Geography Reference
In-Depth Information
are auto-correlated. More complicated models of time series have been applied
to model temporal data, such as Markov chain where the probability distribution of
a value at time t depends only on the value at t-1 (Gilks et al.
1995
).
17.2.4.2
Spatial Data Models
Three statistical models are used to model spatial data (Banerjee et al.
2003
). The
geostatistical model deals with continuous spatial surface with discrete sampled
locations. Tools such as Kriging are used to interpolate unsampled values. The
lattice model (a.k.a. areal model) deals with continuous space partitioned into
regular grids or irregular spatial regions. Interactions between partitions are char-
acterized by the spatial neighborhood relationship (e.g., topological connectivity).
Data models such as the spatial autoregressive regression model (SAR) and Markov
random field (MRF) can be applied on such datasets. Finally, point process is used
to model discrete spatial point data, such as locations of event reports. Typically,
point patterns include completely random, clustered or de-clustered.
Traditional statistical analysis assume that data samples are independently and
identically-distributed. This assumption does not hold for spatial data which exhibits
special features due to its unique spatial structure. However, unique spatial structure
exist in spatial data. First of all, spatial data is highly self-correlated. A fundamental
observation is that “Everything is related to everything, but nearby things are more
related than distant things”, a.k.a. the first law of geography (Tobler
1970
). This
feature of spatial data is called spatial autocorrelation. For example, precipitation
observed at nearby ground stations should be similar. A second feature of spatial
data is the underlying process differ from place to place. For example, in a
spatial point process, data may be clustered in certain regions instead of uniformly
distributed over space.
17.3
Definitions of Change
Intuitively, we find it helpful to classify definitions of “change” in ST data as
either calculus-based or statistics-based. In the calculus-based definitions, data value
in neighboring time instances or spatial locations are compared. By contrast, in
statistics, data is often viewed as samples from the underlying distribution. A
parameter of data distribution (e.g., mean) is employed to measure the difference
between subsets of the data. From these two ways of defining change, we can derive
the change patterns and mining techniques.
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