🍩 Database of Original & Non-Theoretical Uses of Topology
(found 4 matches in 0.001243s)
Hypothesis Testing for Shapes Using Vectorized Persistence Diagrams (2020)Chul Moon, Nicole A. Lazar
AbstractTopological data analysis involves the statistical characterization of the shape of data. Persistent homology is a primary tool of topological data analysis, which can be used to analyze those topological features and perform statistical inference. In this paper, we present a two-stage hypothesis test for vectorized persistence diagrams. The first stage filters elements in the vectorized persistence diagrams to reduce false positives. The second stage consists of multiple hypothesis tests, with false positives controlled by false discovery rates. We demonstrate applications of the proposed procedure on simulated point clouds and three-dimensional rock image data. Our results show that the proposed hypothesis tests can provide flexible and informative inferences on the shape of data with lower computational cost compared to the permutation test.
Functional Summaries of Persistence Diagrams (2018)Eric Berry, Yen-Chi Chen, Jessi Cisewski-Kehe, Brittany Terese Fasy
Revisiting Abnormalities in Brain Network Architecture Underlying Autism Using Topology-Inspired Statistical Inference (2018)Sourabh Palande, Vipin Jose, Brandon Zielinski, Jeffrey Anderson, P. Thomas Fletcher, Bei Wang
AbstractA large body of evidence relates autism with abnormal structural and functional brain connectivity. Structural covariance magnetic resonance imaging (scMRI) is a technique that maps brain regions with covarying gray matter densities across subjects. It provides a way to probe the anatomical structure underlying intrinsic connectivity networks (ICNs) through analysis of gray matter signal covariance. In this article, we apply topological data analysis in conjunction with scMRI to explore network-specific differences in the gray matter structure in subjects with autism versus age-, gender-, and IQ-matched controls. Specifically, we investigate topological differences in gray matter structure captured by structural correlation graphs derived from three ICNs strongly implicated in autism, namely the salience network, default mode network, and executive control network. By combining topological data analysis with statistical inference, our results provide evidence of statistically significant network-specific structural abnormalities in autism.