GMM Gaussian mixture model learning (2), gmm Gaussian

GMM Gaussian mixture model learning (2), gmm Gaussian

(Picture from http://www.cnblogs.com/zhangchaoyang/articles/2624882.html)

If x is two-dimensional, the above formula is:

= Cov (x0, x1) is the covariance between x1 and x0.

Single Gaussian distribution

If feature x is one-dimensional (only the x coordinates of points are taken into account), the Gaussian distribution is: (from this blog)

If the feature is two-dimensional (x and y coordinates, meaning height and weight), the clustering effect should be:

In the above two figures, we use the EM-GMM Algorithm for clustering, using a single Gaussian function to describe a category (male, female ).

For example, one-dimensional Gaussian is used to describe the height distribution of boys and girls.

Gaussian Mixture Distribution

But if the statistics show that the height is both Dutch (high) and Congo (short), what will happen to this single Gaussian Model?

Obviously, it is impossible to describe the height of men and women using a Gaussian distribution. In this way, a Gaussian mixture model is required, such:

[π indicates the proportion of various people (Dutch, Dutch, Congo, and Congo]

Now we have a batch of men's height data (Dutch men + Congo men). We can refer to the EM method of this blog to get

Likewise, we can obtain the dual Gaussian distribution of the height of a woman.

In this way, the gender of "Dutch girl" is determined by the mixed double Gaussian distribution. [Bringing the feature vector X of "Dutch girl" into Gm and Gf to calculate the probability]