Partitioning clustering algorithms for protein sequence data sets

1756-0381-2-3 1756-0381 Research Partitioning clustering algorithms for protein sequence data sets Fayech Sondes sondes_el_feyech@yahoo.fr Essoussi Nadia nadia.essoussi@isg.rnu.tn Limam Mohamed mohamed.limam@isg.rnu.tn

Department of Computer Science, LARODEC Laboratory, Higher Institute of Management, University of Tunis, Tunis, Tunisia

BioData Mining 1756-0381 2009 2 1 3 http://www.biodatamining.org/content/2/1/3 19341454 10.1186/1756-0381-2-3 13 11 2008 02 4 2009 02 4 2009 2009 Fayech et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Background

Genome-sequencing projects are currently producing an enormous amount of new sequences and cause the rapid increasing of protein sequence databases. The unsupervised classification of these data into functional groups or families, clustering, has become one of the principal research objectives in structural and functional genomics. Computer programs to automatically and accurately classify sequences into families become a necessity. A significant number of methods have addressed the clustering of protein sequences and most of them can be categorized in three major groups: hierarchical, graph-based and partitioning methods. Among the various sequence clustering methods in literature, hierarchical and graph-based approaches have been widely used. Although partitioning clustering techniques are extremely used in other fields, few applications have been found in the field of protein sequence clustering. It is not fully demonstrated if partitioning methods can be applied to protein sequence data and if these methods can be efficient compared to the published clustering methods.

Methods

We developed four partitioning clustering approaches using Smith-Waterman local-alignment algorithm to determine pair-wise similarities of sequences. Four different sets of protein sequences were used as evaluation data sets for the proposed methods.

Results

We show that these methods outperform several other published clustering methods in terms of correctly predicting a classifier and especially in terms of the correctness of the provided prediction. The software is available to academic users from the authors upon request.

Background

In bioinformatics, the number of protein sequences is more than half a million, and it is necessary to find meaningful partitions of them in order to detect their functions. Early approaches of comparing and grouping protein sequences are alignment methods. In fact, pair-wise alignment is used to compare and to cluster sequences. There are two types of pair-wise sequence alignments, local and global 12. Smith and Waterman local alignment algorithm 3 helps in finding conserved amino acid patterns in protein sequences. Needleman and Wunsch global alignment algorithm 4 attempts are made to align the entire sequence using as many characters as possible, up to both ends of each sequence. In order to cluster a large data set of proteins into meaningful clusters, the pair-wise alignment is computationally expensive because of the large number of comparisons carried out. In fact, each protein of the data set should be compared to all others of the data set.

For this reason the pair-wise alignment methods are not efficient to cluster a large set of data. These approaches do not consider the fact that the data set can be too large and may not fit into the main memory of some computers.

The main objective of the unsupervised learning technique is to find a natural grouping or meaningful partition using a distance function 56. Clustering is a technique which has been extensively applied in a variety of fields related to life science and biology. In sequence analysis, clustering is used to group homologous sequences into gene or protein families.

Many methods are currently available for the clustering of protein sequences into families and most of them can be categorized in three major groups: hierarchical, graph-based and partitioning methods. Among these various methods, most are based on hierarchical or graph-based techniques and they were successfully established. In fact, COG 7 uses a hierarchical merging of clusters and a manual validation to prevent chaining of multi-domain families. ProtoNet 8 uses a special metric as described by Sasson et al. 9 to merge clusters. Picasso 10 uses multiple alignments as profiles which are then merged hierarchically. ClusTr 11 and GeneRage 12 use standard single linkage clustering approaches. SYSTERS 13 combines hierarchical clustering with graph-based clustering. ProtoMap 14 and N-cut 1516 methods use graph-based clustering approaches. ProClust 17 uses an extension of the graph-based clustering approach proposed by 18. ProClust algorithm is based on transitivity criterion and it is capable of handling multi-domain proteins. TribeMCL 19 applies the Markov clustering approach (MCL) described by Van Dongen 20. This method operates on a graph that contains similarity information obtained by pair-wise alignment of sequences.

