Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Kalisnik, Sara"'
Persistent homology is one of the most popular methods in Topological Data Analysis. An initial step in any analysis with persistent homology involves constructing a nested sequence of simplicial complexes, called a filtration, from a point cloud. Th
Externí odkaz:
http://arxiv.org/abs/2408.11450
We present AuToMATo, a novel clustering algorithm based on persistent homology. While AuToMATo is not parameter-free per se, we provide default choices for its parameters that make it into an out-of-the-box clustering algorithm that performs well acr
Externí odkaz:
http://arxiv.org/abs/2408.06958
Magnitude is an isometric invariant for metric spaces that was introduced by Leinster around 2010, and is currently the object of intense research, since it has been shown to encode many known invariants of metric spaces. In recent work, Govc and Hep
Externí odkaz:
http://arxiv.org/abs/2205.09521
Autor:
Kalisnik, Sara, Lesnik, Davorin
A standard problem in applied topology is how to discover topological invariants of data from a noisy point cloud that approximates it. We consider the case where a sample is drawn from a properly embedded C1-submanifold without boundary in a Euclide
Externí odkaz:
http://arxiv.org/abs/2006.09194
We develop a general framework for the probabilistic analysis of random finite point clouds in the context of topological data analysis. We extend the notion of a barcode of a finite point cloud to compact metric spaces. Such a barcode lives in the c
Externí odkaz:
http://arxiv.org/abs/1903.00470
Autor:
Kališnik, Sara, Lešnik, Davorin
The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring is fully elementary, i.e. we can express symmetric polynomials with elementary ones in a unique way. The result does not
Externí odkaz:
http://arxiv.org/abs/1801.08882
Publikováno v:
SIAM Journal on Applied Algebra and Geometry 3 (2), 337-371 (2019)
We show that an embedding in Euclidean space based on tropical geometry generates stable sufficient statistics for barcodes. In topological data analysis, barcodes are multiscale summaries of algebraic topological characteristics that capture the `sh
Externí odkaz:
http://arxiv.org/abs/1709.02647
Publikováno v:
In Advances in Applied Mathematics October 2021 131
Publikováno v:
Algebr. Geom. Topol. 19 (2019) 657-700
This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding to a homological feature supported over that interval or, equivalently
Externí odkaz:
http://arxiv.org/abs/1604.03596
Autor:
Kališnik, Sara, Lešnik, Davorin
Publikováno v:
In Journal of Symbolic Computation March-April 2021 103:280-299