Terminator Detection by Support Vector Machine Utilizing a Stochastic Context-Free Grammar

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1 Terminator Detetion by Support Vetor Mahine Utilizing a Stohasti Context-Free Grammar Patriia Franis-yon: University of California at Davis, pfranis@udavis.edu Nello Cristianini: University of Bristol (UK), nello@support-vetor.net Stephen Holbrook: awrene Berkeley National aboratory, srholbrook@lbl.gov Abstrat - A 2-stage detetor was designed to find rhoindependent transription terminators in the Esherihia oli genome. The detetor inludes a Stohasti Context Free Grammar (SCFG) omponent and a Support Vetor Mahine (SVM) omponent. To find terminators, the SCFG searhes the intergeni regions of nuleotide sequene for loal mathes to a terminator grammar that was designed and trained utilizing examples of known terminators. The grammar selets sequenes that are the best andidates for terminators and assigns them a prefix, stem-loop, suffix struture using the Coke-Younger- Kasaami (CYK) algorithm, modified to inorporate energy effets of base pairing. The parameters from this inferred struture are passed to the SVM lassifier, whih distinguishes terminators from non-terminators that sore high aording to the terminator grammar. The SVM was trained with negative examples drawn from intergeni sequenes that inlude both featureless and RNA gene regions (whih were assigned prefix, stem-loop, suffix struture by the SCFG), so that it suessfully distinguishes terminators from either of these. The lassifier was found to be 96.4% suessful during testing. INTRODUCTION Two types of transription terminators, named for their operating mehanisms, have been found to exist in bateria: rho-dependent and rho-independent terminators. Detetion of terminators has been hallenging due to the lak of lear signals in their geneti sequene, suh as is provided to protein gene detetion by start and stop odons. However, there are strutural features present in the lass of rhoindependent terminators that may be exploited to aid in their detetion. For a rho-independent terminator, the ability to funtion effetively is largely due to formation of a stem-loop. This seondary struture, rather than sequene, is the phenotype seleted for in the evolutionary proess. The same strutures may result from different sequenes of nuleotides adenine, ytosine guanine and urail (a,,g and u). Therefore sequenes may be evolutionarily related while not onserved, as long as their strutures are onserved by ompensatory mutations. (For example, a stem g pair an be replaed by g, au, ua gu or ug pair.) Unsurprisingly, it has been found that rhoindependent terminators do not share general onsensus sequene [1]. Our approah to terminator detetion is to infer strutural information from sequene alone, then use both sequene and inferred strutural parameters to lassify the sequene as terminator or non-terminator. BACKGROUND Terminator Detetion Transription is the proess by whih a opy of the oding (nontemplate) strand of a gene is produed, exept that thymine (t) in DNA is replaed by urail (u) in RNA, resulting in an RNA transript. The final phase of transription is termination, whih an be signaled in rho-independent terminators by the formation of a stem-loop within the RNA polymerase (RNAP), induing the pausing of the transription elongation omplex (TEC) just as the RNAP enounters weak au bonds at the terminator tail, ausing the dissoiation of the TEC from the RNAP and the release the protein or RNA gene. A model attributed to Carafa et al. [2] desribes DNA sequene for rho-independent terminators. An RNA hairpin (stem-loop) is followed by a 15 nuleotide (nt) long region rih in thymidine (the nuleoside of thymine) whih may be separated by a spaer region of up to 2 nts. An adenoside-rih region was desribed upstream of the hairpin (but not used in their soring system). Fig. 1 depits the anonial terminator, based upon the Carafa model, that was used in this projet. Carafa et al. developed a 2-stage proess to detet and lassify andidate terminators, taking into aount strutural information suh as free energy of the RNA hairpin, along with stem and loop length. Sequene information suh as the number and positions of thymidine residues, and the fration of g pairs in the stem is also used. This algorithm suessfully distinguishes between terminators and both random sequene and protein oding sequene. Other researhers have built upon the Carafa model to reate terminator detetors. The 2-stage proess of Ermolaeva et al. [3] utilized loation and orientation information, their own representation of the stability of stem-loop struture, and the Carafa tail-soring funtion. esnik et al. [4] devised an algorithm utilizing sequene parameters and allowing the user /07/$ IEEE 170

