## 12/30/12

### gaussian mixture modeling tutorial

I created this tutorial for some reason while an undergrad at ASU. I think I had just figured out how to do gaussian mixture modeling (GMM), and I thought it was the coolest thing ever. The original version was a sort of slide show, but that seems hard in blogger...

Here's a Gaussian (bell-curve)

Here's a couple of Gaussians together
(notice that one is taller than the other).

We select one of the Gaussians randomly
(but the taller one has a higher probability of being chosen).

We place a dot beneath the Gaussian
(the dot is more likely to fall toward the center of the Gaussian).

We repeatedly choose a Gaussian and place a dot;
notice the dense clusters beneith each Gaussian.

Here's the dots without the Gaussians.
How can we find the Gaussians now?

Assume we know there are 2 Gaussians.
Make a wild guess about the size, shape and location of these Gaussians
(we'll make one red, and one blue).

Draw a vertical line up from a dot to each Gaussian.

Now stack these lines.

Now paint the dot with the same percentages of red and blue as this line.

Do this for all the dots.

Reconstruct the shape and location of the red Gaussian based on all the red in the dots.
Set the height of the red Gaussian to the amount of red in all the dots.

Do the same for the blue Gaussian.

Now we are ready to repaint the dots given the new Gaussians,
after which we'll reconstruct the Gaussians again...
and again...
and again...

Until they stop changing.
The End.