A small amount of partitioning techniques is used in the protein sequence clustering field. Guralnik and Karypis 21 have proposed one method based on a standard k-means approach where proteins are represented by vectors. However, no tool or database resulting from this interesting work has been made available to the scientific community. JACOP 22 uses the partitioning algorithm implemented under the name PAM (Partitioning Around Medoids) in the R statistical package 23. JACOP is based on a random sampling of sequences into groups. It is available on the MyHits platform 24 where user can submit his own data set. Methods presented bellow are not generally tools since they cannot be applied to cluster a user-provided data set. In fact, several of these methods have been applied to large known data sets and user can only consult the resulting classifications stored in databases. Among the protein sequence clustering methods defined bellow only ProClust, TribeMCL and JACOP are accessed by the community and user can classify his own sequence set.

The main idea here is to design and develop efficient clustering algorithms based on partitioning techniques, which are not very investigated in protein sequence clustering field, in order to cluster large sets of protein sequences. In fact, the number of protein sequences available now is very important (in the order of millions) and hierarchical methods are computationally very expensive so they cannot be extended to cluster large protein sets. However, partitioning methods are very simple and more appropriate to cluster large data sets 22. For these reasons, we propose here new clustering algorithms based on partitioning techniques which aim to find meaningful partitions, to improve the classification's quality and to reduce the computation time compared to the published clustering tools, ProClust, TribeMCL and JACOP, on different data sets.

Several partitioning clustering algorithms have been proposed in literature. K-means 23252627 is a standard partitioning clustering method based on K centroids of a random initial partition which is iteratively improved. LEADER 2829 is an incremental partitioning clustering algorithm in which each of the K clusters is represented by a leader. CLARA (Clustering LARge Applications) 23 is a partitioning algorithm based on a combination of a sampling approach and the PAM algorithm. CLARANS (Clustering Large Applications based on RANdomized Search) 30 algorithm views the process of finding optimal medoids as searching through a certain graph, in which each node represents a set of medoids.

We adapted the partitioning algorithms cited bellows to protein sequence data sets. These proposed algorithms are named: Pro-Kmeans, Pro-LEADER, Pro-CLARA and Pro-CLARANS. Performance measures are used to evaluate the proposed methods and to compare them with ProClust, TribeMCL and JACOP results.

Methods

Algorithms Implementation

To facilitate subsequent discussion, the main symbols used through the paper and their definitions are summarized in Table 1.

Table 1

Summary of symbols and definitions

Symbols

Definitions

Data set of protein sequences to be clustered

Number of clusters

Number of proteins in D

O_i

a protein sequence i in D

Number of iterations

The main objective in the proposed algorithms Pro-Kmeans, Pro-LEADER, Pro-CLARA and Pro-CLARANS is to produce K clusters from a data set D of n protein sequences, so that the objective function f(V) is maximized.

f(V) is the global score function that evaluates the clustering quality and it is as follows

Where R_iis the centroid of the group i for which belong the object O_jand Score (O_j, R_i) is the alignment score of the protein sequences O_jand R_i, calculated as follows

Where S (A_i, B_j) is the substitution score of the amino acid A_iby B_jas determined from a scoring matrix and g(n) is the total cost of penalties for a gap length n. The gap is defined as follows

Where P_ois the gap opening penalty and P_eis the gap extension penalty.

We chose Smith and Waterman local alignment algorithm for computing alignment score. The choice of this algorithm was motivated by the sensitivity for low-scoring alignments 31 compared to heuristic algorithms such as FASTA 32 and BLAST 33, and by execution time 34 compared to Needleman and Wunsch global alignment algorithm.

We present here Pro-Kmeans, Pro-LEADER, Pro-CLARA and Pro-CLARANS partitioning clustering algorithms for protein sequence sets.

Pro-Kmeans algorithm

The Pro-Kmeans algorithm proposed here, starts by a random partition of the data set D into K clusters and then uses the Smith Waterman algorithm to compare proteins of each cluster S_i_{(i ∈ [1..K])}and to compute SumScore(S_i, O_j) of each protein j in S_ias follows

Where m is the size of the subset S_i, for which belongs the object O_j.

