 Open Access
 Total Downloads : 120
 Authors : Ashraf B. ElSisi, Hamdy M. Mousa, Mohamed G. Malhat
 Paper ID : IJERTV3IS070727
 Volume & Issue : Volume 03, Issue 07 (July 2014)
 Published (First Online): 21072014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Reducing SquareError of JarvisPatrick Algorithm for Drug Discovery
Ashraf B. ElSisi, Hamdy M. Mousa, Mohamed G. Malhat Computer Science dept., Faculty of Computers and Information, Menofia University, Egypt
AbstractClustering algorithms play an important role in chemoinformatics and especially in the drug discovery process. Clustering methods may be hierarchical or nonhierarchical. Nonhierarchical algorithms have fast processing for clustering large chemical data sets than hierarchical algorithms. One of the most popular nonhierarchical clustering algorithms that are used in many applications in the drug discovery process is JarvisPatrick algorithm. The applications of JarvisPatrick in the drug discovery process are compound selection, compound acquisition, lowthroughput screening and Quantitative StructureActivity Relationship (QSAR) analysis. JarvisPatrick groups compounds in a cluster based on a three neighborhood conditions. These three conditions groups compounds, which are not similar enough, in the same cluster. Adding dissimilar compounds in the same cluster will lead to poor compound selection, compound acquisition and QSAR analysis. In this paper, standard JarvisPatrick is modified by adding a fourth condition which computed only if the three standard conditions are true. This condition computes the increasing in the value of Square Error (SE) of the cluster by adding a compound and compares it with expected increasing in SE to determine whether to add a compound to the cluster or not. The result shows that our modification produces clusters with more similar compounds and still has fast processing.
KeywordsChemoinformatics; Drug Discovery; Non hierarchical Clustering; JarvisPatrick

INTRODUCTION
The use of clustering for chemical applications is based on similar property and activity principle which states that compounds with similar structures are likely to exhibit similar properties, which known as StructureProperty Relationship (SPR), and similar activities which known as Structure Activity Relationship (SAR) [1]. Clustering algorithms, which are used in chemical application, must group more similar compounds in term of properties or activity in the same cluster based on their structure. Most clustering algorithms for chemical application cover the area of drug discovery process [2, 3]. The drug discovery is the process of making drugs that response to diseases with fewer side effects. It consists of seven steps: disease selection, target hypothesis, leads compound identification, lead optimization, preclinical trial, and clinical trial and pharmacogenomic optimization [4].
Chemoinformatics are used in lead compound identification and optimization steps [5]. Chemoinformatics are the application of informatics methods that are used to
solve chemical problems. It is a new discipline emerging from storing, manipulating, processing, design, creation, organization, management, retrieval, analysis, dissemination, visualization, and use of chemical information. The use of chemoinformatics becomes a critical part of the drug discovery process as it accelerates the drug discovery process and reduces the overall cost [6, 7]. There are many applications of chemoinformatics in the drug discovery such as compound selection, compound acquisition, virtual library generation, virtual screening, QSAR analysis and Absorption, Distribution, Metabolism, Elimination, and Toxicity (ADMET) prediction [811]. Central tasks of most of these applications are the establishment of a relationship between a chemical structure and its biological activity and the prediction of pharmacological properties in addition to lead finding [5, 6].
Clustering algorithms are used in most of these applications as a method of selection, diversity analysis and data reduction. Compared to the other costs of drug discovery, clustering can add significant value at minimal cost [12]. Clustering algorithms divided into two main categories hierarchical and nonhierarchical. JarvisPatrick is one of the most popular nonhierarchical clustering algorithms that has a wide range of applications in chemoinformatics because of it is fast processing for clustering large chemical data sets and ease implementation. Standard implementation of Jarvis Patrick may group compounds in one cluster that are not similar enough because the compounds satisfy the three neighborhood conditions. Adding dissimilar compounds in the same cluster will increase the value of SE in clusters and lead to increase in the SSE (the sum of SE for all clusters) of the produced clusters. SSE is one of the quality measures that used to evaluate clustering algorithm in its ability to group more similar compounds in the same cluster.
Standard JarvisPatrick is modified by adding a condition that will be computed only if the standard JarvisPatrick conditions are true. This condition will determine if to add a compound to a cluster or not. The condition computes the increasing in value of Square Error (SE) of the cluster by adding this compound and compares it with expected increasing in SE. If this increasing is less than or equal to the expected increasing then the compound will be added to the cluster else the compound will not be added. The results show that by adding this condition, JarvisPatrick will not add dissimilar compounds to the same cluster and still has fast processing. The organization of this paper is as following. In
section 2, standard JarvisPatrick and its usage in chemoinformatics are overviewed. In section 3, our modification on JarvisPatrick is proposed. In section 4, modified JarvisPatrick is compared with standard Jarvis Patrick and their implementation and experimental results are discussed. Finally in section 5, conclusion is given.

