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of the concerned dimension. If the dimension is thematic, this will be, for example,
the evolution of the municipalities' density averages over all the period's dates or
the diversity of these evolutions. If the dimension is temporal, this will be the
average density of the municipality B over the period.
The form of the presented queries allows identifying states and approaching
change by comparison, either visual or by a numeric calculation between two dates.
In the first case, this may be the comparison of maps of locations at two dates
(question
where
), or the viewing of the cloud of points crossing values from states at
t1 and at t2 (question
what
). Secondly, the type of change can also be identified, by
evaluating the variation (quantitative or qualitative). This implies having formalized
the order structure of time (variation between two successive dates) in a similar
manner as the spatial dimension is in geographical information systems (a place and
its neighboring places). In this case, we can even express interesting interpretation of
the evolution: for example, when the point of interest is the pattern of the urban
diffusion, we can seek to identify the municipalities whose rate of population
variation between two dates is higher than that of their neighbors.
This stage of exploration, in the sense of sorting, selecting and shaping, is
undoubtedly the one that has taken the most importance in recent years. This is
related to the increase of volumes of available data (often imperfect and not
originating from explicit collection protocols) and to the development of
visualization environment. We have seen that these queries can be increasingly more
complex and produce statistical summaries of different distributions (spatial and/or
statistics). These queries are part of a continuum of processes that range from the
simple exploration to exploratory data analysis or statistical analysis (see Chapter 3).
2.1.3.
Analyzing the evolution of statistical and spatial relationships (challenge 3)
The third challenge requires the implementation of analyses and of statistical
models to describe change. At this stage, to describe does not only mean to represent
the data as in the previous stage. This is the other end of the continuum of analyses
from
showing change
through simple or elaborated queries to
validating
or
invalidating
assumptions about the studied phenomenon. The following example
illustrates the difference: for answering the question “what are the average
population trajectories of the communes located less than 20 km from employment
centers?”, one has to design a model that shows urban growth. By contrast, the very
similar question “is there a significant difference in demographic growth between
the municipalities located less than 20 km and those more than 20 km?” requires the
implementation of a statistical analysis.
Particular attention will be given to the statistical approaches to deal with spatial
dynamics. A first categorization of the mobilized methods can be proposed:
