Naïve Bayesian Classification of Unknown Sequence Fragments based on Chaos Game Representation of Mitochondrial Genomes Vrinda V. Nair 1,2, Lissy Anto P. 1 and Achuthsankar S. Nair 1 1

Centre for Bioinformatics, University of Kerala, Thiruvananthapuram, Kerala, India, Pin -695581. 2 Department of Electronics and Communication Engineering, Government Engineering College, Thrissur, Kerala, India, Pin 680009. Email: [email protected]

Abstract: Various experimental and computational techniques have been reported for biological sequence classification. This paper proposes a novel combined technique of chaos game representation and naïve Bayesian classification, the former for genomic feature extraction and the latter for the subsequent species classification, of unknown mitochondrial genome sequences. The sequences are initially mapped into their Chaos Game Representation (CGR) format. Genomic feature extraction is implemented by computing the Frequency Chaos Game Representation (FCGR) matrix. An order 3 FCGR matrix is considered here, which consists of 64 elements. The 64 element matrix acts as the feature descriptor for classification. A probabilistic model is constructed with a set of training sequences from 6 different categories of organisms. The classification accuracy obtained is above 99% for Vertebrata and Acoelomata groups, above 88% for Fungi and Cnidaria, 80% for Plant and 73.3% for Pseudocoelomata. Keywords: chaos game representation, genomic signature, mitochondrial genomes, naïve Bayesian classifier

1. Introduction Biological sequence classification has been an area of active research in the past and various experimental and computational techniques have been reported. Identification of a species from its genome or genomic fragment is a challenging task. This could be done by extracting distinct genomic features of the categories chosen for classification. This paper explores a novel combined technique of chaos game representation and naïve Bayesian classification, the former for genomic feature extraction and the latter for the subsequent species classification. Species identification based on mitochondrial genomes was implemented and various feature descriptor diagrams drawn by S Narayanan et al. [13]. Principal Component Analysis was employed to obtain a unique feature descriptor. It was shown that the feature descriptors were effective representatives of the structural signature of the species. Eubacterial and archeal genomes were classified with an accuracy of 85% using a naïve Bayesian Classifier based on dinucleotide composition bias by R Sandberg et al. [15]. Protein classification into domains of life was attempted by F

Zanoguera and M de Francesco and the test protein was predicted to be of bacterial or eukaryotic origin with 85% accuracy using a Markov model for compositional bias analysis [18]. Classifications and species identification have also been associated with practical applications such as biodiversity studies [7], forensic investigations [2], food and meat authentication [14], to name a few. Previous works show that analysis of k-tuple compositional bias is a powerful tool for biological sequence classification [18]. This approach characterizes a sequence or a class of sequences by looking at the relative frequencies of the “words” that compose it. The advantage with respect to other methods is that it does not require alignment of the sequences. The advantage of chaos game representation method in this context is double fold. The word frequencies can be obtained from the Frequency Chaos Game Representation (FCGR) matrix [1] [4], which is an alignment free method. Further the CGR images could also be plotted which will simultaneously give a visual representation of the sequences. The visual differences between classes of sequences will thus be evident from the CGR images themselves. CGR images of genomes have been used in the past for domain classifications. Biologically meaningful grouping of species into the three domains of life - eubacteria, archae and eukaryotes were obtained using Euclidean distance between CGR images [4]. It was also shown that subsequences of a genome exhibit the main characteristics of the whole genome. Classification of CGR images of genomes using Principal Component Analysis and neural networks grounded on Curvilinear Component Analysis algorithm (CCA) and Kohonen Map is discussed in [10]. CGR could be constructed from amino acid sequences as well. It was demonstrated that different protein families exhibit distinct patterns in their CGRs with characteristic grid counts [3]. It was shown that CGR could be applied for revealing information relating the primary and 3D structures of proteins [9]. Multifractal and correlation analyses of the measures based on the CGR of amino acid sequences from complete genomes have been reported and attempts have been made to construct a more precise phylogenetic tree of bacteria [17]. In this paper, classification is based on the information content in the image in the form of FCGR matrix. The FCGR