JARVISPATRICK CLUSTERING USAGE IN CHEMOINFORMATICS
Clustering methods are used in a number of disciplines such as computer science, information technology, information system, engineering, bioinformatics and chemoinformatics. The main using of clustering methods in chemoinformatics is to group similar compounds in a cluster based on the underlying distribution of input. After grouping these compounds, the activity of compound is predicted based on known compounds activity that are in the same cluster.
JarvisPatrick is one of the most popular methods that have a wide range of applications in chemoinformatics because of its ability to handle large data sets in reasonable time, ease implementation and the availability of an efficient commercial implementation from Daylight for handling very large data sets [13]. JarvisPatrick is nonhierarchical non overlapping clustering method. Nonoverlapping means that each compound can be only in one cluster. Nonhierarchical means that data set is analyzed to produce a single partition of the compounds resulting in a set of clusters.
Standard JarvisPatrick method proceeds in two levels [14]. In the first level, a list of the top K nearest neighbors (K is usually16) is generated for each compound in the data set. The nearest neighbors are usually determined by the Euclidean distance for numerical descriptor and by the Tanimoto coefficient for binary descriptor [15]. In the second level, the nearestneighbor lists are scanned to create clusters that satisfy the three following neighborhood conditions:

The top K nearestneighbor list of compound i must contain compound j.

The top K nearestneighbor list of compound j must contain compound i.

The top K nearestneighbor lists of compound i and j must have at least KMi common compounds (Kmin is determined by user and in the range 1 to K).
The pairs of compounds, that don't satisfy any of the above three conditions, are not put into the same cluster. The value of top K nearestneighbors specifies the number of compound's neighbors to consider when counting the number of mutual neighbors shared with another compound. This value must be at least 2. Lower values make the algorithm to finish faster, but the final set of clusters will have many small clusters. Higher values cause the algorithm to take longer time to finish, but may result in fewer clusters and clusters that form longer chains. The KMin specifies the minimum
Several modifications have been developed to overcome singletons problem such as:

A variablelength nearestneighbor list [16], a proximity threshold is used to determine a variable number of neighbors for each compound. All neighbors that pass the threshold test are considered as neighbors to this compound. By this modification, outliers are prevented from joining a cluster while preventing the arbitrary splitting of large clusters arising from the limitations imposed by fixed length lists.

Reclustering of singletons [17], standard Jarvis Patrick is applied in an iterative way to remove the singletons. The singletons are assigned to a cluster using less strict parameters than defined by user. This iterative way is repeated until a fewer a specified percentage of singletons remain.

Fuzzy clustering [18], all compounds are assigned a probability that determines the distances of compounds from each cluster. The singletons are assigned to its nearest cluster based on specified threshold probability. For singletons that not exceed threshold, they will be regarded as outliers and remains as singletons.
The applications of JarvisPatrick clustering in chemoinformatics are compound selection, compound acquisition and high throughput screening. In [19], Jarvis Patrick is used to cluster a data set of about 240,000 compounds for compound selection. Singletons are moved to the nearest nonsingleton cluster. Then cluster centroids are calculated for each cluster to select representative compounds based on their closet centroid. In [20], Jarvis Patrick is to assist lowthroughput screening and to support QSAR analysis by analyzing databases for efficient compound acquisition. In [17], JarvisPatrick is used for high throughput screening by the selection of compounds from the corporate database. In [18], JarvisPatrick is used for analysis of the compound database to support high throughput screening.
The previous modifications are developed to overcome the singletons problem. The three neighborhood conditions of JarvisPatrick don't guarantee to group more similar compounds in the same cluster. So, the produced clusters have large SSE values. In the next section, the standard Jarvis Patrick algorithm will be modified by adding a fourth condition to overcome this problem.


