SEKE 2012 Proceedings - Knowledge Systems Institute

pirical evaluation is performed to show the effectiveness of
our regression testing approach. In Section 5, some related
work of regression testing techniques is introduced. Finally,
we conclude and show some future work in Section 6.
2 FCA-based Change Impact Analysis
Table 1. Formal context
M1 M2 M3 M4 M5 M6 M7 M8 M9 M10
C1 × × × × ×
C2 × × × × × ×
C3 × × × ×
C4 × ×
C5 × × × ×
C6 × ×
In this paper, our regression testing is performed based
on the CIA technique. Here we use FCA-based CIA approach
to predict the ripple effects induced by the proposed
changed classes, which we give a simple introduction here.
More details can be referred to our previous work [14].
2.1 Basics for Formal Concept Analysis
Formal Concept Analysis (FCA) is a field of applying
mathematics based on the schematization of concept and
conceptual hierarchy [7]. The input of the FCA process is
the formal context, defined as:
Definition 1 (Formal Context) A formal context is defined
as a triple K =(O, A, R), where R is a binary relation
between a set of formal objects O and a set of formal
attributes A. Thus R⊆O×A.
With the formal context, concept lattice is generated
based on the lattice constructing algorithm [7]. The concept
lattice is composed of a set of formal concepts, defined
as follows:
Definition 2 (Formal Concept) A formal concept is a
maximal collection of formal objects sharing common formal
attributes. It is defined as a pair (O, A) with O ⊆O,
A ⊆A, O = τ(A) and A = σ(O), where τ(A) ={o ∈
O|∀a ∈ A :(o, a) ∈R}∧σ(O) ={a ∈A|∀o ∈ O :
(o, a) ∈R}.
τ(A) is said to be the extent of the concept and σ(O)
is said to be its intent. On the generated concept lattice,
there are relations between these formal concepts, which
forms a partial order on the set of all concepts. We use
the following definition subconcept to denote the relations
between different formal concepts [7]:
Definition 3 Given two concepts Co 1 (O 1 ,A 1 ) and Co 2
(O 2 ,A 2 ) of a formal context, Co 1 is called the subconcept
of Co 2 , provided that O 1 ⊆ O 2 (or A 1 ⊇ A 2 ). we usually
mark such relation as: Co 1 Co 2 ⇐⇒ O 1 ⊆ O 2 ⇐⇒
A 1 ⊇ A 2
The set of all concepts of a formal context forms a partial
order, and composes a concept lattice, defined as follows.
Figure 1. Graphical representation of the concept
lattice
Definition 4 (Concept Lattice) The concept lattice L(Co)
is a complete lattice. L(Co) = {(O, A) ∈ 2 O ×
2 A |O = τ(A) ∧ A = σ(O)}, where infimum and supremum
of two concepts (O 1 ,A 1 ) and (O 2 ,A 2 ) are defined
as: (O 1 ,A 1 ) ∧ (O 2 ,A 2 )=(O 1 ∩ O 2 ,σ(O 1 ∩ O 2 )), and
(O 1 ,A 1 )∨(O 2 ,A 2 )=(τ(A 1 ∩A 2 ),A 1 ∩A 2 ), respectively.
A formal context can be easily represented by a relation
table, as shown in Table 1. In this table, rows represent
formal objects and columns represent formal attributes. A
cross (×) inrowC and column M means that the formal
object C has relationship with formal attribute M. By applying
Galicia tool 1 to the formal context in Table 1, the
concept lattice composed of formal concepts are generated.
Figure 1 shows the corresponding graphical representation
of the concept lattice. Each lattice node on the concept lattice
indicates a formal concept, and is marked with its intent
(I Set) and extent (E Set). The edges between them represent
the containment relationship between concept intents,
which forms a partial (hierarchical) order on the sets of all
concepts.
2.2 Change Impact Analysis
CIA is an important predictive measurement of the ripple
effects induced by the proposed changes. Here, the input of
1 http://www.iro.umontreal.ca/ galicia/
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