2 to define onstraints upon struture. Their thermodynami soring system aounts for the preferene of stem-loop struture over bonding to DNA at the point of transription termination. More reently, de Hoon et al. [5] used a logisti regression model to arrive at a deision rule for prediting rhoindependent terminators in B. subtilis and related speies. While these methods detet more known terminators than Carafa et al., they report a tradeoff between finding more known terminators (true positives) and getting more false positives. Also, this sensitivity/speifiity tradeoff is hard to quantify sine many terminators have yet to be experimentally determined so numbers of true and false positives in these studies are estimates. Some studies ount the terminators found by their algorithm as true positives along with experimentally determined terminators as long as these putative terminators satisfy loation and soring standards. Ermolaeva et al., who reate a polynomial approximation to estimate frequeny of false positives, report finding 567 terminators in E. oli with a onfidene of 98% (meaning 98% of all preditions are estimated to be orret). This is far higher than the number of experimentally determined terminators. At this onfidene they reportedly find 89% of all true terminators. The suess of Hidden Markov models in statistial modeling, database searhing and multiple alignment of both promoters and protein genes has prompted researhers to look to grammars to inorporate long range interations into feature detetion. Hidden Markov models are equivalent to stohasti regular grammars, where sequene is generated from left to right [6]. Features that have stem-loop strutures aused by base pairs that are nested an be generated by a ontext-free grammar, emitting sequene from outside to inside rather than from left to right. Stohasti ontext-free grammars (SCFGs) apture both sequene and strutural information and have been used suessfully to model RNA genes by Eddy and Durbin [7] and trna genes by Sakakibara et al. [8]. Kin et al. [9] used a SCFG as a kernel in the lassifiation of trnas. SCFGs were used to model terminators by Bokhorst and Craven [10], as a test ase to show that a defiient SCFG ould be refined in an iterative proess. Their paper states that preliminary results indiate that the refinement method produed an SCFG that improved the auray of the model, but the suess rates themselves were not reported. For this projet, a Stohasti Context Free Grammar (SCFG) was developed to utilize both sequene and strutural information to detet terminators from genomi sequene. To refine the detetion proess, a support vetor mahine (SVM) was oupled with the SCFG. The SCFG selets likely andidates for terminators from sequene, and designates subsequenes of eah as prefix, stem, loop and suffix. This information is passed to the SVM, whih was trained to distinguish between terminators and those non-terminators that were assigned high sores by the SCFG. The terminator grammar of Bokhorst and Craven was not used, beause the grammar was reported to be defiient. Rather, a grammar was developed to selet sequene that an take on the struture of the anonial rho-indedpendent terminator of Fig. 1. Stohasti Context-Free Grammars A Grammar is a set of rules, alled produtions, together with a set of abstrat symbols alled non-terminals and a set of emitted symbols alled terminals. Together these 3 sets haraterize the set of legal strings, the language of the grammar, whih are those strings that an be derived by iterative appliation of the produtions. Grammars having the set of terminals {a,,g,t} have been used for modeling strings of nuleotides, suh as genes [6][7][8][16][17]. The struture of a stohasti ontext-free grammar is that of its underlying ontext-free grammar G. G an be formally defined as G={N,T,P,S} where N is a finite set of nonterminal symbols ( states ), T is a finite set of terminal symbols ({a,,g,t} for nuleotides), P is a finite set of produtions of the form A Γ, where A N, Γ (NU T)*, and S is the start nonterminal (S N). This means that the right hand side of a prodution may onsist of any ombination of terminals and nonterminals, while the left hand side must be a single nonterminal. A partiular iterative appliation of produtions that result in a string x is referred to as a derivation or may be viewed as a parse tree, Π, for x. An SCFG assigns a probability to eah prodution rule in P suh that all the produtions from any given nonterminal sum to 1. The set of these probabilities is referred to as the parameters of the model, θ. A sequene x may have a higher probability (sore) with one model than with another. The probability P(x,Π G,θ) is the probability that a partiular derivation (parse tree) Π generates string x given struture G of the underlying ontext-free grammar and the probabilities θ assoiated with the produtions. This is simply the produt of probabilities of all the prodution rules used in the parse tree Π for sequene x. An SCFG desribes a joint probability distribution P(x,Π G,θ) over all sequenes x and all possible parse trees Π. SCFGs are generalizations of hidden Markov models (HMMs), whih are