Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition

By G. Singh, Facundo M'emoli, Gunnar E. Carlsson. PBG@Eurographics, 2007

751 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/b768cffc3d2eecdad6bf2dfd9f345a449cc59af7

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Citations in the corpus

On Variational Learning of Controllable Representations for Text without Supervision (2019, methodology): “For a more technical introduction and details, please see Singh et al. (2007).”
Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells (2017, methodology): “[10] use topological data analysis, in particular, the MAPPER algorithm [30], to construct a pseudotemporal ordering of cells.”
Stereotypic Immune System Development in Newborn Children (2018, neutral): “Once bins are constructed, a clustering step is performed on each bin using single linkage clustering with a fixed heuristic for the choice of the scale parameter (Singh et al., 2007).”
A roadmap for the computation of persistent homology (2015, methodology): “In the present article, we focus on persistent homology, but there are other methods in TDA — including the Mapper algorithm [110], Euler calculus (see [59] for an introduction with an eye towards applications), cellular sheaves [32, 59], and many more.”
An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists (2017, methodology): “3 Using covers and nerves for exploratory data analysis and visualization: the Mapper algorithm Using the nerve of covers as a way to summarize, visualize and explore data is a natural idea that was ﬁrst proposed for tda in Singh et al. (2007), giving rise to the so-called Mapper algorithm.”
Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival (2011, methodology): “Mapper (2) is a mathematical tool that uses recent developments in the area of applied topology to identify shape characteristics of data sets.”
Statistical Analysis and Parameter Selection for Mapper (2017, methodology): “In this paper, we study a recent TDA algorithm called Mapper which was first introduced in Singh et al. (2007).”
PAGA: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells (2019, neutral): “PAGA can thus be viewed as an easily interpretable and robust way of perform ing topological data analysis [9, 21] (Additional file 1:Note 3).”