Measuring UML Model Similarity
Jie Su and Junpeng Bao
Department of Computer Science & Technology, Xi’an Jiaotong University, Xi’an 710049, P.R. China
Keywords: UML, XML, Model Similarity Edit Distance Edit.
Abstract: Many user requirements and UML models are similar even if identical, but their application backgrounds
are different. It is a straight and feasible way to mine those similar UML models for a model warehouse and
reuse them so as to improve software development efficiency. The key point in the idea is to measure the
similarity of UML models. We present a Level Edit Distance method to solve the problem. The LED
measures similarity of XML structures instead of UML models. Indeed, UML models are converted to
XML documents according to XMI so that UML model similarity equals to XML document similarity.
However, our method concentrates on the pure structural similarity of UML models in XMI format, namely,
the semantic information is ignored. The LED is different from the traditional Edit Distance. The former
needs only one primitive operation whereas the later needs three. Our preparatory experimental results show
that the LED can keep almost the same distance distribution with the traditional ED and is a little faster than
the latter. We are going to improve the capability of the LED and combine it with a semantic-considered
method in order to precisely evaluate the similarity of user requirements.
1 INTRODUCTION
UML (Unified Modeling Language) is a standard
general-purpose modeling language in the area of
object-oriented software engineering. As a result,
more and more software engineering documents
describe user requirements and build models in
UML. UML models are basic foundation in the
Model Driven Development. It is a fact that many
software developers rebuild a variety of models and
functions again and again. Obviously, a lot of rebuilt
codes are not better than the existed. One reason of
the low reusability is that it is too hard or time
consuming to find the most appropriate model from
a huge mountain of boring model repository.
Whatsoever, many user requirements and UML
models are similar but their application backgrounds
are different. That means their schema and structure
are similar even if identical. Hence, a straight way to
improve the model reusability and software
development efficiency is that to mine the similar
UML models for a model warehouse and reuse them
as far as possible. Our ongoing research aims to
develop an effective method to measuring UML
model similarity so as to improve the reusability of
them.
Instead of straight measuring similarity of UML
models, we exploit XMI (XML Metadata
Interchange) to transfer a UML model into a XML
document so that the similarity of UML models
equals to that of XML texts. A XML text is a
semi-structured text that organizes its content in a
tree structure with labeled tags. The similarity or
identity of two XML texts means that (1) the text
contents are similar or identical between them; (2)
their structures are also similar or identical to each
other. It has to be noted that a XML text is different
form a plain text because the former has explicit tree
structure whereas the latter has not. One of key
points in the XML similarity is the structural
similarity of XML texts. Since XML becomes a
basic standard document format in the World Wide
Web. There are many XML structural similarity
measure approaches. The Edit Distance based
methods are a straight way to measure structural
similarity of XML texts. Another way is to find
similar paths or sub-trees in two XML texts, and
then calculate the portion of similar paths or
sub-trees out of the whole structure tree. The serial
sequence methods convert the tree structure of a
semi-structured text into a sequence of code, and
then calculate the similarity of code sequences to
assess the similarity of semi-structured texts.
Wen (L. Wen, etc. 2008) presented a XML
structural similarity measure method, which is
typical traditional Edit Distance based method. They
convert the tree structure into a node sequence
319
Su J. and Bao J..
Measuring UML Model Similarity.
DOI: 10.5220/0004027303190323
In Proceedings of the 7th International Conference on Software Paradigm Trends (ICSOFT-2012), pages 319-323
ISBN: 978-989-8565-19-8
Copyright
c
 2012 SCITEPRESS (Science and Technology Publications, Lda.)