equivalent to stohasti regular grammars. In addition to primary sequene, modeled in left to right string generation by HMMS, SCFGs model seondary struture in outside to inside generation of strings. The HMM algorithms for solving problems of detetion, alignment and parameter estimation have analogs for families modeled by SCFGs. These dynami programming algorithms start with subsequenes of length zero and onsider larger and larger sequenes by inrementally extending them. In the ase of HMMs, subsequenes are extended leftwards by 1 nt at a time, whereas for SCFG models, subsequenes are extended outwards by 2 nt at a time, apturing pair interations. For this projet, genomi sequene needs to be parameterized into likely terminator struture so the SVM ould be trained to detet whih are terminators. To aomplish this the Coke- 171

3 Younger-Kasaami (CYK) algorithm is used for alignment to the struture and model. Rather than taking the sum of probabilities of parse trees as is done in soring, these alignment algorithms find the argmax of the probabilities for parse trees. The end result is log P(x,Π* G,θ) where Π* is the most likely parse for x given the grammar struture and model. A traebak an be oded to reveal Π*. Support Vetor Mahines Support Vetor Mahines (SVMs) are a relatively reent addition to the field of mahine learning. They were introdued by Vapnik and began to be widely used in lassifiation in the 1990s. SVMs are trained with a learning algorithm from optimization theory that implements a learning bias derived from statistial learning theory to searh a hypothesis spae of linear funtions operating on data that has been embedded into a high dimensional feature spae [11]. A kernel funtion is seleted to perform the embedding suh that the data beomes linearly separable in the high dimensional spae. Basially, an SVM is a hyperplane lassifier whih finds the optimal hyperplane to separate data into lasses. When dividing two lasses, the optimal hyperplane is orthogonal to the shortest line onneting the onvex hulls of the two lasses, and interseting it halfway between the two lasses at a perpendiular distane d from either lass, reating a margin of 2d between the lasses. The support vetors are those elements of the training set that lie on the margins of either lass (at a distane d from the separating hyperplane). It is these training examples that are relevant to the algorithm. It is these training examples, rather than the enters of lusters, that are ritial for finding the margins between the lasses. Complexity of the algorithm may be redued by removing the other training examples from the kernel expansion. It an be shown by geometry that the margin we want to maximize equals 2 / w 2, so the unique optimal hyperplane is found by solving the optimization problem: Minimize T(w) = ½ w 2 (1) Subjet to y i. ((w. x i ) + b) >= 1, i= 1,2,,m where w 2 is the norm of the separating hyperplane, x i is the n dimensional vetor representing the i th data point of m data points and y i is the target (orret) value for that i th data point. The minimization is solved using agrange multipliers and minimizing the agrangian. SVMs have the ability to find a separating hyperplane even if one does not exist in the spae of the input vetor, as long as the training data may be mapped into a higher dimensional feature spae in whih suh a separating hyperplane exists. The kernel funtion is the inner produt in that feature spae, and is used to ompute the separating hyperplane without atually having to arry out the mapping into higher dimensional spae. The ommon kernels used are Gaussian RBF, polynomial, and sigmoidal [12]. To allow for noise in the data that would prelude perfet lassifiation, a slak variable an be introdued in order to relax the onstraints to : Subjet to y i. ((w. x i ) + b) >= 1 - e i, (2) i= 1,2,,m Where slak variables e i >= 0, i= 1,2,,m When e i >1, this allows for a mislassifiation, so Σ i e i is an upper bound on the number of training errors. Changing the objetive funtion to be minimized from ½ w 2 to ½ w 2 + C(Σ i e i ) k allows the influene of outliers to be ontrolled by the user-speified variable C. A lower value of C penalizes errors less, limiting the influene of outliers. This is a quadrati programming problem when the value of k is hosen to be either 1 or 2. For details onerning support vetor mahines and kernels, please see the text by Cristianini and Shawe-Taylor [11]. METHODS Terminator Grammar Beause protein genes are generally easy to detet in bateria due to the presene of start and stop odons, this projet inorporated the often-used strategy of searhing only those regions between protein genes to deteting features suh as terminators. A ruial requirement is that the detetor be able to distinguish terminators from RNA genes, whih also have stem-loops. The terminator struture modeled by the grammar is prefix, followed by stem-loop, followed by suffix. The grammar is simple, using software rules to enfore requirements suh as minimum stem length, rather than ompliating the grammar. Also rather than using a trifuration from the start state into 3 states of prefix, stem-loop and suffix as Bokhorst and Craven (omputationally ostly in the CYK algorithm) this terminator grammar uses a simpler emissions-based approah that requires only a bifuration. Produtions for the terminator grammar are: S R R Rb P P apa` b end where S is the start state, R is the state for rightwise emission, P is the state for pairwise emission and is the state for leftwise emission. 172

