Related papers: Algebraic Topology for Data Analysis
This article deals with OLAP systems based on multidimensional model. The conceptual model we provide, represents data through a constellation (multi-facts) composed of several multi-hierarchy dimensions. In this model, data are displayed…
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…
Identifying molecular signatures from complex disease patients with underlying symptomatic similarities is a significant challenge in the analysis of high dimensional multi-omics data. Topological data analysis (TDA) provides a way of…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation…
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as…
Inferring the parameters of models describing biological systems is an important problem in the reverse engineering of the mechanisms underlying these systems. Much work has focused on parameter inference of stochastic and ordinary…
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…
Topology at the undergraduate level is often a theoretical mathematics course, introducing concepts from point-set topology or possibly algebraic topology. However, the last two decades have seen an explosion of growth in applied topology…
Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights from time-varying data. We will see several applications to…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…
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,…
Data processing systems roughly group into families such as relational, array, graph, and key-value. Many data processing tasks exceed the capabilities of any one family, require data stored across families, or run faster when partitioned…
Data augmentation (DA) is indispensable in modern machine learning and deep neural networks. The basic idea of DA is to construct new training data to improve the model's generalization by adding slightly disturbed versions of existing data…
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…
The history of data analysis that is addressed here is underpinned by two themes, -- those of tabular data analysis, and the analysis of collected heterogeneous data. "Exploratory data analysis" is taken as the heuristic approach that…
We formulate a number of new results in Algebraic Geometry and outline their derivation from Theorem 2.12 which belongs to Algebraic Combinatorics.
Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. One of the main reasons for this growth is the tight…