matrix elements can be considered as multiple features which can be combined to create a powerful classifier. The algorithm of choice is the Naïve (or simple) Bayesian classifier that finds its origins in the Bayesian theory of probability. The main advantage of Bayesian classifiers is that they are probabilistic models, robust to real data noise and missing values [8]. The Naïve Bayesian classifier assumes independence of the attributes used in classification but it has been tested on several artificial and real data sets, showing good performances even when strong attribute dependences are present. In addition, it also has advantages in terms of simplicity, learning speed, classification speed and storage space [5]. The method illustrated in this paper, classifies the unknown subsequence into one among six categories with accuracies of above 85% for four groups and above 70% for the remaining two groups, details of which are reported in Section 3. In this paper, Section 2 gives an introduction on chaos game representation. Section 3 deals with the materials and methods used for classification. Detailed steps are depicted showing the construction of the probabilistic model and method of application of Naïve Bayesian Classifier. Section 4 gives the result of classification and a discussion on the result. Finally, Section 5 gives the conclusion and comparison of result with existing works.

absence of diagonals etc. signifying corresponding sequence characteristics indirectly captured by the signature images. In a CGR, the frequency of occurrence of any oligomer in a sequence can be obtained by dividing the CGR image into a 2nx2n grid. Counting the number of points in each square of the grid gives the number of occurrences of all possible nmers in the sequence. This representation is called Frequency Chaos Game Representation (FCGR), where the frequency of an oligomer is the number of points in the corresponding square. The correspondence between n-mers and the subsquares is shown in Fig. 1. Numerous applications have been reported based on FCGR measures. This was used for developing an algorithm for aligning and comparing whole genomes [12]. Phylogenetic trees were generated using various distance measures derived from FCGR and it was concluded that FCGRs contained major phylogenetic information [16]. In this paper, elements of the FCGR matrix generated using the training sequences acts as multiple feature descriptors used by the naïve Bayesian classifier.

CG

C

CGG

GGG

AGG

TGG

AG

TG

2. Chaos Game Representation The scope of CGRs as useful signature images of biosequences such as DNA has been investigated since early 1990s. CGRs of genome sequences were first proposed by H. Joel Jeffrey [11]. To derive a chaos game representation of a genome, a square is first drawn to any desired scale and corners marked A, T, G and C. The first point is plotted halfway between the center of the square and the corner corresponding to the first nucleotide of the sequence, and successive points are plotted halfway between the previous point, and the corner corresponding to the base of each successive nucleotide. Mathematically, coordinates of the successive points in the chaos game representation of a DNA sequence is described by an iterated function system defined in Eq. (1) Xi = 0.5( Xi − 1 + gix ) Yi = 0.5(Yi − 1 + giy ) (1) g ix and g iy are the X and Y co-ordinates respectively of the corners corresponding to the nucleotide at position i in the sequence [12]. The CGR of a random sequence gives a uniformly filled square. The CGR of DNA sequences plotted for various species gives images illustrating the non-randomness of genome sequences, which indeed means that the sequence has a structure, indirectly captured by the signature image. The CGR for Human Beta Globin exhibits a recursive ‘double scoop’ which corresponds to the sub square CG. Hence the relative sparseness of guanine following cytosine in the gene sequence is inferred [11]. Other features of CGRs include marked diagonals, varying vertical intensities,

A

T

Fig. 1. Correspondence between n-mers and subsquares in a CGR Fig. 2-7 show the CGR plot of mitochondrial genome sequences belonging to 6 different categories of organisms, considered in this paper, where length of sequences are limited to 20000 base pairs. The diversity in the visual pattern of the CGRs is made use of, for classification.