4 Fig.1. Canonial Terminator: Nuleotides (N) of prefix, suffix, stem, loop S N N N N stem: 4-16 pairs of nuleotides NNNNNNNNNN NNNNNNNNNN prefix: 8-10 nts N N R N loop: 2-10 nts N Fig 2. State Diagram for Terminator SCFG.1 t-rih suffix: 8-18 nts A state diagram is represented in Fig. 2, inluding transition probabilities. Probability matries for single emission and pairwise emission omplete the model. A terminator an be modeled using only leftwise (or rightwise) single-emission. However, the outside to inside generation of stem-loop requires an end state from the loop, as well as from either the prefix or suffix. Also, only one transition into the stem-loop is allowed in a terminator, so a single-emission state separate from the loop state is required. This neessitates 2 singleemission states, However, both of them ould just as easily emit either rightwise or leftwise, as with the alternative grammar of Fig. 3. For the purposes of illustrating the grammar, an overly simple toy terminator (Fig. 4) with only 2 nts for prefix, stem length, loop and suffix is used in Fig The appliation of grammar rules that result in the toy terminator are shown in the derivation (Fig. 5) and parse tree (Fig. 6). Fig. 7 illustrates the CYK algorithm that was written to san large setions of genome for loal mathes to the grammar. Although the toy terminator is only 10 nts (too short to be an atual terminator) and the math is global to simplify the illustration, the intergeni strethes of genome searhed may be longer than 5000 nts. For this reason the matrix struture used by the CYK algorithm of this projet is a variant [6] of the familiar NxN (N=string length) struture, whih would require O(MN 2 ) spae and O(MN 3 ) time. Instead, the entire string is searhed for loal mathes of at most length D = min{n, max terminator length}. D is therefore apped at 70, whih.09.1 P.91 shortens the spae requirements of CYK algorithm to O(MND) and time omplexity to O(MND 2 ). The (NxD) matrix struture is depited in Fig. 7, one of whih is required for eah of the M states to make up the full three dimensional data struture. Eah of the MND ells takes time O(1) (proportional to the number of transitions from the state) to fill, exept for state S, whih has a bifuration and so takes O(D) to fill, resulting in total running time of O(MND 2 ). The sore resulting from the CYK algorithm oded for this projet gives a different result that than the familiar log P(x,Π* G,θ), beause a value was added for base pairing (as in the Zuker algorithm [6]), to aount for the effets of energy of folding. The parameters of the grammar model were trained using a randomly seleted subset of the known terminators. Initial priors for emissions and transitions were established by statistial analysis of the training subset as folded by a loally developed rule-based algorithm. This initial model was then used by the grammar to selet a parse (prefix, stem, loop, suffix struture) for eah terminator. Counts were taken of frequenies of emissions and transitions, the model parameters were updated based upon these ounts. The proess was iterated until struture was stable. SOFTWARE AND DATASETS The Support Vetor Mahine toolbox for Matlab, Version 2.51, was used to onstrut and train the SVM that lassified the data [13]. oally developed software produed negative examples, implemented a modified CYK algorithm, trained the terminator SCFG and alulated parameters. Datasoures were the omplete E. oli genome sequene and annotations ompiled at the University of Wisonsin-Madison [14], whih are available on the web. The sequene used was the M54 version of the K-12 MG1655 strain of E. oli. The sequenes used for positive examples were all 109 experimentally determined terminators found within -10 to 60 nts from the end of a gene as doumented by esnik et al. Negative examples were drawn from both strands of the genome. This was aomplished by starting with the entire strand and removing known protein and RNA genes of either strand as well as a trailing region of 300 nts in order to minimize the possibility that unknown terminator sequene would omprise part of the set of negative training examples. The sequenes of the 163 known RNA genes were added to the intergeni sequenes to form the set of sequenes from whih negative examples were drawn. Some of the sequenes were very long (up to 5000 nts) and ontained many loal mathes to the terminator grammar. S X b P P apa` X X bx end Fig. 3. Alternative Terminator Grammar 173