PROPOSED MODIFICATION ON STANDARD JARVISPATRICK
The standard JarvisPatrick will be modified by adding a fourth neighborhood condition that will be computed only if the three previous neighborhood conditions are true. The fourth condition will compute the increasing in SE for a cluster contains compound i after adding compound j to this cluster and compare it with expected increasing in SE. First, for the cluster of n compounds each represented by a vector. The vector of the cluster centroid, x(c), is defined as
=1
number of mutual nearest neighbors that the two compounds must have to be in the same cluster. This value must be at least 1 and must not exceed the value of the K nearest neighbors. Lower values result in clusters that are compact. Higher values result in clusters that are more dispersed.
The standard implementation of JarvisPatrick produces a large number of singletons and clusters with large SSE.
X c = (1 )
x(r)
(1)
Subset Name
Number of Compounds
SE
NCI1
100
25.61546473
NCI2
500
791.56501
NCI3
1000
1838.0002
The centroid is the simple arithmetic mean of the vectors of the cluster members. The SE for a cluster is the sum of squared Euclidean distances to the centroid for all n compounds in that cluster. The SE is defined as
TABLE I. THREE SUBSETS OF NCI DATA SET
SE =
=1
[ ]2(2)
The SSE is the summation of SE for all produced m clusters and is defined as
BCUT descriptor is used to represent compounds in the three subsets [22]. For each NCI subset, 4 runs are recorded with K=16 and KMin= 4, 8, 12 and 14 for each run. Table 2 shows the K, KMin, Number of Clusters (NOC),
=1
SSE =
(3)
Computation time in milliseconds and SSE of standard Jarvis Patrick algorithm. Tables 3, 4, 5 and 6 show the same
The increasing in SE is the difference between the value of SE for the cluster containing i after adding compound j and before adding compound j. The increasing in SE is defined as
Increasing in SE =
(4)
The expected increasing in SE is the SE for data set divided by number of compounds n multiplied with a user specified ratio r; r is a value between 0 and 1. Small values of r will ensure that more similar compounds will be grouped into the same cluster. The expected increasing in SE is defined as
Expected increasing in SE =
information for modified Jarvis Patrick algorithm where r = 1.0, 0.5, 0.1 and 0.01.
Data set Name
K
K
Min
NOC
SSE
Time in Milliseconds
NCI1
16
4
8
13.29864
40
16
8
10
4.069484
20
16
12
28
1.49243
10
16
14
62
0.238635
10
NCI2
16
4
46
44.92072
190
16
8
63
29.30268
140
16
12
200
14.63466
130
16
14
335
2.768861
120
NCI3
16
4
85
43.46274
480
16
8
126
28.03772
420
16
12
387
11.34654
410
16
14
683
6.63129
410
TABLE II. OUTPUT OF STANDARD JARVISPATRICK ALGORITHM
(5)
If increasing in SE is less than or equal expected increasing, then compound j will be added to the cluster containing compound i, else compound j will not be added to this cluster. By adding this modification, fourth condition will produce clusters with less SSE by not adding the compounds that will increase SE than expected increasing into the same cluster. So, compound selection, acquisition and QSAR analysis will be more efficient and the algorithm still has fast processing because the fourth condition will not be computed only if the three conditions of standad JarvisPatrick algorithm are true.