Fig. 2. NC_002767 Hymenolepis diminuta (rat tapeworm) (Acoelomata)

Fig. 3. NC_008411 Chrysopathes formosa (black coral) (Cnidaria)

Fig. 6. NC_001328 Caenorhabditis elegans (roundworm) (Pseudocoelomata)

Fig. 4. NC_001224 Saccharomyces cerevisiae (baker's yeast) (Fungi)

Fig. 7. AC_000021 HomoSapiens (human) (Vertebrata)

Fig. 5. NC_001284 Arabidopsis thaliana (thale cress) (Plant)

3. Materials and Methods 3.1 Dataset Given a whole genomic sequence or a fragment, the paper focuses on identifying its origin. Mitochondrial genomes are

considered here. Mitochondria are small, oval shaped organelles surrounded by two specialized membranes. They are the sites of aerobic respiration, and are the major energy production center in eukaryotes. The low mutation rate in metazoan mitochondrial genome sequence makes these genomes useful for scientists assessing genetic relationships of individuals or groups within a species and for the study of evolutionary relationships [19]. For the same reason, mitochondrial genomes are chosen for the classification attempted in this paper. Mitochondrial genomes were downloaded from the NCBI Organelle database [19]. Mitochondrial genomes are enlisted in the NCBI site under 5 links. They are Metazoa (1456), Fungi (57), Plants (30), Other eukaryotes (49) and Plasmids (23). The number in parentheses shows the number of organisms in each category listed as on 1/1/2009. Out of the major categories of Plant, Fungi and Metazoa, the Metazoan kingdom has the largest number of entries. Those subcategories of the Metazoan kingdom with sufficient number of organisms listed have been used for classification. Fig. 8. shows the tree of organisms in the major Eukaryotic categories, especially the Metazoan subcategories, listed in NCBI, as on 1/1/2009.

Fig 8. Tree showing the number of mitochondrial genomes listed under Eukaryotes in NCBI as on 1/1/2009 In this study, organisms from Plant, Fungi and Metazoa are taken for the classification experiment. Bilateria is a huge group under Metazoa with reasonable number of organisms listed under the Coelomata subgroup further subdivided into Deuterostomia and Protostomia. In this paper, the Metazoan group is represented by Cnidaria, Acoelomata, Pseudocoelomata and Vertebrata. The Protostomian subgroup is deliberately excluded since the CGRs in this group show a number of varied patterns which can hence be taken up as a separate classification problem in itself. Other categories shown could not be included since the number of organisms listed is small and hence sufficient data were not available for training and testing. Table 1. shows the organisms chosen for classification. Table 1. Organisms chosen for classification Sl. No. 1. 2. 3. 4. 5. 6.

Name of the category and abbreviations used Acoelomata (AC) Cnidaria (CN) Fungi (FN) Plant (PT) Pseudocoelomata (PC) Vertebrata (VB) Total

Number of organisms 28 34 57 30 30 1025 1204

3.2 Methodology In this paper, we are trying to classify short genome sequences assuming that they bear the same characteristics as the whole genome [4]. Training as well as test sequences are first mapped into chaos game representation formats. This facilitates easy computation of the corresponding FCGR matrices. We have considered an order 3 FCGR matrix for the classification purpose which in fact corresponds to the tri -nucleotide frequency composition of the genomes. It was shown that a 2nd order FCGR is optimal regarding the choice of order, since it provides major organizational information of a DNA sequence [16]. A better choice of 3 instead of 2 is considered in this paper also taking into consideration, the significance of tri-nucleotides in making up amino acids, which are the building blocks for proteins [13]. The classification method can be divided into four steps. (i) Computing CGR of training sequences, (ii) Computing normalized FCGR of training sequences, (iii) Obtaining the emission matrix and (iv) Classification of an unknown sequence by computing its CGR, normalized FCGR and applying the Naïve Bayesian classification approach. Step 1. In this step, the CGR of each sequence of the training set for each class C m (1< m < 6), is constructed. Step 2. The FCGR matrix for each class of sequences in the training set is separately computed in this step. The FCGR matrix obtained is normalized in order to

accommodate sequences of varied lengths. Let A be an nth order FCGR matrix. Then A contains 2n x 2n elements. Let a i,j (1≤ i ≤ 2n, 1≤ j ≤ 2n) denote the elements in the matrix. Normalised FCGR matrix is defined as shown in Eq. (2) A A= n n 2 2 ∑ ∑ ai , j i =1 j =1 (2) Let elements in A be denoted by b i,j . Then the sum of the elements of matrix A is equal to 1 as given in Eq. (3) 2n 2n