5 loop S t a R t g t t t R t prefix stem suffix R t Fig. 4. Struture of Simplified Terminator P S R t R t R t R t R t t R t t t P t t t Pg t t t tpa g t t t t a g t t t t a g t t tt a g t t tt a g t t = ttagtt Fig. 5. Derivation of Simplified Terminator P g t P a Fig. 6. Parse Tree for Derivation of ttagtt d: j: 1 t 2 ** 3 4 t 5 6 P 7 a P 8 g R P 9 t R 10 t R ** Sore=S Collapsed view of the 4 arrays of the data struture whih together form the 3 dimensional array struture for CYK algorithm Coordinate system: end position j vs subsequene length d, d = j i+1 for subsequene(i:j) being onsidered Horizontal run (light gray) is leftwise emission (prefix of length 2 and loop of length 2): shows path through array for state Knight s path (gray) run is for pairwise emission (stem of length 2): shows path through array for state P Diagonal run (dark gray) is for rightwise emission (suffix of length 2): shows path through array for state R. Global sore onsiders entire string = subsequene(1:10) where j=10, d=10: Sore=S shows path through array for state S ** S R at substring(1:10), adding sores from of substring(1:2) and R of substring(3:10) Fig. 7. State path taken by global CYK algorithm performed on string ttagtt 174

6 EXPERIMENT For eah sequene proessed by the SCFG, the best loal alignments (optimal parses) were determined by the CYK algorithm. This is, in effet, the seletion of prefix, stemloop and suffix strutures for andidate terminators. A subset of 81 known terminator sequenes was randomly seleted for training the parameters of the grammar model, as desribed in the Methods setion. After training, these sequenes were proessed by the SCFG for likely parses of prefix, stem-loop and suffix strutures. Eah of these sequenes ontained one likely parse whih was parameterized, resulting in a total of 81 positive examples with whih to train the SVM. The remaining 28 positive sequenes that had not been used in training the SCGF were then proessed into 28 positive examples with whih to test the SVM. All 163 known RNA genes and the featureless intergeni sequenes were proessed by the SCFG into negative examples. From the prefix, stem-loop and suffix struture inferred by the CYK algorithm for eah example, 17 parameters were extrated. Three parameters represented frations of a,, and t in the prefix. Also extrated was the probability that the stem base pair losing the loop of the example would lose the loop of an atual terminator (as alulated by their frequeny ounts in the 81 training sequenes as folded by the SCFG). The frequenies of the 6 dinuleotide pairs in the stem that were found to aid detetion (at g ta tg g gt) were extrated from the sequene being parameterized. The number of nuleotides between the stem and the first t following it was used, along with the tail soring funtion of Carafa et al. summed over all the nuleotides of the sufffix: T = Σ x n where x n = x n-1 * 0.9 if nth nuleotide is t (3) x n = x n-1 * 0.6 if nth nuleotide is not t Additionally there were 4 strutural parameters: prefix length, stem length, loop length and suffix length. The SCFG sore of the alignment was inluded, resulting in the 17 dimensional input into the SVM for eah example being lassified. All parameters were normalized. Sine there were many more negative than positive examples, negative intergeni and negative RNA gene examples were eah randomly sampled to selet the negative examples for the training and test sets, allowing 5 times as many negative as positive (terminator) examples, proportionately representing featureless intergeni and RNA gene examples. The training set was therefore omprised of the 81 terminators that had been used to train the SCFG, along with negative examples omprised of 376 featureless intergeni examples and 29 RNA genes. SVMs with radial basis, polynomial and linear kernels were onstruted and tested. The most suessful SVM utilized a linear kernel, with C (the upper bound on the agrange multipliers, as disussed above) set to 10, limiting the influene of outliers. The test set was omprised of the 28 terminators that not been used to train the SCFG, along with 130 featureless intergeni examples and 10 negative RNA gene examples. An SVM was trained using the entire training set and tested on the test set. 96.4% were orretly identified (table 1), with detetion of negative examples more suessful than detetion of positives, of whih 92.9% were orretly identified. Three-fold ross-validation (SVM1, SVM2, SVM3 of table 2) was used on the training set (81 positive, 405 negative examples), resulting in average predition auray of 96.1% with improved auray of RNA gene predition (97.0%). DISCUSSION There are 2 major aspets to this detetion method: 1) the seletion of likely andidates from the genome and their parameterization by the SCFG based upon inferring struture as well as upon sequene omposition and 2) the use of an SVM to detet terminators from