Subgraph relative frequency approach for extracting interesting substructur

International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 4, July-August (2013), © IAEME
400
SUBGRAPH RELATIVE FREQUENCY APPROACH FOR EXTRACTING
INTERESTING SUBSTRUCTURES FROM MOLECULAR DATA
Mr. M.A.Srinuvasu1
, Dr. P. Padmaja2
, Mr. Y. Dharmateja3
Department of CSE & IT, GITAM University, Visakhapatnam-530045, INDIA
ABSTRACT
The classification of unseen molecule in molecular data is done by taking the substructures of
the molecule. The mining of interesting substructures in molecular data for classification contain
subgraphs that are characterized by different classes. In this paper, authors suggest a Subgraph
Relative Frequency (SRF) method that screens each frequency subgraph to determine whether the
substructure that occurs frequently is an interesting one or not. SRF thus discovers interesting
subgraphs for each of these classes which are calculated using relative frequencies. To classify an
unknown molecule, SRF first finds the subgraph of the molecule and calculates the interestingness of
the sub-graph for each class, based on the weight. The performance of SRF is compared against
MISMOC and is found to be just as accurate as MISMOC. MISMOC approach requires probability
calculations to find the absolute frequency, thus the complexity is increased. The proposed method
decreases the above complexity by just calculating the relative frequency to determine the
interestingness. The method was experimented on a small predefined molecular data and the analyses
of the result were done. Thus the performance of the proposed SRF approach was found satisfactory
and efficient.
Keywords: Frequent subgraph, graph mining, interestingness, molecular structure classification,
SRF, MISMOC.
I. INTRODUCTION
Data mining tasks help in discovering non-trivial patterns that are difficult to find manually.
Data mining has recently attracted considerable attention from database practitioners and researchers
because of its applicability in many areas such as decision support, market strategy and financial
forecasting. Database technology has been used with great success in traditional data processing. But
with the ability to store enormous amounts of business data, it is important to find a way to mine that
directly from the database and extract nuggets to leverage for business advantage. If the data can be
mined directly, it can be used to find abstractions or relations that improve the understanding of the
INTERNATIONAL JOURNAL OF COMPUTER ENGINEERING &
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ISSN 0976 – 6367(Print)
ISSN 0976 – 6375(Online)
Volume 4, Issue 4, July-August (2013), pp. 400-411
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401
data and help in making business decisions. Transactional mining (association rules, decision trees
etc) can be effectively used to find non-trivial patterns in categorical and unstructured data. For
applications that have an inherent structure (e.g. chemical compounds, proteins) graph mining is
appropriate, because mapping the structure data into other representations would lead to loss of
structure. Various kinds of data such as social network data, Protein and other Bioinformatics data
can be effectively represented as graphs [1]. A graph representation provides a natural way to
express relationships within data. Graph based data mining expresses data in the form of graphs, and
focuses on the discovery of interesting sub-graph patterns [2][3]. Graphs are being increasingly used
to models wide range of scientific data. Such widespread usage of graphs has generated considerable
interest in mining patterns from graph databases. Graph mining is appropriate as compared to other
techniques as mapping them into other representations would lose the inherent structure. Graph
mining uses the natural structure of the application domain and mines over that structure. Graph
mining consists of algorithms like SUBDUE [4] (holder et al.KDD’94 is for the incomplete beam
search, WARMR [5] (Dehaspe et al KDD’98) is used for inductive logical programming. Graph
theory –based approaches are classified into two apriori-based approach [6] and pattern- growth
approach [7][8]. Graph mining methods for mining the frequent subgraphs. Frequent subgraph
mining approaches under the apriori-based approach. FSG [6], FFSM (Fast Frequent Subgraph
Mining) and pattern growth approach are gSpan [9], MoFa [12], Gaston [12] are to follow some
search orders like DFS and BFS. To elimination of duplicates subgraphs it use passive vs active. For
discover order of patterns it like to path, tree, or graph. Graph mining they have classification and
clustering. Graph clustering is finding similarity measures in two ways first is feature-based
similarity and structure-based similarity. Graph classification having four types of approaches [10],
first is local structure based approach, second is graph pattern-based approach, next kernel-based
approach and boosting. MISMOC [13] is the method for discovering the interesting molecule
substructures for classification. RE_MISMOC [14] is a method of improving the MISMOC by the
relative frequency. The format of representing the molecule structures in SMILES notation [15].
Areas of applications are Drug discovery, Protein Folding, Comparative Genomics, Cancer Risk
Assessment, Gene evolution. The size and number of molecular structure databases have been grown
rapidly due to the advances in X-ray diffraction or nuclear magnetic resonance (NMR) technologies.
Molecular databases of nucleotide, genome, protein and nucleic acid, etc, the databases continue to
grow in size and diversity, and there is an increasing need for techniques to be developed to mine
these data for interesting patterns.
II. LITERATUR STUDY
L. B. Holder, et al [4] present a method for Substructure discovery in the SUBDUE system.
This algorithm begins with the substructure matching a single vertex in the graph, selects the best
substructures and expands the instances of these substructures by one neighbouring edge in all
possible ways. It retains the best substructures in a list; the total amount of computation exceeds a
given limit. The evaluation of each substructure is guided by the minimum description length
principle and background knowledge rules provided by the user.
M. Kuramochi et al [6] suggested data mining techniques that are being increasingly applied
to non-traditional domains, existing approaches for finding frequent item sets cannot be used as they
cannot model the requirement of these domains. An alternate way of modelling the objects in these
data sets is to use a graph to model the database objects. This paper describes a computationally
efficient algorithm for finding all frequent sub graphs in large graph databases. We evaluated the
performance of the algorithm by experiments with synthetic datasets as well as a chemical compound
dataset. The empirical results show that our algorithm scales linearly with the number of input
transactions and it is able to discover frequent sub graphs from a set of graph transactions reasonably