The sequence O_jin each cluster S_iwhich has the maximum SumScore(S_i, O_j) is considered as the centroid R_iof the cluster. The Smith Waterman algorithm is used here also to compare each protein O_hof the data set D with centroids and to assign the object to the nearest cluster where the R_ihave the maximum score of similarity with the object O_h. Pro-Kmeans proceeds to this procedure for a number of times, q, in order to maximize the f(V) function. Input parameters are the number of clusters, K, and of iterations, q, and as outputs the algorithm returns the best partition of the training base D and the center, or mean, of each cluster S_i. Pro-Kmeans algorithm is illustrated in Figure 1.

Figure 1

Pseudo code for Pro-Kmeans algorithm

Pseudo code for Pro-Kmeans algorithm.

Pro-LEADER algorithm

Pro-LEADER is an incremental algorithm which selects the first sequence of the data set D as the first leader, and use the Smith Waterman algorithm to compute the similarity score of each sequence in D with all leaders. The algorithm detects the nearest leader R_ito each sequence O_jand compares the score, Score(R_i, O_j), with a pre-fixed Threshold. If the similarity score of R_iand O_j, is more than the Threshold, O_jis considered as a new leader and if not, the sequence O_jis assigned to the cluster defined by the leader R_i. Pro-LEADER is thus an incremental algorithm in which each of the K clusters is represented by a leader. The K clusters are generated using a suitable Threshold value. Pro-LEADER aims also to maximize the f(V) function. Input parameter is the similarity score Threshold to consider an object O_jas a new leader, and as outputs the algorithm returns the best partition of the training base D and the K leaders of the obtained clusters. The Pro-LEADER algorithm is fast, requiring only one pass through the data set D. Pro-LEADER algorithm is depicted in Figure 2.

Figure 2

Pseudo code for Pro-LEADER algorithm

Pseudo code for Pro-LEADER algorithm.

Pro-CLARA algorithm

Pro-CLARA relies on the sampling approach to handle large data sets 23. Instead of finding medoids for the entire data set, Pro-CLARA algorithm draws a small sample S of 40 + 2K sequences from the data set D. To generate an optimal set of medoids for this sample, Pro-CLARA applies the proposed PAM algorithm for protein sequence data sets, Pro-PAM algorithm,

The Pro-PAM algorithm proposed here, selects randomly K sequences from the data set as clusters, and then use the Smith Waterman algorithm to compute the total score TS_ihof each pair of selected sequence R_iand non selected sequence O_h. TS_ihis as follows

Where S_jihis the differential score of each pair of non-selected object O_hin D and selected object R_{i(i ∈ [1..K])}with all non-selected objects O_jin D. S_jihis as follows

Pro-PAM selects the maximal TS_ih, MaxTS_ih. If MaxTS_ihis positive, the corresponding non selected sequence O_hwill be selected, otherwise Smith Waterman algorithm is used to compare each protein O_hof the data set with all medoids R_{i(i ∈ [1..K])}, and to assign the sequence O_hto the nearest cluster. Input parameter of Pro-PAM is the number of clusters, K, and as outputs the algorithm returns the best partition of the protein sequence base and the medoid of each cluster. Pro-PAM algorithm is depicted in Figure 3.

Figure 3

Pseudo code for Pro-PAM algorithm

Pseudo code for Pro-PAM algorithm.

Pro-CLARA uses the optimal set of medoids R_i_{(i ∈ [1..K])}obtained by Pro-PAM and the Smith Waterman algorithm to compare each protein O_hof the data set D with all medoids R_{i(i ∈ [1..K])}, and to assign the sequence O_hto the nearest cluster. In order to alleviate sampling bias, Pro-CLARA repeats the sampling and the clustering process a pre-defined number of times, q, and subsequently selects as the final clustering result the set of medoids with the maximal f (V). Input parameters of Pro-CLARA algorithm are the number of clusters, K, and of iterations, q, and as outputs the algorithm returns the best partition of the training base D and the K medoids of the obtained clusters. Pro-CLARA algorithm is detailed in Figure 4.

