Finite mixture model: decompose a cytogram into "n" sub adjacent asymmetric Gaussian bells. A Mathematica 9 script.

Abstract

The script works with Mathematica (version 9 or latest) however, the Laplacian filter and the finite mixture should be implement with any other mathematical software. The scripts includes different steps: 1) To import the original cytogram and convert it into a matrix f(x,y) of dimension "n x n" 2) To detect all potential pics in f(x,y) with the laplacian filter, 2, and create the list Ln that include the coordinate of each potential peak 3) To extract all i distinct proper subsets of Ln: P(Ln)={{ 1}1,{2}2,{3}3,{ 1, 2} 4……. {1, 2, 3,…, n}i} (where i=2n-1) 3) To run the finite mixture model for each subset 4) To select the bet model with the optimal number of peak according the Bayesian Information Criterion (BIC) descriptor.This script implements the Laplacian filter and the finite mixture approach to decompose a surface into an arbitrary number “n” of bi-dimensional asymmetric Gaussian probability distributions. Finite mixture are widely used in data mining or pattern recognition. Here, this tool in implemented to decompose an arbitrary surface f(x,y) with some peaks and shoulders. This approach can be useful to decompose any bidimensional data array. This document describes how to use this approach to deconvolve a cytogram