402
fast, even though we have to deal with computationally hard problems such as canonical labelling of
graphs and sub graph isomorphism which are not necessary for traditional frequent item set
discovery.
Chan, et al [7] describes an inductive method that is capable of detecting the inherent patterns
in such a sequence and to make predictions about the attributes of future events. Unlike previous AI-
based prediction methods, the proposed method is particularly effective in discovering knowledge in
ordered event sequences even if noisy data are being dealt with. The method can be divided into
three phases: (i) detection of underlying patterns in an ordered event sequence; (ii) construction of
sequence-generation rules based on the detected patterns; and (iii) use of these rules to predict the
attributes of future events.
K. C. C. Chan et al [8] gave a method for the efficient acquisition of classification rules from
training instances which may contain inconsistent, incorrect, or missing information. This algorithm
consists of three phases: (i) the detection of inherent patterns in a set of noisy training data; (iii) the
construction of classification rules based on these patterns; and (iii) the use of these rules to predict
the class membership of an object. Being able to handle uncertainty in the learning process, the
proposed algorithm can be employed for applications in real-world problem domains involving noisy
data.
X. Yan et al [9] discovered a method for frequent graph-based pattern mining in graph
datasets and gSpan (Graph-based substructure patter mining) which is the first algorithm that
explores depth-first search (DFS) in frequent subgraph mining. This algorithm consists of two phases
(i) DFS Lexicographic order (ii) minimum DFS code which forms a novel canonical labelling system
to support DFS search. gSpan discovers all the frequent subgraphs without candidate generation and
false positive pruning.
Winnie W. M. Lam et al [13] describes a novel technique called mining interesting
substructures in molecular data for classification (MISMOC) that can discover interesting frequent
sub graphs not just for the characterization of a molecular class but also for the distinguishing of it
from the others. Using a test statistic, MISMOC screens each frequent sub graph to determine if they
are interesting. For those that are interesting, their degrees of interestingness are determined using an
information-theoretic measure. When classifying an unseen molecule, its structure is then matched
against the interesting sub graphs in each class and a total interestingness measure for the unseen
molecule to be classified into a particular class is determined, which is based on the interestingness
of each matched sub graphs.
Maryam Kohzadi, et al [14] propose a novel technique called RF_MISMOC (Relative
Frequency MISMOC) for computing interestingness of patterns in each class .The performance of
the base algorithm by selecting equal numbers of interesting indicator patterns of classes and also
determining optimum threshold value for selection of indicator patterns. This is an improvement over
the original MISMOC algorithm.
III. RELATED WORK
1. MISMOC algorithm [13] is used in chemical molecular classification by considering the graph
structure for them. MISMOC performs its tasks for searching the frequent subgraphs using an
existing algorithm like FSG [6] or GSpan [7].
Here are some probabilistic formulas for calculating
Discovering interesting frequent subgraphs:

