Probability measures on the space of persistence diagrams

By Yuriy Mileyko, Sayan Mukherjee, John Harer. 2011

313 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/3752b27e2dcdc34c362918dddf43ae0f0f82579a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Mathematical Physics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

On the topology of random complexes built over stationary point processes. (2012, background): “beginning to appreciate the fact that stochasticity underlies their data as a consequence of sampling, and are beginning to build statistical models to allow parameter estimation and inference (e.g., [8, 9, 13, 30, 40]). The results of this paper show that small changes in model structure (such as t”
Statistical topological data analysis using persistence landscapes (2012, background): “There has been progress towards combining the persistence diagram and statistics (Mileyko et al., 2011; Turner et al., 2014; Munch et al., 2013; Chazal et al., 2013; Fasy et al., 2014).”
Statistical Aspects of Wasserstein Distances (2018, background): “See, for example, Mileyko et al. (2011), who introduce a version of the Wasser-stein distance on the space of persistence diagrams, endowing it with a metric structure that allows statistical inference.”
Statistical Analysis of Persistence Intensity Functions (2015, background): “The following question now arises: how do we summarize the diagrams? For example how do we average the diagrams or cluster the diagrams? One approach is based on the notion of Frechet means [18, 27].”
Topological Consistency via Kernel Estimation (2014, background): “Another perspective of persistence homology is as a summary statistic of pout cloud data that is robust to certain invariances, this perspective has been developed in [7, 11, 33, 44].”
Persistence Images: A Stable Vector Representation of Persistent Homology (2015, background): “Furthermore, the bottleneck metric allows one to deﬁne Fr´echet means and variances for a collection of PDs (Mileyko et al., 2011; Turner et al., 2014).”
Persistent Homology Analysis of Brain Artery Trees (2014, background): “[25] to find the center of the data followed by multidimensional scaling to analyze variation about the mean.”
Wasserstein Stability for Persistence Diagrams (2020, unknown): “This is a standard approach to defining the distances and for more details, we refer the reader to [32, 40, 39].”