Information Technology Reference
In-Depth Information
Table 11.1
Abbreviations used throughout the chapter and the sections where those concepts are
defined/explained
Abbreviation
Full name
Definition
AKNN
Adaptive
k
NN
Sect.
11.5.5
BN
k
(
x
)
Bad
k
-occurrence of
x
Sect.
11.4
DTW
Dynamic Time Warping
Sect.
11.3
GN
k
(
x
)
Good
k
-occurrence of
x
Sect.
11.4
h-FNN
Hubness-based fuzzy nearest neighbor
Sect.
11.5.2
HIKNN
Hubness information
k
-nearest neighbor
Sect.
11.5.4
hw-
k
NN
Hubness-aware weighting for
k
NN
Sect.
11.5.1
INSIGHT
Instance selection based on graph-coverage and
Sect.
11.6.1
hubness for time-series
k
NN
k
-nearest neighbor classifier
Sect.
11.2
NHBNN
Naive hubness Bayesian
k
-nearest Neighbor
Sect.
11.5.3
N
k
(
x
)
k
-occurrence of
x
Sect.
11.4
N
k
,
C
(
x
)
Class-conditional
k
-occurrence of
x
Sect.
11.4
Skewness of
N
k
(
x
)
Sect.
11.4
S
N
k
(
x
)
RImb
Relative imbalance factor
Sect.
11.5.5
of the nearest neighbors of
x
belongs to class
C
2
, then this 3-NN classifier recognizes
x
∗
as an instance belonging to the class
C
1
.
We use
N
k
(
)
N
k
(
)
x
to denote the set of
k
nearest neighbors of
x
.
x
is also called
as the
k
-neighborhood of
x
.
Abbreviations used throughout this chapter are summarized in Table
11.1
.
11.3 Dynamic Time Warping
While the
k
NN classifier is intuitive in vector spaces, in principle, it can be applied
to any kind of data, i.e., not only in case if the instances correspond to points of a
vector space. The only requirement is that an appropriate distance measure is present
that can be used to determine the most similar train instances. In case of time-series
classification, the instances are time-series and one of the most widely used distance
measures is DTW. We proceed by describing DTW. We assume that a time-series
x
of length
l
is a sequence of real numbers:
x
.
In the most simple case, while calculating the distance of two time series
x
1
and
x
2
, one would compare the
k
th element of
x
1
to the
k
th element of
x
2
and
aggregate the results of such comparisons. In reality, however, when observing the
same phenomenon several times, we cannot expect it to happen (or any characteristic
pattern to appear) always at exactly the same time position, and the event's duration
can also vary slightly. Therefore, DTW captures the similarity of two time series'
=
(
x
[
0
]
,
x
[
1
]
,...,
x
[
l
−
1
]
)
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