403
Interesting Measures as a Function of the Weight of Evidence:
Based on the mutual information measures, the weight of evidence is
Classification Using a total interestingness Measures
These are the probabilistic calculations in the MISMOC Algorithm.
2. RF_MISMOC [14], Relative Frequency MISMOC is extracted from the technique of mining
interesting substructures in molecular data for classification. This algorithm motive is to
improvement of MISMOC graph based classification by using relative frequency of the interesting
patterns instead of absolute frequency, numIntrsPatterns is the number of all interesting patterns in
one class and numClass is the number of classes in the problem and the F(x).
Determining interesting patterns as follows- First of all convert training data to sequence of
one and zero. Second apply IODLG algorithm to find the patterns with more frequently than minsup,
next compute value of d parameter for all frequency pattern, next select the threshold between 1-2
and select frequently patterns that have a value of d more than the threshold. Next determine
minimum number of interesting patterns that selected in classes. And sort frequent patterns based on
value of d, and select the first minIntrs patterns from each class.
Illustrative example:
To explain the discovery of frequent subgraphs may, we are given three classes of artificial
molecular data shown in Fig. 1. Each of these three classes of data contains eight molecules
represented in SMILES notation [15] and each molecule consists of atoms connected with bonds.
These molecules can be represented as labelled molecular graph with each node used to represent an
atom and each edge as a bond.
Given the set of graph data as shown in Fig.1, frequent subgraphs can be discovered in each
class1, 2 and 3 using a graph-mining algorithm, such as FSG [6]. In FSG algorithm molecular
structures are converted to subgraph structures then finding the interesting relative frequency and the
unseen molecules are predicted. The unseen molecular structures are in Fig. 2(a), 2(b).

404
Fig.1. Training molecular data
Let us consider an unseen molecule like
C[I+](O)O[Mo](N=O)([U]1[U][U][U][U][
U]1)([No]1[No][No]1)C(=O)C(F)(F)F
Fig. 2(a)
C[Pt](C)C([Co]SC#N)[Co++](N=[N+]=[N
H2+])([Pu](N)[Pu]=O)[Y](N)=O
Fig. 2(b)
Fig.2. Unseen molecule

405
III. METHODOLOGY
The (subgraph relative frequency) SRF methodology discovers the unknown molecule
classification. The SRF describes first consider the training molecule data, from that finding the
subgraphs by using FSG [6] algorithm. Based on the FSG it obtains the relative frequency. By
considering relative frequency values evaluate the interestingness frequency subgraphs by threshold.
Consider one unknown molecule not in training molecule data, classifying that unknown molecule
belongs to particular class. The block diagram is shown in Fig 1.
Fig.3. SRF Block Diagram
Subgraph Relative Frequency (SRF)
The unseen molecular classification problem, which this paper organization is to be stated as
follows. Let us consider the predefined molecule structure data G (Fig 2.traing molecule data set),
containing n molecules are pre-classified into p classes, the unseen molecular problem concerned
with the discovering of interesting patterns in the data to “unseen” molecule not in G to be correctly
classified into one of the p class. The n molecules of graph G can be represented as G1, G2,..., Gn ,
where Gi = Gi (Vi, Ei), i {1,....,n},the vertices representing as atom and edge represented as bonds
between atoms. The p classes that the n molecules are their corresponding molecules structures are
classified, which are represented as C(1)
,....C(p)
, where C(i)
={G1
(i)
,....., Gci
(i)
}‫ك‬G,i=1,....,p.
In the following we present the details of SRF technique is effectively improving the accuracy of
molecular graph classification. This SRF performance the several various tasks. It first searches for
the frequent subgraphs by using existing algorithm FSG[6]. Next calculate the relative frequency
value and interesting subgraph frequency and at last unseen molecular classification.
A. Discovering frequent subgraph molecule
To discover frequent subgraph in a molecular data base, there are several graph mining
algorithms to choose.SRF using the FSG graph mining algorithm. Given molecular data set
G={G1,........, Gn}by the algorithm to discover a set of frequent sub graphs F(1)
,...., F(p)
, where F(1)
={
F1
(i)
,......, Fni
(i)
}, i=1,....,p, for each of the corresponding p classes C(i)
,...,C(p)
.
The FSG algorithm can find all the frequent sub graphs in each class of molecular graphs
using the apriori algorithm. Briefly, FSG [6] described as follows. For each C(i)
in G, i =1,....p. FSG
first finds a set of frequent subgraphs of one-edge and two-edge. Based on these two intermediate
subgraphs, it starts to iterate general frequent candidate subgraph. FSG counts the general frequency
candidates and prune subgraphs that do not satisfies the threshold and verifying the same support
condition to prune the lattice of frequent subgraphs. Finally the frequent subgraphs F(1)
,F(2)
,......,F(p)
.where F(i)
contains all the k-frequent subgraphs ,are generated by each class. Let gk
be a k-subgraph
with k-edges, Dk
be the set of all candidate subgraphs with k-edges, Fk(i)
be the set of frequent k-
subgraph for class C(i)
, the algorithm of FGS is summarized in Fig 4.
Training
molecule
data
Finding
sub-graphs
by FSG
Obtains
Relative
frequency
from FSG
table
SRF
condition gets
the interesting
frequency sub
graphs
Classify
the
unknown
molecule

