Assume that the training examples
with
were generated from a mixture of
lines

(1) |

where

(2) |

and the hidden variable if is generated from line and 0 otherwise.

**[1* P]**Derive the update equations for the M-step of the EM algorithm for the variables and .**[2* P]**Implement the EM algorithm for Mixture of Lines using the update equations you derived in 1. Use the provided dataset^{8}to evaluate your implementation. Show some plots of intermediate steps and describe what is happening.

Present your results clearly, structured and legible. Document them in such a way that anybody can reproduce them effortless. Send the code of your solution to mailto:florian.hubner@igi.tugraz.atflorian.hubner@igi.tugraz.at