INF42 - Topological Data Analysis

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Data AnalysisTDA
Overview

TDA

INF421(Conception et analyse d'algorithmes) Projet : Topological Data Analysis

SphereMin

Etant donné un nuage des points, ce programme contient deux fonctions (en 2D et en 3D) qui ont pour le but de calculer la boule minimum qui contient ces points.

draw_circle_points(SphereMin(points, []), points)

Il suffit de lancer directement le programme pour calculer le centre ainsi que le rayon de cette boule et la visualiser.

Čech

Ce programme consiste à afficher et renvoyer des simplexes de Čech (de dimension inférieure à k et de valeur de filtration plus petite que l) ainsi que leur valeur de filtration.

Cech(points, k, l, dim)

Alpha

Ce programme consiste à afficher et renvoyer des simplexes de Alpha (de dimension inférieure à k et de valeur de filtration plus petite que l) ainsi que leur valeur de filtration.

Alpha(points, k, l, dim)

Draw

Ce programme dessine la complexe de Čech et d'Alpha pour les nuages de points 2D. Il suffit de lancer le programme et faire déplacer la barre.

show(Alpha(points, k, l, dim))
show(Cech(points, k, l, dim))

Graph Optimization

Ce programme peut optimizer un graphe et écrire le graphe optimisé et le graph original dans un fichier pour que l'on puisse tester directement sur Ripser.

Il faut d'abord définir le graphe. Trois exemples sont inclus. Il est aussi possible de charger un graph qui est dans un fichier.

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