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subsequences from the transformed angular series. Several fuzzy sets for angles
are predefined to represent semantic concepts understandable to human be-
ing. Finally, an a priori-like fuzzy mining algorithm is proposed to generate
linguistic trends. Appropriate post-processing is also performed to remove re-
dundant patterns. Details of the proposed mining algorithm are described
below.
The proposed mining algorithm for linguistic trends:
INPUT: A time series
S
with
k
data points, a set of
h
membership functions
for angles, a predefined minimum support
α
, and a sliding-window
size
w
.
OUTPUT: A set of linguistic trends.
STEP 1: Transform every two adjacent data points in the time series
S
into
an angle. Assume
S
=(
d
1
,
d
2
,
d
3
,... ,
d
k
). Then the resulting
angular series
S
' is formed as:
S
=(
a
1
,a
2
,a
3
,...,a
k−
1
)
,
where
a
i
is the angle from data point
d
i
to
d
i
+1
.
STEP 2: Transform
S
' into a set of subsequences
W
(
S
) according to the
sliding-window size
w
. That is,
W
(
S
)=
{
s
p
|
s
p
=(
a
p
,a
p
+1
,...,a
p
+
w−
1
)
,p
=1
to k
−
w
}
,
where
a
p
is the value of the
p
-th angle in
S
'.
STEP 3: Transform the
j
-th (
j
=1to
w
) quantitative value (angle)
v
pj
in
each subsequence
s
p
(
p
=1to
k
-
w
) into a fuzzy set
f
pj
,repre-
sented as:
f
pj
1
,
R
j
1
,
f
pj
2
,
f
pjh
R
pjh
R
j
2
,
···
using the given membership functions, where
R
jl
is the
l
-th fuzzy
region of the
j
-th data point in each subsequence,
h
is the number
of fuzzy memberships, and
f
pjl
is
v
pj
's fuzzy membership value in
region
R
jl
.Each
R
jl
is called a fuzzy term.
STEP 4: Calculate the scalar cardinality of each fuzzy term
R
jl
as:
k
−
w
count
jl
=
f
pjl
.
p
=1
STEP 5: Collect each fuzzy term to form the candidate 1-patternsets
C
1
.
STEP 6: Check whether the support (=
count
jl
/
(
k
w
)) of each
R
jl
in
C
1
is larger than or equal to the predefined minimum support
value. If
R
jl
satisfies the above condition, put it in the set of large
1-pattern-sets (
L
1
). That is:
−
L
1
=
{
R
jl
|
count
jl
≥
α,
1
≤
j
≤
p
+
w
−
1
and
1
≤
l
≤
h
}
.