IMPLEMENTATION ND EXPERIMENTAL RESULTS The implementations of the algorithms are in JAVA, under
Windows7 operating system, Intel corei5, 2.5 GHz and Ram 4 GB. NCI data set, one of the most popular data set, is used for experimental [21]. Three random subsets are taken from NCI data set with the following number of compounds and SE as shown in Table 1.
Subset Name
K
K
Min
NOC
SSE
Time in Milliseconds
NCI1
16
4
10
4.926679
80
16
8
11
3.459389
30
16
12
28
1.457589
30
16
14
62
0.232923
10
NCI2
16
4
48
39.88919
270
16
8
65
24.27115
150
16
12
201
11.79896
140
16
14
335
2.768861
140
NCI3
16
4
84
40.29349
620
16
8
126
23.87385
460
16
12
378
11.19564
450
16
14
659
6.579031
430
TABLE III. OUTPUT OF MODIFIED JARVISPATRICK ALGORITHM WHERE R = 1.0
NCI3
16
4
171
5.603048
570
16
8
198
4.629283
470
16
12
420
1.893126
440
16
14
677
0.592186
430
TABLE IV. OUTPUT OF MODIFIED JARVISPATRICK ALGORITHM WHERE R = 0.5
MJP r=1.0
MJP r=0.5 MJP r=0.1 MJP r=0.01
4
SJP
Sum of Square Error
Subset Name
K
K
Min
NOC
SSE
Time in Milliseconds
NCI1
16
4
25
0.897523
70
16
8
25
0.896463
50
16
12
36
0.530665
20
16
14
64
0.177409
10
NCI2
16
4
61
11.57974
290
16
8
76
8.472676
170
16
12
208
3.491306
150
16
14
336
1.312308
140
NCI3
16
4
91
25.03054
600
16
8
133
16.17223
480
16
12
382
5.916373
440
16
14
662
2.095064
440
TABLE V. OUTPUT OF MODIFIED JARVISPATRICK ALGORITHM WHERE R = 0.1
Fig.1 shows the SSE for the Standard JarvisPatrick (SJP) and Modified JarvisPatrick (MJP) where r = 1.0, 0.5, 0.1 and
14
12
10
8
6
4
2
0
Subset Name
K
K
Min
NOC
SSE
Time in Milliseconds
NCI1
16
4
13
2.894775
90
16
8
13
2.878076
30
16
12
30
0.858161
20
16
14
62
0.232923
20
NCI2
16
4
52
29.29845
270
16
8
67
16.73628
180
16
12
203
7.632148
150
16
14
336
2.705852
140
NCI3
16
4
84
39.44875
610
16
8
126
23.02911
460
16
12
378
9.807962
430
16
14
659
5.191356
410
0.01 for the three subsets. As shown in Fig.1, our approach produces clusters with less or equal SSE than SJP for all subsets with KMin = 4, 8, 12 and 14. For example in NCI1 subset when KMin = 4, SJP produces clusters with SSE equal 13.2986 and MJP produces clusters with SSE equal 4.9266 where r = 1.0, 2.8947 where r = 0.5, 0.8975 where r = 0.1 and 0.0313 where r = 0.01. When KMin = 14, SJP produces clusters with SSE equal 0.2386 and MJP produces clusters with SSE equal 0.2329 where r = 1.0, 0.2329 where r = 0.5, 0.1774 where r = 0.1 and 0.0194 where r = 0.01. From previous results, as the value of KMin increase, MJP produces clusters with SSE less than or equal to SJP. When K Min decrease, MJP produces clusters with SSE less than SJP for all values of r.
Value of KMin
Subset Name
K
K
Min
NOC
SSE
Time in Milliseconds
NCI1
16
4
70
0.031339
70
16
8
70
0.031339
50
16
12
72
0.02826
30
16
14
78
0.01946
10
NCI2
16
4
117
2.293131
270
16
8
130
1.933292
180
16
12
237
0.764977
140
16
14
348
0.368605
140
TABLE VI. OUTPUT OF MODIFIED JARVISPATRICK ALGORITHM WHERE R = 0.01
(a)
14
12
8
NCI1
50
Sum of Square Error
40
30
20
10
0
4 8 12 14
Value of KMin
(b)
SJP
MJP r=1.0 MJP r=0.5 MJP r=0.1 MJP r=0.01
NCI2
45
35
25
15
5
SJP
MJP r=1.0 MJP r=0.5 MJP r=0.1
MJP r=0.01
Value of KMin
14
12
8
MJP r=1.0
MJP r=0.5 MJP r=0.1 MJP r=0.01
4
SJP
400
350
300
250
200
150
100
50
0
NCI2
Value of KMin
14
12
8
4
5
NCI3
Sum of Square Error
Number of Clusters
(c)
Figure 1. SSE of SJP and MJP for three subsets where r = 1.0, 0.5, 0.1 and 0.01
Fig.2 shows the number of clusters generated by SJP and MJP where r = 1.0, 0.5, 0.1 and 0.01 for the three subsets. As shown in Fig.2, the number of clusters generated by our approach is large than or equal to the number of clusters generated by SJP for all subsets with KMin = 4, 8, 12 and 14. For example in NCI1 subset when KMin = 4, SJP produces 8 clusters and MJP produces 10 clusters where r = 1.0, 13
MJP r=1.0
MJP r=0.5 MJP r=0.1 MJP r=0.01
4
SJP
80
70
60
50
40
30
20
10
0
Number of Clusters
clusters where r = 0.5, 25 clusters where r = 0.1 and 70 clusters where r = 0.01. When KMin = 14, SJP produces 62 clusters and MJP produces 62 clusters where r = 1.0, 62 clusters where r = 0.5, 64 clusters where r = 0.1 and 78 clusters where r = 0.01. From previous results, as the value of KMin increase MJP and SJP produce similar number of clusters and when KMin decrease MJP produces more clusters than SJP for all values of r.
Value of KMin
14
12
8
NCI1
(a)
(b)
Value of KMin
14
12
8
MJP r=1.0
MJP r=0.5 MJP r=0.1 MJP r=0.01
4
SJP
700
600
500
400
300
200
100
0
NCI3
Number of Clusters
(c)
Figure 2. Number of Clusters of SJP and MJP for three subsets where r = 1.0, 0.5, 0.1 and 0.01
Fig.3 shows the time required in milliseconds for SJP and MJP where r = 1.0, 0.5, 0.1 and 0.01 for the three subsets. As shown in Fig.3, The time required for our approach is large than or equal to the time required for SJP for all subsets with KMin = 4, 8, 12 and 14. For example in NCI1 subset when KMin = 4, SJP takes 60 milliseconds and MJP takes 60 milliseconds where r = 1.0, 90 milliseconds where r = 0.5, 70 milliseconds where r = 0.1 and 70 milliseconds where r =

