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Unit 9: Metrics

9.3.1 Definition of PSI (Percentage of Shared Ideas) Notes
Although the semantic metrics proposed by are not subject to distortions due to programming
language or programmer style as traditional metrics are, they still have one obstacle: they require
a knowledge base with a conceptual graph structure in order to be calculated. Not all knowledge
bases have such a structure. Therefore, proposed semantic metrics, including PSI, that can be
calculated using any knowledge base that associates.
Concepts or keywords with classes and their member functions, regardless of how the knowledge
base is implemented.
The PSI is the number of concepts or keywords shared by at least two member functions of a
class, divided by the number of concepts or keywords belonging to any member function in
the class. PSI for class Ca is defined as follows.
| {
x
xx ΠI ^ $ i jx ΠI ^ ΠI )}
,(
ai
aj
a
PSI =
{| I ^ $ k y ( ΠI )}
yy Œ
ak
a
For 1_ i, j, k _ |Fa|, or 0 if no ideas are associated with any function of the class.
For example, define class Ca to contain four member functions and a total of ten ideas (concepts
or keywords from the knowledge base) associated with member functions to make up the
following sets: Ia1 = {i3, i4, i5}, Ia2 = {i4, i5, i6}, Ia3 = {i1, i2}, and Ia4 = {i6, i7, i8, i9, i10}.
In this example, ideas i4, i5, and i6 are common to at least two member functions; the others
are not. Therefore, PSI for class Ca = 3/10 = 0.30.
9.3.2 Syntactic Cohesion Metrics
One of the majority usually cited suites of metrics is that proposed by Chidamber and Kemerer
Chidamber and Kemerer proposed these metrics, many people have analyzed, criticized, and
proposed their own versions of these metrics. We will compare the performance of PSI to six
versions of LCOM (lack of PSI= (1). (See Table 9.2)

Table 9.2: Definition of Various LCOM Matrices

Definition Reference
LCOM LCOM = the set of pairs of member functions with no [9]
instance variable used by both members in the pair
LCOM1 [13] added the constraint that a pair of member functions [13]
containing a member function and itself should not be
counted. Inherited instance variables are not counted.
LCOM2 [8] specified a pair of member functions could not include [8]
the member function and itself. Inherited instance variables
do not count.
LCOM3 An undirected graph has edges that are pairs of member [23] [19]
functions with at least one attribute variable in common.
LCOM3 = number of connected components of the graph.
LCOM4 A variation of LCOM in which there is an edge in the graph [19]
for each function that calls another function in addition to
the edges for functions that share attribute variables.
LCOM5 LCOM 5 is specified from the perspective of the number of [13]
functions accessing each attribute.

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