Maximum likelihood
3, 4, 5, 6, 7
m = 5
μ = 5
σ2 = 2
3, 9, 9, 3
μ = 6
σ2 = 9
Gaussians
– functional form
– fit from data
– multivariate gaussians
Expectation maximization
P(x) = Σi=i k P(c=i)p(x|C=i)
πi μiΣi
EM versus K-mean
minimize: -Σj log p(xjlσΣ1k)+ cosf k
guess
run EM
remove
clustering
– k-means, em
