GeometricClusterAnalysis.jl

Documentation for GeometricClusterAnalysis.jl

This set of functions is not a Julia package. Here you'll find a series of examples and methods that can be used to approximate compact subsets in noisy datasets. It could be use for clustering too.

• Functions
• Bregman divergences
• • Basic definition
  • The relation with some families of distributions
  • Bregman divergence associated to the Poisson distribution
  • Clustering data with a Bregman divergence
  • Trimming
  • Implementation
  • Application of the algorithm
• Fake datasets
• • Three curves dataset
  • Infinity symbol dataset
  • Fourteen segments dataset
  • Two spirals dataset
• The Three-Curves example
• • Generate the dataset
  • Hierarchical clustering
• Hierarchical clustering based on a union of ellipsoids
• • Example of two spirals
  • Data generation
  • Computation of the union of ellipsoids with the kPLM function
  • Clustering based on the persistence of the union of ellipsoids filtration
  • Removing outliers
• Different clustering for different methods
• • k-PLM
  • k-PDTM
  • q-witnessed distance
  • Power function
  • DTM filtration
  • ToMaTo
• Robust approximations of compact sets
• • Example
  • The distance-to-measure (DTM)
  • DTM computation for a noisy sample on a circle
  • Approximating $\mathcal{K}$ with a union of $k$ balls - or - the $k$-power-distance-to-measure ($k$-PDTM)
  • Approximating $\mathcal{K}$ with a union of $k$ ellipsoids - or - the $k$-power-likelihood-to-measure ($k$-PLM)
  • Detecting outliers - Trimmed versions of the $k$-PDTM and the $k$-PLM
  • Compute the trimmed k-PLM values of parameter q
  • The sublevel sets
• Types

Installation

To use this package, you first need to install Julia.

Clone this repository to get the library and all examples:

git clone https://github.com/pnavaro/GeometricClusterAnalysis.jl
cd GeometricClusterAnalysis.jl

Install dependencies

$ julia --project
               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.8.5 (2023-01-08)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

julia> import Pkg

julia> Pkg.instantiate()

Plots.jl package is not a direct dependency but it is very useful

julia> Pkg.add("Plots")

IJulia and jupytext are also good choices to edit and run examples. With jupytext you can open the .jl scripts in examples directory with Jupyter.

If it doesn't work, you can still convert Julia scripts with

jupytext --to ipynb example.jl

• To install the Jupyter Julia kernel and jupytext

julia> Pkg.add(["Conda", "IJulia"])
julia> using Conda
julia> Conda.add(["jupyter", "jupytext"])
julia> using IJulia
julia> notebook(, detached = true)

If you want use R with Julia, install the package RCall.