When KMin = 14, SJP takes 10 milliseconds and MJP takes 10 milliseconds where r = 1.0, 20 milliseconds where r = 0.5, 10 milliseconds where r = 0.1 and 10 milliseconds where r = 0.01. From previous results, as the value of KMin increase MJP and SJP take similar computation time and when KMin decrease MJP takes more time than SJP for all values of r. The increasing in time for MJP represents the overhead time needed to process the fourth condition.
100
Time in Milliseconds
80
60
40
20
0
4 8 12 14
Value of KMin
(a)
SJP
MJP r=1.0 MJP r=0.5 MJP r=0.1 MJP r=0.01
condition. The increasing in time needed by our approach is overhead time to apply the fourth condition.


CONCULSION
NCI1
The demands of clustering data sets of several million compounds with highdimensional representations led to the widespread adoption of a few inherently efficient and optimally implemented methods. JarvisPatrick is one of the most popular clustering methods that have many applications in chemoinformatics such as compound selection, compound acquisition, leadfinding and QSAR analysis. In this paper, standard JarvisPatrick is modified in order to group more similar compounds in the same cluster and avoiding adding compounds to clusters that will increase SSE. The results show that our modification produces clusters with less SSE than standard JarvisPatrick. So, compound selection, acquisition and QSAR analysis will exhibit better efficiency and at the same time JarvisPatrick still has fast processing. In the future work, Modified JarvisPatrick will be applied for large chemical data sets and will be compared with ward clustering algorithm.
SJP
300
250
200
Time in Milliseconds
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150
MJP r=1.0
100
50
0
700
Time in Milliseconds
600
500
400
300
200
100
0
4
8
12
14
Value of KMin
(b)
4 8 12 14
Value of KMin
(c)
MJP r=0.5
MJP r=0.1
MJP r=0.01
SJP
MJP r=1.0 MJP r=0.5 MJP r=0.1 MJP r=0.01
NCI3

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