EM CODE IN MATLAB with examples

I would like to know how EM matab code dealing with attached data to solve missing label problem.

see problem 1 as follows:

• Save “hw3.mat” in your Matlab working directory.

• In Matlab, type “load hw3.mat”

• Then type “who”, you will find three matrices named “hw3_1”, “hw3_2_1” and “hw3_2_2”.

• Each of these matrices has a size of 2×100, i.e. 2 rows and 100 columns. Each column is a 2-D observation vector.

Problem 1: The sample vectors in “hw3_1” are drawn from a Gaussian Mixture Model (GMM) with two mixtures, which can be expressed as

where x, µ1, µ2 are 2×1 vectors, and Σ1, Σ2 are 2×2 matrices, and ρ is the mixing parameter.

Use Expectation-Maximization (EM) algorithm to estimate the parameters µ1, µ2, Σ1, Σ2 and ρ.

Hint: Let the initial ρ0=0.5, and assume the first 50 samples are from p1(x) and the next 50 samples are from p2(x). Use Maximum Likelihood method (CPE646-4, page 19) to estimate the initial µ1, µ2, Σ1, Σ2

Problem 2: The sample vectors in “hw3_2_1” are from class ω1 and sample vectors in “hw3_2_2” are from class ω2

1. Use Parzen window method to estimate the class conditional density functions p(x|ω1) and p(x|ω2) for every x in {-4:0.1:8, -4:0.1:8}; use “mesh” function in Matlab to plot the results; and then classify x=[1,-2]t based on the estimation. Let h1=2.

1. Construct a Probabilistic Neural Network (PNN); and classify x=[1,-2]t. Let σ=0.2.