A GENERAL DATA MINING MODEL

Anita Wasilewska, Department of Computer Science, 
State University of New York, Stony Brook, NY, USA

Ernestina  Menasalvas, Facultad de Informatica,
Universidad Politecnica de Madrid, Madrid, Spain

ABSTRACT

We usually view Data Mining results and present them to the user
in their  syntactical descriptive  form as it is  the most natural
form of communication. But the Data Mining process is deeply
semantical in its nature. The algorithms  process records
(semantics) finding similarities which are then presented in a
descriptive i.e. syntactic form.  Our General Model addresses this
the semantics-syntax duality inherent to any Data Mining process.

Moreover, our General Model  formalizes the definition of Data
Mining as the process of information generalization. In the model
the Data Mining algorithms are  defined as generalization
operators. We use our framework to show that only three
generalizations operators: classification, clustering, and
association operator are needed to express all Data Mining
algorithms for classification, clustering, and association,
respectively. Moreover, we formally prove  that classification,
clustering and association analysis fall into three different
generalization categories.

Finally, we examine, as a particular case, a General Classification 
Model. In particular, we define the notion of truthfulness, or 
a degree of truthfulness of syntactic descriptions obtained by 
any classification  algorithm, represented within the Model 
by a classification operator. We use our framework to prove that 
for any classification operator (method, algorithm) the set of all 
discriminant rules that are fully true (partially true) form 
semantically the lower approximation (approximate lower approximation) 
of the class they describe. The set of characteristic rules
describes semantically  its upper approximation.

The notion of  the  approximate lower approximation extends to any 
classification operator (method, algorithm) the ideas first expressed 
in 1986 by Wong, Ziarko, Ye, and in the VPRS model of Ziarko.