منابع مشابه
Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem
Persistent homology, a central tool of topological data analysis, provides invariants of data called barcodes (also known as persistence diagrams). A barcode is simply a multiset of real intervals. Recent work of Edelsbrunner, Jabłoński, and Mrozek suggests an equivalent description of barcodes as functors R → Mch, where R is the poset category of real numbers and Mch is the category whose obje...
متن کاملConfidence Sets for Persistence Diagrams
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features as one varies a tuning parameter. Features with short lifetimes are informally considered to be “topological noise,” and those with a long lifetime are considered to be “topological signal.” In this paper, we bring some statis...
متن کاملFréchet Means for Distributions of Persistence Diagrams
Given a distribution ρ on persistence diagrams and observations X1, ...Xn iid ∼ ρ we introduce an algorithm in this paper that estimates a Fréchet mean from the set of diagrams X1, ...Xn. If the underlying measure ρ is a combination of Dirac masses ρ = 1 m ∑m i=1 δZi then we prove the algorithm converges to a local minimum and a law of large numbers result for a Fréchet mean computed by the alg...
متن کاملContinuation of Point Clouds via Persistence Diagrams
In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point cloud, is differentiable. This allows us to apply the Newton-Raphson continuation method in this setting. Given an original point cloud P , its persistence di...
متن کاملPersistence Diagrams of Cortical Surface Data
We present a novel framework for characterizing signals in images using techniques from computational algebraic topology. This technique is general enough for dealing with noisy multivariate data including geometric noise. The main tool is persistent homology which can be encoded in persistence diagrams. These diagrams visually show how the number of connected components of the sublevel sets of...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2006
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-006-1276-5