Database Reference
In-Depth Information
Table 1. Table of symbols
Symbol
Definition
A metric space
,d
R
A database relation
Squema of relation R
R
Metric data domains
j
,
k
S
j
, S
k
Attribute of a relation,
S
Ì
,
S
Ì
j
j
k
k
δ
()
Distance function or dissimilarity function
d
g
Similarity aggregation function
ξ
Query radius
k
Maximum number of elements to be returned in a query
g
Grip factor
Q
Set of query centers
s
q
Query center,
s
q
Î
Q
of elements from one attribute and from distinct attributes sharing the same domain can be compared.
The symbols employed in this chapter are summarized on Table 1.
There are several types of similarity queries that can be employed to compare multimedia data. A
similarity query is expressed using a similarity predicate. There are basically two families of similarity
predicates: those limiting the answer based on a given similarity threshold ξ, and those limiting the
answer based on the number
k
of elements that should be retrieved. Moreover, the operators involved
in similarity queries can be either unary or binary.
Similarity Selections
Similarity selections are performed by unary operators that compare the elements of
S
j
with one or more
reference elements
s
q
Î given as part of the predicate. A similarity selection over an attribute
S
j
of
the relation
R
can be represented as
(ˆ
j
σ
<
predicate
R
where the selection predicate has the form
)
selection
−
>
j
q and
θ
denotes a similarity operator. This predicate expresses a similarity comparison between
the set of values
S
j
S
Q
Ì , called the reference or
query centers set, taken from the domain
j
and given as part of the query predicate. The answer of a
similarity selection is the subset of tuples
t
i
from
R
whose values
s
i
from attribute
S
j
meet the selection
predicate. It is important to note that similarity selections exhibit properties distinct from those of the
traditional selections (for example, they do not possess the commutative property, see (Ferreira, 2009),
so we use the
(
ˆ
s symbol instead of the traditional σ.
Ì of an attribute
S
j
and a set of constant values
Q
j
j