Figure 4

Pseudo code for Pro-CLARA algorithm

Pseudo code for Pro-CLARA algorithm.

Pro-CLARANS algorithm

Pro-CLARANS algorithm starts from an arbitrary node C in the graph, C = [R₁, R₂,..., R_k], which represents an initial set of medoids. Pro-CLARANS randomly selects one of C neighbors, C*, which differs by only one sequence. If the total score of the selected neighbour, TS_ih(Equation (5)), is higher than that of the current node TS'_ih, Pro-CLARANS proceeds to this neighbor and continues the neighbor selection and comparison process. Otherwise, Pro-CLARANS randomly checks another neighbor until a better neighbor is found or the pre-determined maximal number of neighbours to check, Maxneighbor, has been reached. In this study Maxneighbor is defined as proposed by 30

Where the maximal number of neighbours must be at least a threshold value 250 or obtained using the number of clusters K and the number of sequences, n, in the data set as: 1.25%*K*(n-K).

Pro-CLARANS algorithm aims to maximize the total score, TS_ih

Pro-CLARANS algorithm use then the Smith Waterman algorithm to compute the similarity score of each sequence O_hin D with each medoid R_{i(i ∈ [1..K])}and to assign it to the nearest cluster. The algorithm repeats the clustering process a pre-defined number of times, q, and selects as the final clustering result the set of medoids with the maximal f (V). Input parameters of Pro-CLARANS algorithm are the number of clusters, K, and of iterations, q, and as outputs the algorithm returns the best partition of the training base D and the K medoids of the obtained clusters. Pro-CLARANS algorithm is detailed in Figure 5.

Figure 5

Pseudo code for Pro-CLARANS algorithm

Pseudo code for Pro-CLARANS algorithm.

The proposed algorithms presented here have been implemented in Java package. All of these algorithms used the EMBOSS ftp://emboss.open-bio.org/pub/EMBOSS/ implementation of the Smith and Waterman local alignment algorithm for computing alignment score.

BLOSUM62 (Blocks Substitution Matrix) 35 was chosen to compute amino acids substitution scores 36. We chose the default penalties proposed by Smith and Waterman EMBOSS implementation as gap opening (P_o) and gap extension penalties (P_e) (P_o= 10 and P_e= 2).

Performance measure

To evaluate the Pro-Kmeans, Pro-LEADER, Pro-CLARA and Pro-CLARANS clustering algorithms, a large data set, Training data set, is used. We obtained from the training phase K clusters and each cluster is defined by a medoid (centroid or leader). The training phase results are used to cluster a different data set named, Test data set. Smith Waterman algorithm is used to compare each protein sequence on the test data set with all medoids R_{i(i ∈ [1..K])}obtained from the training phase, and to assign each sequence to the nearest cluster. The predicted family group of each sequence is which of the nearest medoid.

The results obtained from the test phase are used to calculate the Sensitivity and the Specificity of each algorithm and to compare them with results of the published clustering tools, ProClust, TribeMCL and JACOP, tested on the same set: "Test data set".

Sensitivity specifies the probability of correctly predicting a classifier and it is defined as

and Specificity the probability that the provided prediction is correct and it is defined as

where TP (True Positives) is the number of correctly identified true homologues pairs, FN (False Negatives) is the number of not identified true homologues pairs and FP (False Positives) is the number of non-homologue pairs predicted to be homologue. A pair of sequences is considered truly homologous, if both are in the same family group.

