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In-Depth Information
Fig. 5. The notion of the
LCSS
matchingwithinaregionof
δ
&
ε
for a sequence. The
points of the two sequences within the gray region can be matched by the extended
LCSS
function.
controls how far in time we can go in order to match a
given point from one sequence to a point in another sequence. The constant
ε
The constant
δ
is the matching threshold (see Figure 5).
The first similarity function is based on the
LCSS
and the idea is to
allow time stretching. Then, objects that are close in space at different
time instants can be matched if the time instants are also close.
Definition 4.
We define the similarity function
S
1 between two sequences
A
and
B
,given
δ
and
ε
, as follows:
)=
LCSS
δ,ε
(
A, B
)
S
1(
δ, ε, A, B
min(
n.m
)
Essentially, using this measure if there is a matching point within the
region
we increase the
LCSS
by one.
We use function
ε
1 to define another, more flexible, similarity measure.
First, we consider the set of translations. A translation simply causes a
vertical shift either up or down. Let
S
F
be the family of translations. Then a
f
c
belongs to
F
f
c
(
A
a
x,
1
+
c,...,a
x,n
+
c
function
). Next, we define
a second notion of the similarity based on the above family of functions.
if
)=(
Definition 5.
Given
δ, ε
and the family
F
of translations, we define the
similarity function
S
2 between two sequences
A
and
B
, as follows:
S
2(
δ, ε, A, B
)=max
fc∈F
S
1(
δ, ε, A, f
c
(
B
))
