• Corpus ID: 237371746

Stitch Fix for Mapper and Topological Gains

  title={Stitch Fix for Mapper and Topological Gains},
  author={Youjia Zhou and Nathaniel Saul and Ilkin Safarli and Bala Krishnamoorthy and Bei Wang},
The mapper construction is a powerful tool from topological data analysis that is designed for the analysis and visualization of multivariate data. In this paper, we investigate a method for stitching a pair of univariate mappers together into a bivariate mapper, and study topological notions of information gains, referred to as topological gains, during such a process. We further provide implementations that visualize such topological gains for mapper graphs. 
1 Citations
Adaptive Covers for Mapper Graphs Using Information Criteria
  • N. Chalapathi, Youjia Zhou, Bei Wang
  • 2021 IEEE International Conference on Big Data (Big Data)
  • 2021
The mapper construction is a widely used tool from topological data analysis in obtaining topological summaries of large, high-dimensional point cloud data. It has enjoyed great success in data


Kepler Mapper: A flexible Python implementation of the Mapper algorithm
The Mapper algorithm is developed to facilitate graphical exploration of topological data structures and its use in multiple domains, including political science, biology, and sports analytics.
Convergence between Categorical Representations of Reeb Space and Mapper
Using tools from category theory, it is formally proved that the convergence between the Reeb space and mapper is proved in terms of an interleaving distance between their categorical representations.
Topological Analysis of Nerves, Reeb Spaces, Mappers, and Multiscale Mappers
It is shown that the one-dimensional homology of the nerve complex N(U) of a path-connected cover U of a domain X cannot be richer than that of the domain X itself, which means that no new H_1-homology class can be "created" under a natural map from X to the nerve complexes.
Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization
This work presents a state‐of‐the‐art report on scalar field comparison using topological descriptors, and provides a taxonomy of existing approaches based on visualization tasks associated with three categories of data: single fields, time‐varying fields, and ensembles.
Reeb graphs for shape analysis and applications
An overview of the mathematical properties of Reeb graphs is provided and its history in the Computer Graphics context is reconstructed, with an eye towards directions of future research.
Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition
The method, called Mapper, is based on the idea of partial clustering of the data guided by a set of functions defined on the data, and is not dependent on any particular clustering algorithm, i.e. any clustering algorithms may be used with Mapper.
Extracting insights from the shape of complex data using topology
The method combines the best features of existing standard methodologies such as principal component and cluster analyses to provide a geometric representation of complex data sets to find subgroups in data sets that traditional methodologies fail to find.
Joint Contour Nets
  • H. Carr, D. Duke
  • Computer Science, Medicine
    IEEE Transactions on Visualization and Computer Graphics
  • 2014
The first algorithm for constructing the Joint Contour Net is reported, and some of the properties that make it practically useful for visualisation are demonstrated, including accelerating computation by exploiting a relationship with rasterisation in the range of the function.
The Shape of an Image - A Study of Mapper on Images
A customized construction for Mapper on images is provided, a fast algorithm to compute it, and a simple procedure is provided that guarantees the equivalence of Mapper to contour, join, and split trees on a simply connected domain.
Pheno-mapper: an interactive toolbox for the visual exploration of phenomics data
The main advantage of Pheno-Mapper is that it provides rich, interactive capabilities in the exploratory analysis of phenomics data, and it integrates visual analytics with data analysis and machine learning in an easily extensible way.