Protein sequence data sets

To evaluate the performance of the proposed clustering algorithms Pro-Kmeans, Pro-LEADER, Pro-CLARA and Pro-CLARANS, and to compare their results with the available graph-based clustering tools ProClust and TribeMCL and the only available partitioning clustering tool JACOP, protein sequence families with known subfamilies/groups are considered. Protein sequences of HLA protein family have been collected from ftp://ftp.ebi.ac.uk/pub/databases/imgt/mhc/hla. From this set, we have randomly selected 893 sequences named DS1 and grouped into 12 classes. Protein sequences of Hydrolases protein family have been collected from http://www.brenda-enzymes.org/. Hydrolases protein family sequences are categorized into 8 classes according to their function and 3737 sequences, named DS2, have been considered from this family. From Globins protein family 37, sequences have been collected randomly from 8 different classes and 292 sequences, named DS3, have been selected from the data set IPR000971 in http://srs.ebi.ac.uk. Thus, totally 28 different classes containing sequences are considered as they have been classified by scientists/experts.

The data set considered has a total of 4922 sequences, named DS4, out of which 3500 sequences (practically 70% of the dataset DS4) are randomly for training, and 1422 for testing (practically 30% of the dataset DS4). The same method to obtain the training and the test sets are used on DS1, DS2 and DS3: randomly 70% of the set is selected for the training set and 30% for the test set [see Additional file 1].

Additional File 1

Training and test data sets. The file contains text files which correspond to the used data set in this study in fasta format. The file contains two directories: the training base which has 3500 sequences and the test base which has 1422 sequences. The considered data set, named DS4, has a total of 4922 sequences out of which 3500 sequences (practically 70% of the dataset DS4) are randomly selected for training, and 1422 for testing (practically 30% of the dataset DS4). This dataset contains proteins selected from HLA (DS1), Hydrolases (DS2) and Globins (DS3) protein families.

Click here for file

Results and Discussion

Experiments are conducted on Intel Pentium4 processor based machine, having a clock frequency of 2.4 GHZ and 512 MB of RAM. Experimental results are obtained using default values as follows. In Pro-Kmeans, Pro-CLARA and Pro-CLARANS algorithms, the number of iterations q is fixed to 5 30 and the number of clusters K is fixed to 28. After a number of simulations, we find that the best clustering results are obtained when the parameter K = 28 38. In Pro-LEADER algorithm, the Threshold value is fixed to 350 after a number of simulations 28.

Experimental results of Pro-Kmeans, Pro-LEADER, Pro-CLARA, Pro-CLARANS, ProClust, TribeMCL and JACOP algorithms on DS1, DS2, DS3 and DS4 are summarized in Table 2.

Table 2

Performance of the three other tools (ProClust, TribeMCL and JACOP) and our four proposed methods on DS1, DS2, DS3 and DS4 data sets with respect to two clustering quality measurements: Sensitivity (Sens.) and Specificity (Spec.)

Algorithms

DS1

DS2

DS3

DS4

Sens.

Spec.

Sens.

Spec.

Sens.

Spec.

Sens.

Spec.

ProClust

50.64

56.77

48.71

61.86

46.09

55.14

46.39

51.07

TribeMCL

46.09

52.89

41.42

52.14

41.04

47.48

51.22

56.46

JACOP

99.92

66.27

99.96

70.06

99.96

73.96

99.92

94.42

Pro-Kmeans

92.38

99.90

55.32

98.01

63.30

96.92

56.06

99.56

Pro-LEADER

90.21

91.40

53.15

91.24

52.96

74.06

23.34

95.70

Pro-CLARA

93.60

99.92

73.28

99.26

81.53

98.60

77.84

99.66

Pro-CLARANS

93.10

99.90

78. 62

98.70

76.24

97.34

62.06

99.09

DS4 is a very large data set which contains all sequences of DS1 (HLA protein family), DS2 (Hydrolases protein family) and DS3 (Globins protein family).

In our experiments, the use of partitioning clustering methods Pro-Kmeans, Pro-LEADER, Pro-CLARA, Pro-CLARANS and JACOP have improved sensitivity and specificity of hierarchical methods, ProClust and TribeMCL.

We have demonstrated the performance of the proposed Pro-Kmeans, Pro-LEADER, Pro-CLARA, Pro-CLARANS algorithms for the clustering of protein sequences using similarity.

