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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
The obtaining process of spatial data includes cognition,
surveying, interpreting, data input, data processing and data
representation. The uncertainties of spatial data stem from two
parts. On the one hand, they stem from instability of natural
phenomena and incompleteness of men's cognition. On the
other hand, the process of spatial data capture and handling
bring a lot of uncertainty. In addition, these uncertainties can be
propagated from the former phase into the latter one, and
accumulated in different laws (Figure 1).
2.2 Uncertainty Measurement and Propagation of Spatial
Data
At present, a great deal of research have been developed in
some areas, such as positional uncertainty and its propagation,
especially the uncertainty of points, lines, polygons or areas.
Therein, the uncertainty of points and lines is the basis of
polygons and areas. Some uncertainty models have been
constructed, including standard ellipse model (Mikhail and
Ackerman, 1976) and circle normal model (Goodchild,
1991) of point position, Epsilon-band model (Chrisman,
1982) and error band model (Dutton, 1992) of line position.
For last years, the study of spatial data quality control data put
emphasis on the spatial positional uncertainty, but little on
attribute uncertainty. In recent years, some scholars studied the
attribute uncertainty of GIS data (Liu, 1999; Ehischlager,
2000; Shi, 2002). Usually, positional uncertainty and attribute
uncertainty were studied respectively. Shi (2000) constructed
“S-band” model that combine positional uncertainty with
attribute uncertainty. Zhang (1999) constructed field model
that position uncertainty and attribute uncertainty are described
in uniform.
Real World
Concept >
Model
; Uncertainty Origins =
aet certains.
$n
The spatial uncertainty propagation problem can be formulated
mathematically as follows:
Yis) = Opt(Di(e), ---, Dm(e)) (1)
Let Y(s) be the output of GIS operation Opi(e) on the
m spatial data sets. The operation Opt(«) may be one of the
various operations in GIS such as intersection of data sets. The
principle of the spatial uncertainty propagation analysis is to
determine the spatial uncertainty in the output Y(e) given the
operation Opt(«) and spatial uncertainties in the data sets. The
spatial uncertainty propagation is relatively easy when the
operation Opf(e) is a linear function, which can be performed
by error propagation law. However, few of operation Opt(e)
were linear or could be solved by simple calculation. However,
in general, rigorous methods and functions will be very
troublesome. The Monte Carlo method (Openshaw, 1989) uses
an entirely different approach to determine the uncertainty of
geospatial objects. In this method, the results of Equation (1)
are computed repeatedly, with input value
D -[D,,D,,---, D,,] that are randomly sampled from their
joint distribution. The outputs of the equation construct random
samples, in which their distribution parameters. such as mean
value and variance, can be estimated. The Monte Carlo method
may be a general method for uncertainty handling, and can be
applied to the computation processing of spatial or attribute
data. An outstanding advantage of Monte Carlo method is able
to provide the entire distribution of output data at an arbitrary
level of accuracy. The other advantages of this method are easy
implementation and more general application. However, this
method is more intensive computationally.
Processed
Spatial Data
“Propagation.
Figure 1. Uncertainty origins and uncertainty propagation of spatial data
3. UNCERTAINTY ANALYSIS IN SPATIAL
KNOWLEDGE DISCOVERY
The uncertainties in spatial knowledge discovery may exist in
the process of spatial data selection, spatial data preprocessing,
data mining, knowledge representing and uncertain reasoning.
The study on the uncertainties of spatial data themselves are
very important for spatial knowledge discovery, for the original
data of spatial knowledge discovery stem from uncertain spatial
database or uncertain spatial data sets being analyzed.
Moreover, uncertainties in spatial data may directly or
indirectly affect the quality of spatial knowledge discovery
(Miller and Han, 2001). At the same time, a lot of uncertainties
259
exist in spatial knowledge discovery. Moreover, uncertainties
will be propagated and accumulated in spatial knowledge
discovery process (Figure 2). The uncertainties of every phase
will be analyzed briefly as follows:
At the phase of spatial data selection, Uncertainties mainly stem
from a subjectivity of selecting object data according to the task
of spatial knowledge discovery, including what data should be
collected, and how much data is enough, also these spatial data
necessarily embody some kinds of errors or uncertainties.
Spatial data preprocessing mainly include data cleaning, data
transformation and data discretization, in which many
uncertainties will be produced if we do not adopt appropriate
uncertainty handling methods. Data discretization is to divide a
