortcomings, such aslack of large-scale benchmarking or missing state-of-the-art methods. In this…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…

Tensors are ubiquitous in statistics and data analysis. The central object that links data science to tensor theory and algebra is that of a model with latent variables. We provide an overview of tensor theory, with a particular emphasis on…

Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…

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 present a short tutorial and introduction to using the R package TDA, which provides some tools for Topological Data Analysis. In particular, it includes implementations of functions that, given some data, provide topological information…

This is an expository article about operads in homotopy theory written as a chapter for an upcoming book. It concentrates on what the author views as the basic topics in the homotopy theory of operadic algebras: the definition of operads,…

In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

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…

This paper introduces new methodology based on the field of Topological Data Analysis for detecting anomalies in multivariate time series, that aims to detect global changes in the dependency structure between channels. The proposed…