Databases Reference
In-Depth Information
In this section, we explain three examples with respect to the three-layered
framework. The classification is corresponding to the function-oriented view,
evaluation and measurement theory is corresponding to the theory-oriented
view, and the explanation-oriented data mining extends the procedure-
oriented view. We demonstrate how these three views are enriched by the
conceptual framework, especially the philosophy layer study.
4.1 Classification on the Three-Layered Framework
Classification is considered as one of the most important tasks of data mining.
It is therefore associated with the function-oriented view that we discussed in
Sect. 2. Partitions and coverings are two simple and commonly used knowledge
classifications of the universe. A partition of a finite universe is a collection of
non-empty, and pairwise disjoint subsets whose union is the universe. A cov-
ering of a finite universe is a collection of non-empty and possibly overlapped
subsets whose union is the universe. Partitions are a special case of coverings.
Knowledge is organized in a tower (hierarchy) or a partial ordering. Based
on the above discussion, we have partition-based hierarchy and covering-based
hierarchy. Hierarchy means that the base or minimal elements of the order-
ing are the most fundamental concepts and higher-level concepts depend on
lower-level concepts [19]. Partial ordering means that the concepts in the hi-
erarchy are reflexive, anti-symmetric and transitive. The first-level concept
is formed directly from the perceptual data [13]. The higher-level concepts,
representing a relatively advanced state of knowledge, are formed by a process
of abstracting from abstractions [13]. On the other hand, the series of lower-
level concepts, on whom the higher-level concept is formed, are not necessarily
unique in content. Within the requisite overall structure, there may be many
alternatives in detail [13].
The natural process of knowledge cognition follows the hierarchy from
lower-level concepts to higher-level according to the intellectual dependency.
The revise process does exist because of impatience, anti-effort, or simple
error. Peikoff analyzes that the attempt to function on the higher levels of
complex structure without having established the requisite base will build
confusion on confusion, instead of knowledge on knowledge. In such minds,
the chain relating higher-level content to perceptual reality is broken [13].
A virtual space that can hold knowledge as concepts is called a concept
space, namely, it refers to the set or class of the concepts. If we consider the
data mining process as searching for concepts in a particular concept space,
we need to study different kinds of concept spaces first. Inside the concept
space, the concept can be represented and discovered. Generally, a concept
space
S
can hold all the concepts, including the ones that can be defined
as a formula, and the ones that cannot. A definable concept space
DS
is a
sub-space of the concept space
S
. There are many definable concept spaces
in different forms. In most situations, one is only interested in the concepts
in a certain form. Consider the class of conjunctive concepts, that formula
