Applications of Frequent Pattern Mining - Frequent Pattern Mining - page 448

Another interesting application in such contexts is the discovery of interesting
spatial association rules . The integration of such methods with commercial database
systems in order to determine spatial association rules has been a key research goal
[ 47 , 48 ]. Spatial association rules determine the implicit correlations between objects
which contain both spatial and non-spatial attributes. Note that a spatial object may
contain both spatial attributes and other non-spatial ones. For example sea-surface
temperatures may correspond to spatial locations and temperature values. In such
cases, consider the rule:
The temperature in the northern regions is usually low.

This is a spatial association rule, which contains both spatial and non-spatial at-
tributes. In some applications, temporal components may also be associated with
such rules. It is important to note that it is often quite complex to find the appropriate
resolution at which the spatial association rules my be found. This may also result
in challenges in terms of computational efficiency. An important methodology in or-
der to substantially reduce the computational cost is that of progressive refinement.
Therefore, the spatial association rules are first determined at a coarser resolution,
and only promising candidates are explored for further mining [ 67 ]. The idea is to
use rough spatial approximations such as minimum bounding rectangles in order to
determine the frequent pattern candidates. These candidates are then further explored
at a finer spatial resolution. A system prototype for this class of spatial data mining
methods is provided in [ 57 ]. A similar methodology has been used in order to mine
co-location patterns [ 131 , 143 ]. In these methods, the idea of spatial continuity is
used in order to refine the pattern mining process. The idea is that spatially close
objects are often more likely to exhibit interesting correlations that objects, which are
spatially further apart. An overview of methods for spatial data mining is provided in
[ 97 , 68 ]. A further temporal component to this analysis in the form of spatiotemporal
patterns is provided in [ 28 ].
It should be pointed out that many forms of image and multimedia data may
be considered spatial data, since spatial locations are often associated with pixels.
Similarly, other non-spatial attributes such as color may also be associated with the
different locations. Many of the techniques, which have been discussed above for
the case of spatial data, can also be applied to such kinds of multimedia data. For
example, methods for classification of images with the use of association rules is
discussed in [ 20 ]. In general, spatial methods for classification may be extended to
images by using appropriate features to represent the pixels in the images.

11 Software Bug Detection

Software programs can be considered structured entities which can be represented as
graphs. Such graphs often have a “typical” structure in the case of normal software
programs. These can be represented in the form of normal patterns in the underlying
graph structured data. These are referred to as software behavior graphs . Different