Experiments show also that on the considered data sets DS1, DS2, DS3 and DS4, the higher probability of correctly predicting a classifier (Sensitivity) is obtained using JACOP method. Pro-CLARA method gives the higher probability that the provided prediction is correct (Specificity) although that, Pro-Kmeans, Pro-LEADER, and, Pro-CLARANS obtain also good results. The use of Pro-LEADER method on very large and heterogeneous set, DS4, is not very valuable. In fact the number of not identified true homologues pairs (False Negatives) is very important for that, the obtained Sensitivity is limited to 23.34.

Pro-Kmeans, Pro-LEADER, Pro-CLARA and Pro-CLARANS result confirm that those proposed partitioning methods are valuable, reliable tools for the automatic functional clustering of protein sequences. The use of these methods instead of alignment methods or the classic known clustering methods by biologists can improve the clustering sensitivity and specificity and reduce significantly the computational time. The proposed methods can be used by new biologists especially to cluster a large data set of proteins into meaningful clusters in order to detect their functions.

Conclusion

Similar protein sequences probably have similar biochemical function and three dimensional structures. If two sequences from different organisms are similar, they may have a common ancestor sequence and hence they are said to be homologous. Protein sequence clustering, using Pro-Kmeans, Pro-LEADER, Pro-CLARA and Pro-CLARANS methods helps in classifying a new sequence, retrieve a set of similar sequences for a given query sequence and predict the protein structure of an unknown sequence. We noticed that the classification of large protein sequence data sets using clustering techniques instead of only alignment methods reduce extremely the execution time and improve the efficiency of this important task in molecular biology.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

SF incepted and directed the research and wrote the manuscript. NE and ML participated in the coordination and the direction of the whole study. All authors read and approved the final manuscript.

