Dir_Proc

Dirichlet process collapsed Gibbs for infinite Gaussian mixtures

Dependencies and prerequisites

• Julia Lang (v>0.6) with the following packages installed

  • DataFrames
  • Distributions
  • StatsFuns
  • Clustering
  • ArgParse

More information on how to install Julia in your machine can be found here. The prerequisite packages can be downloaded the following way:

 Pkg.add("DataFrames")
 Pkg.add("Distributions")
 Pkg.add("StatsFuns")
 Pkg.add("Clustering")
 Pkg.add("ArgParse")

Infinite Gaussian mixtures

The prior mean vector μ0 and the prior covariance matrix Λ0 have been set to a d dimensional 0 vector and a diagonal matrix with entries 1/(d * w), where w is the diagonal elements of the covariance matrix of the data, where d is the dimension of the data set. User is free to change these values in the script.

The parameter α that control the assignment of the data in a new cluster is set to 1. More information about DP can be found here.

Instructions

The DP clustering can be performed as

julia DP_CS.jl -d Dataset -i No_of_iterations -k Initial_number_of_clusters

where

• -d : Dataset of interest (N x d)
• -i : Number of iteration for the Gibbs sampler
• -k : Initial number of clusters

The results of the clustering are saved in a .csv file named DP_clustering.csv

Example

We simulated a 5 dimensional dataset consisting of 4 clusters. Each cluster has a different mean vector and the same covariance matrix. After downloading the data and the true cluster allocation, you can run the DP Gibbs Sampler as

julia DP_CS.jl -d Sample_data.csv -i 15 -k 10

starting with 10 clusters for 15 iterations.

In order to validate our clustering, knowing the true cluster allocation of the observations, we use the following script which calculates the Rand Index between the true cluster allocation and the allocation under the DP model

using DataFrames
using Clustering

rca = readtable("sample_rca.csv",header= false)
dpca = readtable("DP_clustering.csv",header= false)

randindex(Array(rca),Array(dpca))[1]

The Rand Index is equal to 1, which results that the clustering under the DP model is perfect