∑ ∑ bi , j = 1

i =1 j =1

(3) In this paper, n is taken as 3. So an FCGR matrix of size 23 x 23 is obtained, thus comprising of 64 elements. The 64 element matrix is treated as the feature vector for Bayesian classification. Step 3. In this step a probability model is implemented using the normalized FCGR matrix computed in Step 2. Suppose there are NCm sequences in the training set of class C m , (1≤m≤6). Then, we have an NCm × 64 matrix as the feature space corresponding to each class C m . Let us denote this as F m (1≤m≤6). Each element of F m is denoted by f k,p (1≤k≤ Ncm , 1≤p≤64). Each column of F m represents one feature of the class. We now divide the total range of the values in each column to 10 intervals with interval size given by d m,p as shown in Eq. (4) ⎞ ⎛ ⎜ Max [ fk , p ] − Min [ fk , p ] ⎟ k =1, NCm k =1, NCm ⎠ ⎝ dm, p = 10 (4) for 1≤m≤6 and 1≤p≤ 64. A probability matrix is now constructed by inspecting the normalized FCGR matrix computed in Step 2, and identifying the interval into which it each element falls. The frequency of occurrence of values in each of the 10 intervals, recorded for sequences in the training set is denoted as Q m,p,t (1≤m≤6, 1≤p≤64, 1≤t≤10). The probability matrix, corresponding to each class, denoted as E m,p,t is computed by dividing the frequency of occurrence, Q m,p,t by the number of sequences, NCm as in Eq.(5) Qm, p ,t Em, p , t = NCm (5) where 1≤ m ≤6, 1≤p≤64 and 1≤ t ≤ 10. The 64x10 probability matrix thus obtained for each class C m , is also referred to as the emission matrix since it resembles symbols being emitted from states with the estimated probabilities. Step 4. This is the classification step. Now if an unknown input sequence is given to the classifier, initially, the CGR is constructed. Subsequently, the normalized FCGR matrix is computed. The 64 element test vector is then fed to the classifier for class C m , for all m. The probability corresponding to each element in the test vector P(T p ) is obtained by scanning the Step 3, for each emission matrix E m,p,t computed in class m.

The naïve Bayesian classifier classifies a sequence to belong to a class C m if the product of probabilities for that class and its apriori probability is maximum. 3.3

Naïve Bayesian Classifier

Bayesian statistics handle conditional probabilities, that is, given that event A has occurred, how likely is event B to occur, P(B\A) [6], [15]. The probability of identifying a sequence to belong to class C m can be used to calculate the probability of a sequence to belong to a class C m , P(C m \S), by Bayes’ rule as given in Eq. (6) P(S \ Cm )P(Cm ) P(Cm \ S ) = P (S ) (6) For a particular class C m , the Naïve Bayesian classifier assumes each feature to be independent. Hence the probability of a sequence to belong to a class C m is as given in Eq. (7) 64

P(S \ Cm ) = ∏ P(Tp \ Cm ) p =1

(7) i.e. the product of probabilities of each feature P(T p ) is evaluated for each class. P(S), probability of finding sequence S is constant; it is independent of class, hence excluded. The apriori probability of finding the different classes, P(C m ) is evaluated. The classifier identifies the sequence to belong to that class which gives the highest probability, i.e maximum P(C m \S).

