A new compressed cover tree for k-nearest neighbour search and the stable-under-noise mergegram of a point cloud

05/20/2022
by   Yury Elkin, et al.
0

This thesis consists of two topics related to computational geometry and one topic related to topological data analysis (TDA), which combines fields of computational geometry and algebraic topology for analyzing data. The first part studies the classical problem of finding k nearest neighbors to m query points in a larger set of n reference points in any metric space. The second part is about the construction of a Minimum Spanning Tree (MST) on any finite metric space. The third part extends the key concept of persistence within Topological Data Analysis in a new direction.

READ FULL TEXT

page 20

page 22

page 24

page 27

page 29

page 34

page 37

page 38

research
07/22/2020

The mergegram of a dendrogram and its stability

This paper extends the key concept of persistence within Topological Dat...
research
11/30/2021

A new compressed cover tree guarantees a near linear parameterized complexity for all k-nearest neighbors search in metric spaces

This paper studies the classical problem of finding all k nearest neighb...
research
05/04/2023

Towards Stratified Space Learning: 2-complexes

In this paper, we consider a simple class of stratified spaces – 2-compl...
research
03/09/2021

On the Complexity of the CSG Tree Extraction Problem

In this short note, we discuss the complexity of the search space for th...
research
01/17/2022

Paired compressed cover trees guarantee a near linear parametrized complexity for all k-nearest neighbors search in an arbitrary metric space

This paper studies the important problem of finding all k-nearest neighb...
research
08/09/2021

Topological Art in Simple Galleries

Let P be a simple polygon, then the art gallery problem is looking for a...
research
01/12/2021

Towards Stratified Space Learning: Linearly Embedded Graphs

In this paper, we consider the simplest class of stratified spaces – lin...

Please sign up or login with your details

Forgot password? Click here to reset