Related papers: Connecting the Dots: Discovering the "Shape" of Da…
Data science offers a powerful tool to understand objects in multiple sciences. In this paper we utilize concept of data science, most notably topological data analysis, to extend our understanding of knot theory. This approach provides a…
Topological data analysis asks when balls in a metric space $(X,d)$ intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this principle to the traditional core geometric concept of curvature.…
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
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…
Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recent efforts to broaden these ideas to model spatial…
A graph is a data structure composed of dots (i.e. vertices) and lines (i.e. edges). The dots and lines of a graph can be organized into intricate arrangements. The ability for a graph to denote objects and their relationships to one…
In architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on point-sets. Shapes made with points can be understood more generally as finite arrangements…
Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…
Normally we judge Topological shapes analytically but they hide significant amount of data in them about coordinate planes and ordered & unordered paris. In this article we will build our intuition and find those datas.
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…
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…
Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data,…
Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and…
Topological methods are very rarely used in structural health monitoring (SHM), or indeed in structural dynamics generally, especially when considering the structure and topology of observed data. Topological methods can provide a way of…
The root is an important organ of a plant since it is responsible for water and nutrient uptake. Analyzing and modelling variabilities in the geometry and topology of roots can help in assessing the plant's health, understanding its growth…
Some of the basic concepts of topology are explored through known physics problems. This helps us in two ways, one, in motivating the definitions and the concepts, and two, in showing that topological analysis leads to a clearer…
Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…
Topological data analysis provides a collection of tools to encapsulate and summarize the shape of data. Currently it is mainly restricted to \emph{mapper algorithm} and \emph{persistent homology}. In this paper we introduce new…
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…