these high soring andidates utilizing the extrated features. The suess rates reported in tables 1 and 2 give a measure of how well the SVM aomplished the lassifiation that it was trained to do. It is worthwhile to also evaluate eah omponent of the 2-stage system. The SCFG retained loal mathes that sored above the utoff, resulting in all known terminators being seleted as likely terminators, along with 1063 more andidates from among the negative examples. As desribed in the Bakground setion, there is a sensitivity/speifiity tradeoff: if the SCFG were to funtion alone as a detetor, the utoff sore would be raised to have fewer false positives but redued sensitivity of about 89% as with the tradeoff seleted by Ermolaeva et al. Instead, utoff was seleted to allow 100% sensitivity for the SCFG alone, allowing the SVM to refine the predition. After passing these andidates through SVM, the sensitivity of the 2-stage terminator detetor was redued to 92.9%, but the SVM was able to weed out 97.1% of the false positives it was given (assuming none of the negative examples are as-yetundisovered terminators). This was after the SCFG had already filtered out 89% of non-terminator sequene (as ompared with 9% of known terminator sequene. A Reeiver Operating Charateristis (ROC) urve is perhaps the best way to view the full situation of tradeoff between sensitivity and speifiity. If the area under the ROC urve is 0.9 or above, the lassifier is onsidered good. As shown in Fig. 8, the SCFG alone has good performane: the area under ROC = 0.97, but when oupled with the SVM, performane is better: area under ROC = Beause of the strutural similarity of RNA genes and terminators, the suesses of both the SCFG and SVM omponents in distinguishing them was of interest. The SCFG was about as effetive in filtering out non-terminator sequene from RNA genes as from featureless intergeni 175

7 sequene. However, performane of the SVM omponent was better for negative examples drawn from featureless intergeni than RNA gene sequene, indiating room for improvement in the SVM. FUTURE WORK The SCFG-SVM terminator algorithm would be more useful if a detetor trained using examples from a wellannotated speies ould be used on an evolutionarily related but newly sequened speies with no known terminators. Future work would inlude testing this transferability by using the E. oli terminator detetor on a different, but losely related speies whose terminators are known. The SCFG omponent of the detetor might work better if the loop state was separate from the prefix state, allowing for different emissions parameters. Another way to improve the SCFG might be to hange the grammar struture to allow for single emission in the middle of the terminator stem, whih is a part of the esnik model left out of this grammar in order to simplify it. Different approahes might be tried to address the far greater numbers of negative examples than positive examples provided to the SVM. The approah of Meraz et al. [15] might improve SVM performane by using suessive iterations of a support vetor mahine to selet improved urrent negative sets by seleting for maximum dissimilarity to the positive set but also maximum distane to the negative set. The net effet is that the SVM deision boundary shrinks loser and loser to the positive set. Alternatively, it might improve results to use different C values for positive and negative examples suh that the C value for positive examples is higher, weighting them more in the lassifiation proess. Also, the SVM might be better at deteting RNA genes if a greater proportion of the negative examples were drawn from RNA genes. CONCUSION The appliation of mahine learning methods in the detetion of terminators poses a hallenge due to the nature of their evolutionarily onserved phenotype, whih is the seondary struture that the terminator takes on during transription. The hallenge is that given only sequene information, something must be inferred about the struture of the terminator. While a SCFG performed reasonably well by itself in deteting terminators, a 2-stage detetor worked better. Seleting andidates from the genome, inferring strutural parameters by utilizing their most likely parse (rather than soring), and then training an SVM to disriminate between the andidates resulted in a good detetion system for terminators. ACKNOWEDGMENTS Nello Cristianini was partially supported by NIH Grant No. R33HG , "Deteting Relations Among Heterogeneous Datasets". This work was supported by grant 5RO1H from the NHGRI to S.R.H. TABE 1: TEST RESUTS OF SVM TERMINATOR CASSIFIER terminator terminator neg ex neg ex RNA genes RNA genes total total orret wrong orret wrong orret wrong orret wrong SVM TABE 2: RESUTS OF CROSS VAIDATION OF TRAINING SET FOR SVM TERMINATOR CASSIFIERS terminator terminator neg ex neg ex RNA genes RNA genes total total orret wrong orret wrong orret wrong orret wrong SVM SVM SVM AVE

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