4. Results and Discussion The FCGR matrix elements which correspond to distinct genomic features of organisms are treated as the feature vector for Bayesian classification. Fig. 9. shows the feature vectors generated, corresponding to the 6 categories chosen for classification. The plot shows the average over the training set for each FCGR matrix element. The distinctness of each vector is apparent from the displayed graph. Roughly 50% of the total number of sequences from the dataset mentioned in Section 3.1 in each category was chosen as training sequences and the remaining as test sequences. Classification was performed as discussed in Section 2. As mentioned in Step 3 in Section 2, each column of the feature space was divided into 10 intervals in order to build the probabilistic model which was then used for classification. Apart from dividing the range into 10 intervals, the method was tried on intervals of 5, 15 and 20 as well. The classification accuracy obtained for all the four cases were recorded. The plot of accuracy obtained for each of the categories with intervals 5, 10, 15 and 20 is shown in Fig. 10. It is seen that an interval of 10 is optimum since, it gives better accuracy for almost all the categories considered. For different intervals chosen it is seen that Vertebrates give an accuracy of above 99% for all intervals which suggest that significant classification can be achieved even with number of intervals as low as 5. The accuracy for each category with an interval of 10 is separately listed in Table 2.

Fig. 9. A subset of the feature vector for each classification categories Test sequences as short as 300 base pairs in length could be identified correctly with an accuracy of 86.72%. Further with 625 base pairs the accuracy achieved was 94.14 and 97.85 for 1250 base pair length, increasing further up the curve.

Fig. 10. Accuracy Vs Intervals for the probabilistic model. Table 2. Classification accuracy Sl. No. 1. 2. 3. 4. 5. 6.

Category Acoelomata (AC) Cnidaria (CN) Fungi (FN) Plant (PT) Pseudocoelomata (PC) Vertebrata (VB)

Accuracy % 100 88.24 88.46 80 73.33 99.41

Another interesting experiment carried out was repeating the same experiment by reducing the length of the test sequences substantially. The test was done on Vertebrates which forms the major part of the data set. The result is shown graphically in Fig. 11.

Fig. 11. Length of sequence Vs accuracy

5.

Conclusion

Classification of anonymous mitochondrial genome sequence fragments was implemented using chaos game representation and naïve Bayesian classifier. Chaos game

representation was used to extract the feature vector by taking the Frequency Chaos Game Representation (FCGR) matrix. The elements of the matrix were treated as multiple independent features. A probabilistic model was built based on the feature space of training sequences. The naïve Bayesian classifier was used to classify a test sequence into any one of the six classes considered in this paper. All organisms within a category share common features in their CGR which facilitates classification into the respective categories. At the same time, the subtle differences among species can also be tracked on closer inspection of their CGRs, which could then be used as useful species markers. The method reported in this paper provides a quantitative measure of classification when compared to other competing methods which give only visual representations of the feature descriptors. Two other competing methods of which one uses naïve Bayesian Classifier, classifies organisms into the two kingdoms of eubacteria and archea with an accuracy of 85% while the other classifies origin of protein sequences into one of the two categories of bacteria or eukarya with 85% accuracy. Classification to other kingdoms and subfamilies with better precision and improved accuracy is not seen reported. When compared to methods where classification was attempted using CGR images, the method reported in this paper has the advantage that although the method is based on CGR, no image need essentially be generated for classification. The method reported in this paper classifies organisms into Acoelomata and Vertebrata categories with an accuracy of above 99%, Cnidaria and Fungi with an accuracy above 88%, Plant with an accuracy of 80% and Pseudocoelomata with 73%. It was observed that Vertebrates could be classified with an accuracy of above 99% with number of intervals as low as 5 in the probabilistic model. It was also seen that test sequence fragments as short as 300 base pair length belonging to the Vertebrata category could be identified with an accuracy of 86.72%, increasing further with length of the sequence for 512 test sequences whereas competing methods report 85% accuracy for 400 base pair length tested on 100 sequences. Hence it can be concluded that that this method is suitable for species classification especially for identifying Vertebrate sequences.

