"CS229-LECTURE13" Gaussian mixture model

The content of this section:

1, mixed Gaussian model;

2, the mixed Gaussian model is applied to the mixed Bayesian model; (Application: text clustering )

3, combined with EM algorithm, discuss the factor analysis algorithm;

4. Useful properties of Gaussian distribution.

Mixed Gaussian model

Apply Generalized em algorithm flow (download note) to mixed Gaussian model

Factor analysis Model

The basic purpose of factor analysis is to use a few factors to describe the link between many indicators or factors , that is, the relevant relatively close several variables in the same class, each type of variable becomes a factor, with fewer factors reflect the most information of the original data. using this technology, we can easily identify the major factors that affect consumer buying, consumption, and satisfaction, and how they influence the use of this research technology, and we can also do pre-analysis of market segmentation .

The basic idea of factor analysis method
By studying the internal structure of the correlation coefficient matrix of variables, we find out the few random variables that can control the few random variables of all variables to describe the correlation between multiple variables, but here the few. Several random variables are not observable, often called factors. Then the variables are grouped according to the size of the correlation, but the correlations between the variables in the same group are higher, but the correlations of the variables are lower in different groups.
Factor rotation, in the actual application factor analysis, there is a phenomenon which is difficult to explain, the root cause is the contradiction between the model and the actual data, and its direct cause is not clear the contribution of the factor to the variable. It is assumed that this can be achieved by rotating the axes without changing the covariance structure of the factor.
Steps to calculate the factor analysis method:

The first step: standardize the raw data.

The second step: establish the correlation coefficient r of the variable.
The third step: finding the characteristic root of R is very corresponding to the unit eigenvector.

Fourth step: The maximum orthogonal rotation of the factor load array is performed.

Fifth step: Calculate the factor score.

Scenario: Number of data dimensions >> samples

Derivation of factor analysis model

EM Solution Parameters

"CS229-LECTURE13" Gaussian mixture model