A Grid-based Approach for Convexity Analysis of a Density-based Cluster

This paper presents a novel geometrical approach to investigate the convexity of a density-based cluster. Our approach is grid-based and we are about to calibrate the value space of the cluster. However, the cluster objects are coming from an infinite distribution, their number is finite, and thus, the regarding shape will not be sharp. Therefore, we establish the precision of the grid properly in a way that, the reliable approximate boundaries of the cluster are founded. After that, regarding the simple notion of convex sets and midpoint convexity, we investigate whether or not the density-based cluster is convex. Moreover, our experiments on synthetic datasets demonstrate the desirable performance of our method.

READ FULL TEXT

page 4

page 6

research
01/31/2021

Exact Recovery of Clusters in Finite Metric Spaces Using Oracle Queries

We investigate the problem of exact cluster recovery using oracle querie...
research
08/07/2023

Cluster-Aware Grid Layout

Grid visualizations are widely used in many applications to visually exp...
research
09/22/2020

Strongly Convex Divergences

We consider a sub-class of the f-divergences satisfying a stronger conve...
research
05/22/2018

Convexity Shape Prior for Level Set based Image Segmentation Method

We propose a geometric convexity shape prior preservation method for var...
research
03/31/2023

All-path convexity: Combinatorial and complexity aspects

Let be any collection of paths of a graph G=(V,E). For S⊆ V, define I(S...
research
05/21/2022

New quality measures for quadrilaterals and new discrete functionals for grid generation

In this paper, we review some grid quality metrics Robinson1987, Lo1989,...
research
02/20/2020

Cutting Corners

We define and study a class of subshifts of finite type (SFTs) defined b...

Please sign up or login with your details

Forgot password? Click here to reset