which contains tag and left bracket, and then extract
subsequences. They believe that the similarity of
sub-sequences is equal to that of the XML structure.
In this paper, we concentrate on the problem of
pure structural similarity of UML models in XMI
format. That means the tag semantic information is
discarded. We present a modified Edit Distance
method, called Level Edit Distance (LED), to
calculate the similarity of two tree structures based
on only 1 primitive operation. Whereas the
traditional edit distance needs 3 primitive operations,
including change, insertion and deletion.
Additionally, LED calculates level distance at each
level and then sums them up with different weight to
get the final distance between trees. But Wen
calculates distance only on the sub-sequences.
2 MEASURE OF STRUCTURAL
SIMILARITY
2.1 Similarity Principles
An UML model can be exactly converted into a
XMI document, i.e. a well formed XML text so that
the similarity of UML models equals to that of XML
texts. A XML text contains both structural
information and semantic information. But in this
paper, we consider only structure information,
ignore semantic information. Because we aim to find
more similar models in a repository and try to
improve the reusability of various models.
Obviously, the high level model and general model
contains less semantic information so as to guarantee
their application to different backgrounds.
Additionally, they are more abstract and comply
with platform independent philosophy. In terms of
reusability, semantic information tends to obstruct
the model similarity. In fact, the abstract structures
of UML models in different application backgrounds
may be very similar even if identical. The most
differences in various user requirements are often
from semantic narrative texts. So we omit a model’s
semantic information and remain its structure
information in order to compare models in a higher
and more abstract level. We believe it is helpful to
improve the reusability of models. As a result, the
method proposed in this paper concentrates on the
pure structural similarity of UML models in XMI
format. Indeed, it is the similarity of trees.
The Fig. 1 shows 4 trees extracted from 4 XML
texts. However, the similarities among each other of
them are depended on our subject definition. There
are different principles so that the similarity
relationships among the 4 trees are various.
Figure 1: Pure structure of 4 XML documents.
According to the traversing sequence in a tree,
we define two principles to decide the relationships
among the tree structural similarities.
Principle 1: To compare two trees in deep first
way. Namely, two trees are compared from left to
right. For example, in the Fig. 1, according to this
principle, the similarity between tree a and b is
greater than that between a and d. Also, the
similarity between tree a and c is greather than that
between a and d, i.e.
sim(a,b) > sim(a,d) and sim(a,c) > sim(a,d)
Where sim(a,b) means the structural similarity
between tree a and b.
Principle 2: To compare two trees in broad first
way. Namely, two trees are compared from up to
bottom. It implies that the more differences at the
lower level, the more differences between two trees.
The root of a tree is level 0. According to this
principle, the relationships among the structural
similarities are:
sim(a,c) > sim(a,d) > sim(a,b)
Because the tree a and c are still identical at the
level 2 but tree a is different from d at that level.
Tree a and b are different from the level 1.
In this paper our method complies with the
principle 2, and the lower level will has a great
effect on the whole similarity. Indeed a 10 based
level weight is attached to each level in our method.
2.2 Similarity Algorithm
Wen’s method is a typical traditional Edit Distance,
which is the minimum operation cost to transform
one string to another with three primitive operations
including change, insertion and deletion.
Given two XML document d
1
and d
2
, the ED of
Wen’s method is defined as follows.
ICSOFT 2012 - 7th International Conference on Software Paradigm Trends
320

Table 1: The node sequences of 4 trees after null nodes inserted.
Tree
Level 0
Level 1
Level 2
Level 3
(a)
N
0
N
0.1
N
0.2
Null
N
0.1.1
N
0.1.2
N
0.2.1
N
0.2.2
Null
Null
Null
Null
Null
(b)
N
0
N
0.1
N
0.2
N
0.3
N
0.1.1
N
0.1.2
N
0.2.1
N
0.2.2
Null
N
0.3.1
N
0.3.2
Null
Null
(c)
N
0
N
0.1
N
0.2
Null
N
0.1.1
N
0.1.2
N
0.2.1
N
0.2.2
Null
Null
Null
N
0.2.2.1
N
0.2.2.2
(d)
N
0
N
0.1
N
0.2
Null
N
0.1.1
Null
N
0.2.1
N
0.2.2
N
0.2.3
Null
Null
Null
Null
Table 2: The final code sequences of 4 trees.
Tree
Level 0
Level 1
Level 2
Level 3
(a)
1
1
1
0
1
1
1
1
0
0
0
0
0
(b)
1
1
1
1
1
1
1
1
0
1
1
0
0
(c)
1
1
1
0
1
1
1
1
0
0
0
1
1
(d)
1
1
1
0
1
0
1
1
1
0
0
0
0
)}(),(max{
),(
),(
21
21
21
dlendlen
ddOPN
ddED 
(1)
where OPN(d
1
, d
2
) denotes the minimum cost of
operations to change the node sequence of d
1
to that
of d
2
. The len(d
1
) denotes the length of node
sequence of d
1
.
But we think 1 primitive operation is enough to
compare two strings. We present a Level Edit
Distance method (LED) that needs one operation to
change one string to another. We believe this
method is more simple, understandable and easier to
implement. The reduction of primitive operations
has no effect on the structural similarity relationship.
In the next section, the experimental results prove
that LED and ED produce almost the same results.
The steps of measuring pure structural similarity
of XMI by LED are:
(1) To traverse a XMI document structure in the
Broad First way to produce a sequence of node with
it’s position code.
(2) To compare two node sequences at each
identical
position, insert a node in a certain position if it is
absent in one sequence.
(3) To encode the inserted node as 0, the original
node as 1.
(4) To compute the distance between the codes
of each level in two tree structures. The distance
between codes of the i level in tree a and tree b is
denoted by LED(a,b,i), which is measured as
follows,
)}1,(),1,(max{
0)0,,(
)1(),,(),,(
1





ibNiaNm
baLED
iibaHibaLED
m
f
f
(2)
where N(a,i-1) the number of nodes at the level i-1
in the tree a. H
f
(a,b,i) denotes the Hamming distance
between the codes that present at the level i and
belong to the same father node at the level i-1. It
implies that the same father node in two trees may
contain different children nodes so that we exploit
the Hamming distance to measure this difference.
For example, the Fig. 1 shows four structures of
XML documents. Their LEDs at each level are
different from each other.
(5) To sum the LED at each level with level
weight to get the final LED between two trees as
follows.