Computational Molecular Biology – An Introduction Clote P Backofen R John Wiley & Sons, Ltd 2000 10902160 Bioinformatics – Sequence and Genome Analysis Mount DW Cold Spring Harbor Laboratory Press, New York 2002 Identification of common molecular subsequences Smith TF Waterman MS J Mol Biol 1981 147 195 197 10.1016/0022-2836(81)90087-5 7265238 A general method applicable to the search for similarities in the amino acid sequence of the proteins Needleman SB Wunsch CD J Mol Biol 1970 48 443 453 10.1016/0022-2836(70)90057-4 5420325 Discovering Data Mining: From Concept to Implementation Cabena P Prentice Hall PTR, Upper Saddle River, NJ 1998 Data mining and knowledge discovery: Making sense out of data Fayyad UM IEEE Expert 1996 11 20 25 10.1109/64.539013 The COG database: an updated version includes eukaryotes Tatusov R Fedorova N Jackson J Jacobs A Kiryutin B Koonin E Krylov D Mazumder R Mekhedov S Nikolskaya A Rao B Smirnov S Sverdlov A Vasudevan S Wolf Y Yin J Natale D BMC Bioinformatics 2003 4 41 222959 12969510 10.1186/1471-2105-4-41 ProtoNet 4.0: a hierarchical classification of one million protein sequences Kaplan N Sasson O Inbar U Friedlich M Fromer M Fleischer H Portugaly E Linial N Linial M Nucleic Acids Res 2005 33 Database D216 8 539961 15608180 The metric space of proteins-comparative study of clustering algorithms Sasson O Linial N Linial M Bioinformatics 2002 18 Suppl 1 S14 21 12169526 Picasso: generating a covering set of protein family profiles Herger A Holm L Bioinformatics 2001 17 3 272 9 10.1093/bioinformatics/17.3.272 11294792 Improvements to CluSTr: the database of SWISS-PROT + TrEMBL protein clusters Kriventseva E Servant F Apweiler R Nucleic Acids Res 2003 31 1 388 9 165482 12520029 10.1093/nar/gkg035 GeneRAGE: a robust algorithm for sequence clustering and domain detection Enright A Ouzounis C Bioinformatics 2000 16 5 451 7 10.1093/bioinformatics/16.5.451 10871267 Large scale hierarchical clustering of protein sequences Krause A Stoye J Vingron M BMC Bioinformatics 2005 6 15 547898 15663796 10.1186/1471-2105-6-15 ProtoMap: automatic classification of protein sequences and hierarchy of protein families Yona G Linial N Linial M Nucleic Acids Res 2000 28 1 49 55 102438 10592179 10.1093/nar/28.1.49 Normalized cuts and image segmentation Shi J Malik J Proceedings of the IEEE conference on Computer Vision Pattern Recognition 1997 731 737 An optimal graph theoretic approach to data clustering: theory and its application to image segmentation Wu Z Leahy R PAMI 1993 11 1101 1113 ProClust: improved clustering of protein sequences with an extended graph-based approach Pipenbacher P Schliep A Schneckener S Schönhuth A Schomburg D Schrader R Bioinformatics 2002 18 Suppl 2 S182 91 12386002 Clustering protein sequences-structure prediction by transitive homology Bolten E Schliep A Schneckener S Schomburg D Schrader R Bioinformatics 2001 17 10 935 41 10.1093/bioinformatics/17.10.935 11673238 An efficient algorithm for large-scale detection of protein familes Enright A Van Dongen S Ouzounis C Nucleic Acids Res 2002 30 7 1575 84 101833 11917018 10.1093/nar/30.7.1575 Graph clustering by flow simulation Van Dongen S Phd Thesis University of Utrecht, The Netherlands 2000 A scalable algorithm for clustering sequential data Guralnik V Karypis G SIGKDD Workshop on Bioinformatics, BIOKDD 2001 JACOP: a simple and robust method for the automated classification of protein sequences with modular architecture Sperisen P Pagni M BMC Bioinformatics 2005 6 216 1208858 16135248 10.1186/1471-2105-6-216 Finding Groups in Data: An Introduction to Cluster Analysis Kaufman L Rousseeuw P John Wiley & Sons, Inc., New York 1990 MyHits: improvements to an interactive resource for analyzing protein sequences Pagni M Ioannidis V Cerutti L Zahn-Zabal M Jongeneel C Hau J Martin O Kuznetsov D Falquet L Nucleic Acids Res 2007 35 Web server W433 37 1933190 17545200 10.1093/nar/gkm352 Algorithms for Clustering Data Anil KJ Richard CD Prentice-Hall 1988 Clustering and the continuous k-means algorithm Faber V Los Alamos Science 1994 22 138 144 Algorithm AS136: A k-means clustering algorithm Hartigan J Wong M Applied Statistics 1979 28 100 108 10.2307/2346830 Incremental clustering for dynamic information processing Can F ACM Trans Inf Syst 1993 11 2 143 164 10.1145/130226.134466 Cluster analysis algorithms Spath H Ellis Horwood, Chichester, UK 1980 Efficient and Effective Clustering Methods for Spatial Data Mining Ng R Han J Proceedings of International Conference on Very Large Data Bases Santiago, Chile 1994 144 155 Assessing sequence comparison methods with reliable structurally identified distant evolutionary relationships Brenner SE Chothia C Hubbard TJ Proc Natl Acad Sci USA 1998 95 6073 6078 27587 9600919 10.1073/pnas.95.11.6073 Improved tools for biological sequence comparison Pearson WR Lipman DJ Proc Natl Acad Sci USA 1988 85 2444 2448 280013 3162770 10.1073/pnas.85.8.2444 Basic local alignment search tool Altschul S Gish W Miller W Myers E Lipman D J Mol Biol 1990 215 403 410 2231712 A comparison of four pair-wise sequence alignment methods Essoussi N Fayech S Bioinformation 2007 2 166 168 Performance evaluation of amino acid substitution matrices Henikoff S Henikoff J Proteins 1993 17 49 61 10.1002/prot.340170108 8234244 Positionsgenaues Alignment von Proteinse-quenzen Schneckener S PhD Thesis Universität zu köln 1998 The Universal Protein Ressource (UniProt): an expanding universe of protein information Cathy H Nucleic Acids Res 2006 34 87 191 10.1093/nar/gkl485 How many clusters are best? Dubes RC Pattern Recogn 1987 20 6 645 663 10.1016/0031-3203(87)90034-3