Derivation of plsa Formula

Likelihood functions of complete data in plsa:

Indicates whether the topic of the J-th word in document I is K. If K is K, it is 1; otherwise, it is 0.

Correspondingly, the log likelihood function is as follows:

Then Q function is

There are two constraints:

The following parameters are obtained by using the Laplace multiplication method.

Laplace function:

Then, evaluate the parameters respectively:

Solution Process: (1) is used as an example to convert (1) into the following form:

This coefficient is changed to 1, so we have obtained

,

Then, enter the result into (1) to obtain

Similarly, it can be obtained.

Then there are

Derivation completed

Refer:

1. http://luxinxin.is-programmer.com/user_files/luxinxin/File/plsanote.pdf

2. http://blog.csdn.net/yangliuy/article/details/8330640