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97527 (
=
3
×
59
C
3
), and that of
F
6
,
F
7
,or
F
8
is 32509 (
=
59
C
3
). Therefore, the total
number of facial feature values is 393530.
The facial features belonging to
F
i
are denoted by
{
,...,
f
i
,
n
i
}
f
i
,
1
,where
n
i
is the
=
=
=
=
=
number of facial features belonging to
F
i
.Thatis,
n
1
n
2
1711,
n
3
n
4
n
5
97527, and
n
6
=
32509. For instance,
f
1
,
1
is the normalized length of the
line segment formed by
p
1
and
p
2
. Similarly,
f
1
,
2
is computed from
p
1
and
p
3
.
n
7
=
n
8
=
4
Facial Expression Recognition
The proposed facial expression recognition is performed by clustering the frame
images in a video. In our clustering approach, a single cluster represents a single
facial expression. The clustering is done for each type of facial feature (i.e.,
F
1
to
F
8
) on the basis of k-means method. Then, the resulting eight sets of clusters are
integrated into a single set of clusters by the ensemble clustering.
4.1
Ensemble Clustering
Ensemble clustering is a kind of metaclustering method that integrates diverse sets
of clusters (called
weak clusters
) into a single set of clusters (called
strong clusters
).
Generally, the discrimination ability and the robustness to outliers of the strong
clusters are better than those of weak clusters.
There are several clustering methods to generate weak clusters. In the proposed
method, we use k-means method due to its conciseness. There also exist several en-
semble clustering method. We use the cluster-based similarity partitioning algorithm
(CSPA) because it has relatively small computational complexity [8].
4.2
Constructing Weak Clusters
A total of eight sets of weak clusters are constructed using the facial features
F
1
to
F
8
. A set of weak clusters for
F
i
is represented as
,where
K
is the number of clusters and is equivalent to the number of facial expressions.
This set of weak clusters is generated based on k-means method by using a set of
feature vectors
{
C
i
,
1
,...,
C
i
,
K
}
(
i
=
1
,...,
8
)
as its input.
N
is the number of frame images.
X
i
,
j
is a
feature vector obtained from the
j
-th frame image and can be given by the equation
X
i
,
j
=(
{
X
i
,
1
,...,
X
i
,
N
}
f
i
,
1
(
x
j
)
,...,
f
i
,
n
i
(
x
j
))
. Here,
f
i
,
k
(
x
j
)
is the feature value of
f
i
,
k
for the
j
-th
frame image.
4.3
Feature Selection
Using all the feature vectors to construct a set of weak clusters imposes considerable
computational cost because the number of facial feature values (
n
i
) is quite large. In
order to reduce the computational cost, we define the usefulness of the facial features
and make use of a small number of useful facial feature values. The usefulness is
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