406
Fig. 4. Algorithm of FSG
B. Discovering interesting frequent subgraphs by SRF
The aim of FSG [6] to discover the frequent subgraph F(i)
={F1
(i)
,......., Fni
(i)
}, i=1,..., p in each
of the corresponding graph class C(1)
,....., C(p)
. A frequent subgraph, which appears frequently in one
graph, may also do so in another and such frequent subgraphs are not interesting for classification. In
this paper, we presenting a methodology that is SRF used to identify the interesting subgraphs that
are interesting and useful for classification. This methodology is based on the relative frequency
values on use of simple arithmetic calculation and the algorithm given in Fig. 5.The calculation of
discovering the relative frequency of F1
(i)
for C(1)
is F1
(i)
( C(i)
) - (least frequency of F1
(i)
in all of the
classes) repeat the iteration for rest of the relative frequency values of a graph molecule in a classes
C(i)
. The interesting frequency subgraph are shown in table I and found by using the D, the highest
relative frequency value of a subgraph F1
(i)
for a class C(i)
subtracted from the second highest relative
frequency value of a subgraph F1
(i)
for a class C(i)
. If D ≥ 30% of class size based on this condition
the interesting relative subgraphs are classified. The set of interesting frequent subgraph discovered
from each of C(1)
,....., C(p)
is denoted as F′(i)
= {F1
′(i)
,...., Fn
′(i)
},i=1,...,p respectively.

407
Fig.5. Algorithm of SRF
C. Classification of unseen molecule of a class.
Given the interesting frequent subgraphs F1
′(1)
,...., Fn
′(p)
, discovering for each corresponding p
classes C(1)
,...., C(p)
,an “unseen” molecule graph is not in graph data G, classified by matching it
against the subgraphs in each of F′(i)
,i=1,...,p.
SRF computes the total interestingness defines as summation of the total interesting frequent
subgraphs F1
′(i)
for against G to classified into C(i)
as follows:
I(i)
(G) = I(G‫א‬ C(i)
/G‫ב‬ C(i)
|G is characterized by F1
′(i)
,...., Fn
′(i)
)
ൌ ෌ IሺG ‫א‬ Cሺiሻ/G ‫ב‬ Cሺiሻ|G
௡௜
௝ୀ଴
is characterized by Fj
′(i)
)
The total interestingness for G classified into each of C(1)
,...,C(p)
is determined and SRF assign G to
the class, which gives the greatest total interesting measure.

408
Table I: Interestingness of FSG
Molecule and
Smiles Notation
Class
1
Class
2
Class
3
S1
(i)
N=O
7
0
8
1
7
0
S2
(i)
C[Pt](C)C
2
0
5
3
6
4
S3
(i)
N[Pu+][Pu]=O
4
2
5
3
3
0
S4
(i)
ClC(Cl)Cl
5
4
1
0
1
0
S5
(i)
OS(O)(=O)=O
5
5
0
0
1
1
S6
(i)
OP(O)(O)=O
1
0
5
4
1
0
S7
(i)
N=[N+]=[N-]
1
0
3
2
1
0
S8
(i)
F[C](F)(F)=O
0
0
1
1
4
4
S9
(i)
BBB=BBB(BOB=O)B=BB=B/B
1
0
1
0
4
3
S10
(i)
[U]1[U][U][U][U][U]1
1
0
4
3
4
3
S11
(i)
C[I](O)O
5
3
2
0
3
1
S12
(i)
N[Y]=O
3
2
2
1
1
0
S13
(i)
[No]1[No][No]1
4
0
4
0
4
0
S14
(i)
[Ir]1[Ir][Ir][Ir]1
4
0
5
1
4
0
S15
(i)
N#[S]
3
1
2
0
4
2

