Image Analysis, Classification and Change Detection in Remote Sensing, 3rd Edition

Gaussian mixture clu stering 343

At any stage of the iteration of the FMLE algorithm, the cur rent estimate

for the log-likelihood for the datas et ca n be shown to be given by (Bishop,

1995)

m

X

ν=1

log p(g(ν)) =

K

X

k=1

m

X

ν=1

[u

kν

]

o

log u

kν

. (8.44)

Here [u

kν

]

o

is the “old” value of the posterior cla ss membership probability,

i.e., the value determined on the previous step.

8.3.2 Simulated annealing

Notwithstanding the initialization procedure, the FMLE (or E M) algorit

hm,

like all iterative methods, may be trapped in a local optimum. A remedial

scheme is to apply a technique called simulated ann ealing. The membership

probabilities in the early iterations are ...