GeoComputation - GeoComputation - page 15

live in a world where computer speeds are doubling almost annually. Flexible area definition of
censuses is just one potential area of need and GC is one way of achieving it.
1.7.6 P arallel S Patial c laSSification M ethodS
An obvious response to the spatial data explosion is to apply multivariate data summarising tools,
particularly classification, to the largest available databases. GC is also about rediscovering legacy
methods and then scaling them up for a large data era. Thirty years ago, the best (and most famous)
cluster analysis package had an observation limit of 999. This would now be considered totally
ridiculous, completely unnecessary and a severe limitation. However, legacy methods can also usu-
ally be improved and replaced by more flexible and less assumption ridden more modern devel-
opments. The K -means technology of the 1970s that ran on a mainframe has now been replaced
by unsupervised neural networks that run on parallel supercomputers and even workstations; see
Openshaw (1994c), Openshaw et al. (1995) and Openshaw and Turton (1996) for details. On the
Cray T3D with 256 processors, a single run takes 10 h, but the results are quite different from those
produced by a more conventional method and may be substantially better and tell a very different
story about the structure of Britain's residential neighbourhoods. See Adnan et al. (2014) on recent
advances and research in this area.
1.7.7 P arallel g eograPhical P attern and r elationShiP S PotterS
A major by-product of the GIS revolution of the mid-1980s has been to add geographic x , y
co-ordinates to virtually all people and property-related computer systems and to create multi-
ple layers of other digital information that relate to the physical environment and which may be
regarded as being related to it (as possible predictor variables). The success of GIS has created a
growing imperative for analysis and modelling simply because the data exist. The problem now
is how to do exploratory analysis on large databases, when there is little or no prior knowledge
of where to look for patterns, when to look for them and even what characteristics these might be
based on. It goes without saying that the methods also have to be easy to use, automated, readily
understood and widely available - a most difficult requirement but, nevertheless, a most important
challenge for GC to consider.
One possible solution is by Openshaw et al. (1987) who describe a prototype GAM able to
explore a spatially referenced child cancer database for evidence of clustering. The GAM used a
brute force grid search that applied a simple statistical procedure to millions of locations in a search
for localised clustering. Fortunately, the search is highly parallel although it was originally run on a
serial mainframe where the first run took 1 month of computer time. Subsequent work was done on
Cray-XMP and Cray 2 vector supercomputer systems although the problem is not naturally a vector-
izable one; see Openshaw and Craft (1991). A parallel version of the latest GAM/K code has been
developed for the Cray T3D written in MPI, but it will also now run on a PC in a few hundred sec-
onds (if the Monte Carlo simulation option is not selected). More powerful computing is now needed
only if the quality of the apparent results is of interest or concern. Previously it had to be used even
to produce crude results. For many spatial analysis applications, the crude results may well be suf-
ficient, but if these are not, then it is now possible to use HPC to validate them (Openshaw, 1998b).
The same basic GAM type of brute force approach has been used to search for spatial relation-
ships. The Geographical Correlates Exploration Machine (GCEM/1) of Openshaw et al. (1990)
examines all 2 m −1 permutations of m different thematic map layers obtained from a GIS in a search
for localised spatial relationships. The GCEM was developed for a Cray Y-MP vector process. It is
massively parallel because each of the 2 m −1 map permutations is independent and can be processed
concurrently. It will now run on a PC. In both cases, the speed-up in computer hardware speeds
has allowed very computationally intensive GC methods to filter down to the desktop. Yesterday's
supercomputers are today's workstations and it is likely that this process will continue for at least a