References [1] J S Almeida, J A Carrico, A Maretzek, P A Noble and M

Fletcher, Analysis of genomic sequences by chaos game representation. Bioinformatics, Vol. 17, No. 5, Jan. 2001, pp. 429–437. [2] H Andréasson , A Asp, A Alderborn, U Gyllensten, M Allen, Mitochondrial sequence analysis for forensic identification using pyrosequencing technology. Biotechniques, Vol. 32, No.1, Jan. 2002, pp.1246,128,130-3. [3] S Basu, A Pan, C Dutta and J Das, Chaos game representation of proteins. J Mol Graph Model., Vol. 15, Oct. 1997, pp. 279–289. [4] P J Deschavanne, A Giron, J Vilain, G Fagot and B Fertil, Genomic signature: characterization and

classification of species assessed by chaos game representation of sequences. Mol Biol Evol., Vol. 16, June 1999, pp. 1391–1399. [5] P Domingos and M Pazzani, On the optimality of the simple Bayesian classifier under zero-one loss. Gregory Provan, Machine Learning, Kluwer Academic Publ., Netherlands, July 1997, pp. 103-130 [6] R Durbin, S Eddy, A Krogh and G Mitchison, Biological Sequence Analysis, Cambridge University Press, Cambridge, 1998. [7] J W Fell, T Boekhout, A Fonseca, G Scorzetti and A Statzell-Tallman, Biodiversity and systematics of basidio-mycetous yeasts as determined by large-subunit rDNA D1/D2 domain sequence analysis, Int J Syst Evol Microbiol., Vol. 50, May 2000, pp. 1351-1371. [8] L De Ferrari and S Aitken, Mining housekeeping genes with a Naive Bayes classifier. BMC Genomics, Vol. 7:277, Oct. 2006. [9] A Fiser, G E Tsunady and I Simon, Chaos game representation of protein structures. J Mol Graph., Vol. 12, Dec. 1994, pp. 302–304. [10] A Giron, J Vilain, C Serruys, D Brahmi, P. Deschavanne, B Fertil, Analysis of parametric images derived from genomic sequences using neural network based approaches, Int. Joint Conf. on Neural Networks (IJCNN’ 99), NJ, Jul., 1999, Vol. 5, pp. 3604- 08. [11] H J Jeffrey, Chaos game representation of gene structure. Nucleic Acids Res., Vol. 18, No. 8, Mar. 1990, pp. 2163–2170. [12] J Joseph and R Sasikumar, Chaos game representation for comparison of whole genomes. BMC Bioinformatics, Vol.7: 243, May 2006. [13] S Narasimhan, S Sen and A Konar, Species identification based on mitochondrial genomes. International Conference of Cognition and Recognition ( ICCR 2005), Mysore, India, 2005, 22-23 Dec. 2005. [14] G Rastogi, S M Dharne, S Walujkara, A Kumara, S M Patolea and S Y Shouche, Species identification and authentication of tissues of animal origin using mitochondrial and nuclear markers. Meat Science, Vol. 76, No. 4, Aug. 2007, pp. 666-674. [15] R Sandberg, G Winberg, C I Branden, A Kaske, I Ernberg and J Coster, Capturing Whole – Genome characteristics in short sequences using a naive Bayesian classifer. Genome Res., Vol. 11, May 2001, pp. 1404-09. [16] Y Wang , K Hill, S Singh and L Kari. The spectrum of genomic signatures: from dinucleotides to chaos game representation. Gene, Vol. 346, Jan. 2005, pp.173–185. [17] Z G Yu V Anh and K S Lau, Chaos game representation of protein sequences based on the detailed HP model and their multifractal and correlation analyses. J Theor Biol., Vol. 226, No.3, February 2004, pp. 341–348. [18] F Zanoguera and M de Francesco, Protein classification into domains of life using Markov Chain Models. in Proc. 2004 IEEE The Computational Systems Bioinformatics Conference (CSB 2004). 16-19 Aug. 2004, pp. 517-519 [19] http://www.ncbi.nlm.nih.gov/Genomes/ ORGANELLES/ organelles.html, January 2009.

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game representation and naïve Bayesian classification, the former for genomic feature extraction and the latter for the subsequent species classification. Species identification based on mitochondrial genomes was implemented and various feature descriptor diagrams drawn by S Narayanan et al. [13]. Principal Component.

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