Zobrazeno 1 - 10
of 101
pro vyhledávání: '"Vejdemo-Johansson, Mikael"'
Publikováno v:
2021 IEEE International Conference on Big Data (Big Data)
Topology can extract the structural information in a dataset efficiently. In this paper, we attempt to incorporate topological information into a multiple output Gaussian process model for transfer learning purposes. To achieve this goal, we extend t
Externí odkaz:
http://arxiv.org/abs/2310.19960
In this paper, we present an algorithm that computes the generalized \v{C}ech complex for a finite set of disks where each may have a different radius in 2D space. An extension of this algorithm is also proposed for a set of balls in 3D space with di
Externí odkaz:
http://arxiv.org/abs/2209.15574
Publikováno v:
Foundations of Data Science, 2021
Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow
Externí odkaz:
http://arxiv.org/abs/2006.02554
Autor:
Vejdemo-Johansson, Mikael
Publikováno v:
Georgian Mathematical Journal. 2018 Dec 1;25(4):629-35
Building on Kadeishvili's original theorem inducing $A_\infty$-algebra structures on the homology of dg-algebras, several directions of algorithmic research in $A_\infty$-algebras have been pursued. In this paper we will survey work done on calculati
Externí odkaz:
http://arxiv.org/abs/1912.00472
Autor:
Vejdemo-Johansson, Mikael
We describe three identification spaces of the square, interesting choices of immersion into $\mathbb{R}^3$, and a process to construct 3d-printable models of their parametrizations.
Externí odkaz:
http://arxiv.org/abs/1909.05893
In this paper we propose a computationally efficient multiple hypothesis testing procedure for persistent homology. The computational efficiency of our procedure is based on the observation that one can empirically simulate a null distribution that i
Externí odkaz:
http://arxiv.org/abs/1812.06491
The Mapper algorithm does not include a check for whether the cover produced conforms to the requirements of the nerve lemma. To perform a check for obstructions to the nerve lemma, statistical considerations of multiple testing quickly arise. In thi
Externí odkaz:
http://arxiv.org/abs/1808.09933
We describe Fibres of Failure (FiFa), a method to classify failure modes of predictive processes using the Mapper algorithm from Topological Data Analysis. Our method uses Mapper to build a graph model of input data stratified by prediction error. Gr
Externí odkaz:
http://arxiv.org/abs/1803.00384
Autor:
Vejdemo-Johansson, Mikael
The growth function is the generating function for sizes of spheres around the identity in Cayley graphs of groups. We present a novel method to calculate growth functions for automatic groups with normal form recognizing automata that recognize a si
Externí odkaz:
http://arxiv.org/abs/1711.01256
Calculating and categorizing the similarity of curves is a fundamental problem which has generated much recent interest. However, to date there are no implementations of these algorithms for curves on surfaces with provable guarantees on the quality
Externí odkaz:
http://arxiv.org/abs/1410.2320