multivariate gaussian

This post only shows the intuition of multivariate gaussian. It does not contain any detailed explaination.

You can use R or other language plot the multivariate gaussian:

bivn <- mvrnorm(1000, mu = c(0, 0), Sigma = matrix(c(1, 0, 0, 1), 2))
bivn.kde <- kde2d(bivn[,1], bivn[,2], n = 50)
persp3D(bivn.kde$x, bivn.kde$y, bivn.kde$z, phi=20, theta=0)

The last several pictures are coming from Andrew Ng’s lecture.