Database Reference
In-Depth Information
11.5.3
Posture Transition and Posture Transition Sparse Code
The PO and PSC methods do not consider the temporal arrangement of postures
in the map. They only consider the occurrence and the frequency of the individual
nodes for indexing. We observe that these methods involve making significant effort
to maintain the marginal histogram of the SSOM indices (first order statistics). This
fact suggests that the indexing schemes based only on first order statistics may
not sufficient. Thus, a higher order statistic is employed for analysing the SSOM
trajectory.
The first order statistic employed by PO and PSC captures only the properties
of individual nodes, ignoring the inter-dependencies between nodes in the dataset.
On the other hand, second order statistics consider the position of nodes relative to
one another in the SSOM trajectory. Since the gesture contains postures which have
somewhat strong correlation with their neighbour, the adoption of the second order
statistics, such as covariance and co-occurrence matrix, are more appropriate for
capturing the dependency between the pairs of postures from the SSOM trajectory.
Based on this discussion, a feature extraction based on posture transition (PT) is
obtained as follows.
Given that
u
t
is the index of a map unit, the function in Eq. (
11.6
) creates
S
=
(
—the set of indices of map units treated as a set of symbols. The
u
t
value of consequent points of a gesture remains the same, since consequent points
are generally close in the input data space. Therefore, consequent equal values of
u
t
are replaced with single values which result in the following definition [
338
]:
u
1
,...,
u
t
,...,
u
T
)
u
1
,...,
u
m
,...,
u
M
}
u
i
=
u
i
−
1
,∀
Tr
=
N
(
S
)=
{
:
M
≤
T
,
i
∈
[
2
,
M
]
,
(11.11)
where
N
is a function that removes consecutive equal
u
t
value and
Tr
is the
mapped gesture, representing the trajectory on the SSOM. With the arrangement
in Eq. (
11.11
), the dependencies among neighboring nodes can be conveniently
investigated.
The Markov random process is employed to model the trajectory. To capture
the dependencies between SSOM nodes in the trajectory, the horizontal Markov
empirical transition matrix [
345
] of the dataset in
Tr
is calculated. The matrix's
element is given by:
(
.
)
M
−
1
u
i
=
u
i
+
1
=
i
=
1
ʴ
(
m
,
n
)
∑
u
i
+
1
=
u
i
=
p
h
(
n
|
m
)=
(11.12)
M
−
1
u
i
=
i
=
1
ʴ
(
m
)
∑
where
u
i
and
u
i
+
1
are a pair of neighboring node indices,
M
is the size of
Tr
, and
m
,
n
∈{
1
,...,
C
}
.
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