Biology Reference
In-Depth Information
Algorithm 2.
The EM Method.
Initialization
:
i n ta t
with
N
points,
initial guesses for the parameters
c
1
,
c
2
, Σ
1
,
Σ
2
,
π
D
Iteration
:
Step 1:
For all
x
i
∈D
compute
the “responsibilities” :
πφ
1
(
x
i
)
πφ
1
(
x
i
)+(1
p
1
(
x
i
)=
π
)
φ
2
(
x
i
)
,
−
p
2
(
x
i
)=1
−
p
1
(
x
i
)
.
Step 2
update
the centers and covariances:
p
k
(
x
i
)
j
=1
p
k
(
x
j
)
i
=1
N
c
k
=
x
i
,
p
k
(
x
i
)
j
=1
p
k
(
x
j
)
(
x
i
−
i
=1
N
Σ
k
=
c
k
)
T
,
k
=1
,
2
c
k
)(
x
i
−
Step 3
update
the mixing probabilities (weights):
π
=
i
=1
p
1
(
x
i
)
N
Step 4
stop
or
return
to step 1
Remarks
(a) The “responsibilities” in Step 1 correspond to the cluster membership
probabilities in Algorithm 1.
(b) Step 1 requires, for each data point, both the Mahalanobis distance (2.2),
and the evaluation of the density (2.35).
(c) Step 2 is computationally similar to Step 3 of Algorithm 1.
(d) The stopping rule (Step 4) is again the convergence of centers as in Al-
gorithm 1.
2.4.1.
A Comparison of the PDQ Algorithm (Algorithm 1) and the EM
Method (Algorithm 2)
(a) The EM Algorithm is based on maximum likelihood, and therefore de-
pends on the density functions in the mix, requiring different compu-
tations for different densities.
The PDQ Algorithm is parameter free,
Search WWH ::
Custom Search