n
i
i
ibaLEDbaLED
0
10),,(),(
(3)
where LED(a,b)denotes the final distance between
tree a and tree b, i denotes the level of the tree
structure, n denotes the max level between the tree a
and tree b.
3 PREPARATORY EXPERIMENT
It is not easy to collect a large scale of the UML2.0
based materials. We download 150 UML model
documents from the OMG Formal Specifications
website
*
and select 50 XMI documents to test our
idea. The LED value of each document pair is
computed to get a LED based similarity matrix,
which is compared with Wen’s ED based similarity
matrix.
The Figure 2 compares the ED and LED
distances of a selected XMI document to all the
other 49 XMI documents. The distance distributions
*
http://www.omg.org/spec/
Measuring UML Model Similarity
321

over 2 matrices are very similar except a few points,
such as the 36th XMI pair in the figure 2. We check
the XMI pair and find that it has a very big
difference at some levels as shown in table3.
Table 3: The LED value of the 36th pair at each level.
level
0
1
2
3
4
5
6
LED
0
1
98
185
79
48
16
It is clear that the difference of the nodes in the
two trees at the level 2 is 98 so that
LED(a,b,2)10
-2
=0.98. That indeed leads to 0.9
increment at the level 1. In a similar way, the
difference at the level 3 is 0.185, which leads to 0.1
increment at the level 1 and 0.08 at the level2. These
excess increments disturb the final similarity
evaluation. It implies that 10 is not the best level
weight’s base.
Table 4: Running time of LED and ED.
Number of XML
Total Size in MB
Running time in second
ED
LED
10
0.5713
2.6400
2.5469
50
1.52
35.6559
34.7809
100
4.45
216.9690
195.9379
200
10.42
808.546
809.9219
400
28.8
3359.5620
3330.3129
However, the LED has the same resolution
ability with ED whereas LED needs only 1 primitive
operation. In order to precisely evaluate the
difference between LED and ED, we calculate the
standard deviation of them as follows.



P
i
i
dd
P
DE
1
2
)(
1
(4)
Where P is the number of XML document pairs.
iii
EDLEDd 
denotes the difference between
the LED of the ith XMI document pair and the ED
of that pair. The
d
is the average of
i
d
. The
standard deviation of the difference between LED
and ED over 50 XMI documents is 0.2462.
In order to test the speed of the methods, the 50
XMI documents are duplicated many times to get
the 100, 200 and 400 XMI test documents, as shown
in the table4, which compares the running time of
two methods. The fact is that LED is a little faster
than ED.
4 CONCLUSIONS
In order to efficiently reuse amount of existed UML
models and effectively evaluate the similarity of
requirement documents, we present a modified edit
distance method, called LED, to measure the
similarity of UML models in XMI format. The main
contributions of the LED are:
Figure 2: The ED and LED of the selected XML document
to the others.
(1) LED needs only 1 primitive operation
whereas the traditional edit distance needs 3
operations. As a result, the LED is easy to
understand and program. Additionally, LED is a
little faster than ED.
(2) LED ignores the tags’ semantic so as to
measure the pure structure similarity. In this way, it
is easy to find the similar requirement in spite of
different application background. That is to say, it is
useful for developer to concentrate on upper level
abstract model and promote reusability of existed
models.
(3) LED considers the difference at each level
and assigns greater weight to lower level. So it
satisfies our up-down comparison intuition. The far
small detail branches in trees have small effect on
the similarity.
However, the LED method has a few defects that
lead to a jump of the extreme wide layer. We will
find a better level weight to solve the problem.
Furthermore, the semantic information is crucial to
finally fulfil the user requirements. LED can be used
to find the appropriate models at the start of the
development, not the whole life cycle. We are going
to research a semantic-included XMI similarity
measure model to solve the issue.
ICSOFT 2012 - 7th International Conference on Software Paradigm Trends
322

ACKNOWLEDGEMENTS
This research is supported by National Natural
Science Foundation of China (Grant 60903123), the
Fundamental Research Funds for the Central
Universities and the Baidu Theme Research Plan on
Large Scale Machine Learning and Data Mining.
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