Database Reference
In-Depth Information
Figure 2. Examples of similarity queries considering the Euclidean distance. (a) Range selection. (b)
k-Nearest-Neighbor selection considering k=4. (c) Aggregate Range selection. (d) k-Aggregate Nearest
Neighbor selection considering k=1 and g=2. (e) Range join. (f) k-Nearest Neighbors join considering
k=2. (g) k-Closest Neighbors join considering k=3
where
δ
is a distance function over
j
,
Q
is the set of query centers,
s
i
is a dataset element, and the
power
g
∈ is a non-zero real value that we call the
grip factor
of the similarity aggregation function.
Considering Equation 1, the aggregate range and the aggregate
k
-nearest neighbor queries applied over
a unitary set
Q
correspond to the traditional range and
k
-NN queries respectively.
It is important to note that, different values for the grip factor
g
can provide interesting different in-
terpretations. For example,
g
= 1 defines the minimization of the sum of the distances,
g
= 2 defines the
minimization of the mean square distance (see Figures 2(c) and (d)), and
g
= ∞ defines the minimization