409
Comparison of the proposed (SRF) with MISMOC and RF_MISMOC
In this paper SRF address that discovering the interestingness of FSG [6] and “unseen”
molecule classification, by using the relative frequency values. This is to be solved by using the
simple arithmetic calculation and reduces the time complexity form the MISMOC. In MISMOC[13]
is done the same thing discovering the interestingness measure of FSG [6] and “unseen “molecule
classification by using the absolute frequency value and doing the probability calculation it shows
that more complexity. While comparing these to methodologies of the result shows the same.
RE_MISMOC [14] is shown the improved performance of MISMOC graph classification algorithm
by taking relative frequency of pattern in each class, by selecting equal number of interesting
indicator pattern class and determined optimal threshold value for the selection of indicator
performance. In this paper, considering the relative frequency and discovering the “unseen” molecule
classification for a class which is not done in RF_MISMOC. Thus the performance of SRF approach
is to discovering the interesting relative frequency and “Unseen” molecule classification is efficient.
IV. EXPERIMENTAL RESULTS
The interestingness of subgraphs using SRF and MISMOC for the above example is
calculated as follows.
Consider an unknown molecule
Mo
N
O
O
No
No No
U
U
U
U
U
U
O
F
F
F
HO
I+
H3C
C[I+](O)O[Mo](N=O)([U]1[U][U][U][U][U]1)
([No]1[No][No]1)C(=O)C(F)(F)F
Fig. 2(a)
These are S1, S8, S10, S11, S13 sub graphs from the table I
The calculation using MISMOC is Class 1 interestingness = Sum of d values for the class 1
of the subgraphs S1, S8, S10, S11, S13 found in unknown molecule= −11.326.Class 2
interestingness = Sum of d values for the class 1 of the subgraphs S1, S8, S10, S11, S13 found in
unknown molecule = -9.104. Class 3 interestingness = Sum of d values for the class 1 of the
subgraphs S1, S8, S10, S11, S13 found in unknown molecule=2.390. Based on the interestingness
values we can classify the unknown molecule. Classification = Class 3.
The calculation using SRF is Class 1 interestingness =2+0+0+0+0=2(2 for S1 relative value in class
1, 0 for S8 relative value in class 1, 0 for S10 relative value in class 1, 0 for S11 relative value in
class 1, 0 for S13 relative value in class 1).Class 2 interestingness = 1+1+1+3+0=6. Class 3
interestingness=3+0+4+3+0=10 Based on the interestingness values classify the unknown molecule.
Classification = Class 3.

410
Consider an unknown molecule
C[Pt](C)C([Co]SC#N)[Co++](N=[N+]
=[NH2+])([Pu](N)[Pu]=O)[Y](N)=O
Fig. 2(b)
These are S2, S3, S10, S7, S12, S15 sub graphs from the Table I.
The calculation using MISMOC is Class 1 interestingness = Sum of d values for the class 1
of the subgraphs S2, S3, S10, S7, S12, S15 found in unknown molecule = −8.034.Class 2
interestingness = Sum of d values for the class 2 of the S2, S3, S10, S7, S12, S15 found in unknown
molecule = -0.719. Class 3 interestingness = Sum of d values for the class 3 of the subgraphs S2, S3,
S10, S7, S12, S15 found in unknown molecule = -16.704. Based on the interestingness values
classify the unknown molecule. Classification = Class 2.
The calculation using SRF is Class 1 interestingness = Sum of relative values for the class 1 of the
subgraphs S2, S3, S10, S7, S12, S15 found in unknown molecule=4. Class 2 interestingness = Sum
of relative values for the class 2 of the subgraphs S2, S3, S10, S7, S12, S15 found in unknown
molecule=8. Class 3 interestingness = Sum of relative values for the class 3 of the subgraphs S2, S3,
S10, S7, S12, S15 found in unknown molecule=6. Based on the interestingness values classify the
unknown molecule. Classification = Class 2. Similarly perform for classification of class 1 also.
V. CONCLUSION
In this paper, we introduced a new graph – mining technique called SRF (subgraph relative
frequency) to discover the unknown molecule subgraphs from graph databases. In SRF, instead of
the absolute frequency subgraph considering the relative frequency value.SRF methodology is best
and effective way to discover the interesting frequent subgraphs for a class and determine the unseen
molecules substructures classification. This algorithm gives less time complexity from previous
methods.
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