——————————————————————————————
Programming HW 7: EM Mixture of Gaussians
——————————————————————————————
Homework:

The objective of the homework was to implement EM fitting of a mixture of gaussians on a two-dimensional dataset using Python. 

——————————————————————————————
Files:

hw7.py		-Contains EM Gaussian Mixture procedures and call method,including graphing procedure


	

(The graphing procedure uses the matplotlib python library, which does not work on the cycle machines. 
——————————————————————————————
Algorithm:

The mix.py file contains all of the procedures for the EM mixture of gaussians model. 

Once this initialization is complete, the program enters an iteration procedure over the E-step and the M-step. The program terminates this procedure when the log likelihood of the result is seen have converged.

	
E-Step:

The E-step does the same calculations as explained in class.

	
M-Step:

All formulate come from notes sectcion 17. mixture of Gussian.
	

Log Likelihood:


The log likelihood value is calculated as follows:
ln(p(X|mu,sigma,lambda) = ( from 1 to N sum(ln( from 1 to k sum(( from 1 to k sum(lambda[j] * N(X(n)|mu(j),sigma(j)) ) )) )) )

——————————————————————————————
Instructions: (Run the following command in terminal).

The second command line argument should be file name.
The second command line argument should be either ‘tied’ or ‘separate’ indicating what kind of covariance matrices you would like to be used. 
The thrid command line argument should be an integer value indicating how many gaussians you would like to have in your mixture.
For instance:

python hw7.py points.dat tied 10
(This will run the program on a ‘tied’ covariance matrix, for a mixture of 10 gaussians).

python hw7.py points.dat separate 5
(This will run the program on ‘separate’ covariance matrices, for a mixture of 5 gaussians).

——————————————————————————————
Output: 

performace plot for train set 

performace plot for test set