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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol XXXV. Part B2. Istanbul 2004
with inaccurate, uncertain and incomplete information.It is
suitable for spatial data mining based on the uncertainty of
attributes and provide a new approach for GIS attribute analysis
and knowledge discovery.In spatial data mining,the application
of rough set can analyze the importance, uncertainty,
consistency and dependent index of attributes,study the effect
of attributes’ dependent index on decision-making, reduce the
data, attribute table and attributes’ dependent index, discovery
the relativity of data, evaluate the absolute and relative
uncertainty of data, and obtain causality in the data, produce
minimum decision and classification algorithm, etc.
3. ROUGH SET
3.1 Basic conception
Assume a domain set U of a target,let X c U , and R indicates
an equivalent relation, When X is the ombination of some basic
categorieses of R ,then X can be defined by R;otherwise X can
not be defined by R. The sets which can be defined by R are
subsets of the domain set, which are called R accurate sets, and
can be precisely defined in the knowledge base K.On the
contrary, the sets which can not be defined by R can not be
defined in the knowledge base, which are called R rough sets.
Routh set can be described by two accurate sets and a boudery
set:
Lower Approxmate Set of X on R is definded as:
R(X)zYiYeU/R£F»Yc.x!
Upper Approxmate Set of X on R is definded as:
R(X)=Y{¥eU/RE»Y1 X =D}
Boundary Set of X on R is definded as:
Mm (X)I=R (X)Y-R (X)
posR(X)=R_(X) is defined as positive domain
while negR(X)-U-R (X) is defined as negative domain
32 Knowledge representation, Reduction, and Core
Knowledge representation is achieved through knowledge
expression system. Its basic composition are object sets whose
knowledge is described by the attributes of targets and
themselves.
A knowledge representation system can be expressed by
Sz«U C, DV, F»
where U is the domain set.
C U U is attribute set, C —Ííaj, a», ..., ay] is the condition
attribute set (note should be taken that C contains spatial
constraint conditions), D ={d,,d>, ..., d,} is the decision
attribute set,
V is the field collection composed of CU U, viz. V *UscA V, V,
is the field of attribute p, /'is an information function, viz. f£.
U xA4—V,
Let attribute set:
B = tb , Das b, K > A j = AE Y. zm V X He X Vis xK x ‘
bm
Define the map 7:
UV, to represent attribute value of field B.
R upper set of condition set C about domain set U can be
expressed as: U/R,-
R upper set of decision set D about domain set U can be
expressed as: U/R y:
Define U/R; as the equivalent of a transaction, then U/R is the
transaction of condition, U/R), is the transaction of decision.
Then the upper approximate about the condition set for decision
transaction is:
C(D,)={C IC, eU/RGCO ^D, «o
Do
UA
CA
Then the lower approximate about the condition set for decision
transaction is:
C (D) = 1 A c, € iJ / RCE cn. }
Let the two sets G and R, r is an equivalent relation in R, g is an
equivalent relation in G, if pos ir (G)7 posg(G), Then r in G
is omissible.
If no element in R can be omissible, then R is independent.
Let H < R.H is independent, if pos; (G)= posg(G), then H is
the reduction of G by R. From the definition, the lower
approximate of G about H and R is the same, which maintains
the classification of R and G. The all intersection of the relation
in R forms the core of R and marked as core(R),viz.core(R)N
red(R). The attributes in core set is the key factors that affect
classifation based on R.
3.3 Dependent index of Decision Transaction
C; is the condition of U/Rc,and D; is the decision of U/Rp,let
decision transaction based on condition transaction can be
mapped as CF;;C;D; and CF, =card" (C;ND)/card(C; , if
condition transaction C; is belonged in the lower approximate
C (Dj if decision transaction , CF;=1I;otherwize if condition
transaction C; is belonged in in U-C(QD) CF.
4. A KDD MOTHED BASED ON ROUGH SET
4.1 Spatial Object Information Tables
The knowledge representation system describes the domain set
as a two-dimentional table in which each row indicates an
object and each column indicates an attribute.Here,the attributes
can be divided into condition attribute and decision-maiking
attribute. In the process of knowledge discovery, condition
attribute should be reduced first to remove repeated rows,then
redundant attribute in each decision-making should be
reduced.To reach the minimum decision rules in application, we
should select effective attributes to indicates the domain set
properly or approximately.
4.2 Minimum rule generation algorithm based on Rough
Set
Generally, decision-makers have priori knowledge to the weight
of every condition attribute. The weight is used for weighing
the relative importance of attribute. In various decision-making,
the same attributes may have different influence on decision-
making, namely the weight is sensitivfe to the decision-making
environment. The dependent index of attribute expresses the
influence of the attribute on decision rule under present data
environment, but can not reflect the decision-maker's priori
knowledge. So, it is a comparatively reasonable method to
combine them to select effective attribute. The processes are
describled as follows.
1. Propose two-dimentional data view, i.e. decision rule table,
composed of condition attribute and decision attribute in the
domain set;
Determine the data classification standard, express the
attribute values in a standardized way, and remove
N
unnecessary attributes;
If the decision rules of the knowledge expression system are
exclusive, we can classify it into two sub-tables: one is an
inclusive decision table; the other is an exclusive decision
table. The latter is a kind of knowledge which can not be
extracted from the present information, so we just deal with
the former.
Lo
