Report: EM implementation for GMM

coursework requirement

Implement training and testing algorithms for GMM. Programmes must be written in C/C++ or python or Matlab.
Use train.txt for training and check the result on dev.txt. The complexity of GMM and initialisation of GMM will be decided by you.
Once the final GMM configuration is fixed, you will perform classification on test.txt and save the result in the same format as dev.txt.
Final submission should include:
- a. Detailed report including:
  - i. Initialisation of GMM
  - ii. GMM parameter tuning process (likelihood change, result on dev.txt etc.)
  - iii. Analysis and discussion
- b. Classification result: test.txt with label
- c. Source code or tools which can be compiled and/or run under windows or linux machine (Ubuntu)

K: number of GM
- hyper parameter
$\mu_i$: expected value
- np.random.random((K, D)) * np.mean(x, axis=0)
- D: dim
- x: input data
$\Sigma_i$: covariance
- [np.mat(np.eye(D)) for _ in range(K)]
- D: dim
$\pi_i$: mixing probability
- temp = np.random.random(K)
- pi = temp / np.sum(temp)

Why acc != 100% in test data
- Because some points are too far from it's origin GM's center, and too near to another's.