Table 1 shows the performance of five one-class classifiers as well as two-class naïve Bayes and two-class SVM for comparison. The results of the one-class approaches show a slight superiority for OC-Gaussian and OC-KNN over the other one class methods based on the average of the MCC measurement. However, accuracy is less than the two-class approaches by about ~8%–10%. During the training stage of the one-class classifier we have set the 10% of the positive data, whose likelihood is furthest from the true positive data based on the distribution, as "outliers" in order to produce a compact classifier. This factor might cause a loss of 10% of information about the target class which might also result in reducing performance compared to the two class approach.

Xue, et al 11 reported a sensitivity of 0.93 and specificity of 0.88 using two-class SVM on the human miRNA with the same number of negative examples (1,000) as we used. Computing the MCC for their results gives MCC = 0.81. OC-KNN with the same data (Human) achieves slightly better results with MCC = 0.86 while comparable results are obtained with OC-Gaussian. See the column "MCC" under Human and the rows of "OC-Gaussian" and "OC- KNN" in Table 1. The two-class implementations in Table 1 are also superior with Human (MCC = 0.98 for SVM and MCC = 0.92 for naïve Bayes).

Nam, et al 8 used a hidden Markov model (HMM) to classify the human miRNA along with 1,000 negative examples to estimate the performance of their approach. They report 0.73 for sensitivity and 0.96 for specificity (MCC = 0.71). All the OC-methods outperform this algorithm except the OC-SVM which is about the same.

The aim of this section is to evaluate the performance of the one-class classification considering different features suggested by other studies 101117. We used the MCC measurement for comparison purposes.

The triplet-SVM classifier is a 2-class tool developed by Xue, et al 11 that does not rely on comparative genomic approaches. The data consist of training and testing set and these were used to evaluate the performance of one-class approaches. We used the positive 163 human pre-miRNAs for training and then tested with the 30 human pre-miRNAs as positive and 1,000 pseudo pre-miRNAs as negative class. The different performances of one-class approaches are presented in Table 2. Many of the results have higher sensitivity but lower specificity than the 2-class, although some of the difference may be attributable to the different feature set. However, two-class naïve Bayes and two-class SVM (using our features) outperform these results by about 11% and 17% respectively based on the MCC measurement with Human miRNAs in Table 1.

RNAmicro1.1 is another miRNA prediction tool developed by Hertel and Stadler 17 that relies mainly on comparative sequence analysis using two-class SVM. The positive set includes 295 alignments of distinct miRNA families obtained from the union of animal miRNAs contained in the Rfam 6.0 (276 are considered with the refined list provided by the authors). The negative set (about 10,000 provided as a new list by the authors) is constructed mainly from tRNA alignments. We have chosen randomly 1,000 to match the same size of negative class used by us and other studies. The results of one-class approaches (Table 2) are comparable (an advantage for most of the one-class methods of about 3% from the results reported by the authors). As observed earlier, two-class naïve Bayes and two-class SVM (based on our features) outperform these results by about 9% with similar data (All-miRNA).

PSoL is an iterative method developed by Wang, et al. 16 to predict ncRNA genes from the E. coli genome and to define an optimized negative class using two-class SVM. It selects an initial negative set from an unlabelled set, and then uses two-class SVM to expand the negative set gradually by reassigning from the unlabelled data. The expansion is continued until the remaining unlabeled set is reduced to a predefined size N and this set is considered to be positive predictions. We used the same data as the authors used in their study – 321 positive examples along with 11,818 unlabeled examples – for the comparison with OC-SVM using linear kernel. We followed their assessment steps using 5-fold cross validation. OC-SVM reached a sensitivity of 0.73 with specificity of 0.92. This is comparable to the PSoL recovery rate (sensitivity) of about 0.8 when the expansion is stopped at N = 1,000.

The EBV genome has been extensively studied 91819 and an estimate of 20–30 EBV miRNAs has been reported. However, additional miRNA may remain to be discovered in the EBV genome. We downloaded the whole genome of the Epstein Barr virus (Human herpes virus 4, NC_007605 version NC_007605.1 GI: 82503188) with length of 171,823 nt, from the NCBI website 20, and passed it through the pipeline shown in Fig. 1, which is similar to the one used in Yousef et al. 13. Thirty-two mature miRNAs reported in Rfam 21 (Release 8.1: May 2006) were used to estimate the sensitivity of each trained type of classifier (Table 3). As a comparison with the two-class approach, the same experiment was carried out using the BayesMiRNAfind classifier 13. We generated 5,207 candidates at step 2 (Fig. 1) but only 1,251 passed the potential stem-loop filter at step 3. At step four 68,702 mature miRNA candidates were produced from the 1,251 pre-miRNA candidates.

As shown in Table 3, all the one-class methods are able to recognize most of the reported virus miRNA with sensitivity of 72%–90%. OC-PCA has the highest sensitivity when trained by All-miRNA or Human miRNAs, whereas OC-Kmeans is superior when trained by Mouse miRNAs. BayesMiRNAfind succeeds in achieving 84% sensitivity along with 165 reported new predictions.

Rfam miRNAs registry Release 8.1: (May 2006) 21 includes a new list of human miRNA (462 stem-loop sequences) and we also used this new data to train the one-class methods. These results are presented in the last column of Table 3. In this study, 18 of the 462 new human miRNAs were discarded since they fail to form a stem-loop structure based on mfold. The new one-class results with this data set are better than those determined with the previous list of human miRNAs or to the other data sets included in Table 3. We believe this is because the "recent human " list is richer and cleaner as the number of miRNAs listed is almost double the previous one, and it is not surprising that the performance of classifiers improves as the number of positive examples for training increases. The two-class BayesMiRNAfind was also retrained with the new human miRNA sequences and with different numbers of negative examples. The best results obtained were with 200 negative examples yielding 94% (30/32) sensitivity along with 276 new miRNA predictions.

Generally, approximately 4% of the new miRNA candidates (~200/5,207) were identified by the computational procedure (Fig. 1, compare step 6 with step 3) while about 88% (28/32) of the known miRNAs were retrieved (Table 3). Using different filters (score, conservation, common, etc,) can reduce the number of miRNA predictions; for example, selecting 0.25 as a threshold (step 7 in Fig. 1) for OC-Gaussian with All-miRNA model (See Fig. 2) will recover 97% of the captured true miRNA (0.97*28) while reducing the new miRNA prediction by 42%. A threshold of 0.3 recovers 40% of the captured miRNA (0.4*28) and a reduction of about 95% of the new miRNA predictions. The choice of the threshold is arbitrary and it determines the number of the final predictions. However, one can set a threshold that captures 70–80% of the true miRNA to have reliable predictions. To assess our predictions we have used the triplet-SVM classifier tools 11 to evaluate the OC-Gaussian results. 87% of the known miRNA captured by OC-Gaussian classifier were confirmed by the triplet-SVM classifier and 13% of our new miRNA predictions were confirmed as well. This interesting result suggests that combining different methods may lead to classifying miRNAs more accurately. This also may strengthen our main purpose: to reduce the false positive predictions while obtaining high sensitivity when analyzing a large genomic sequence.

We begin by describing features of miRNA extracted from both secondary structure and sequences. We adopted the structural features from our two-class miRNA prediction method 12 for the development of a one-class method. For the positive (miRNA) class, the 21 nt of the mature miRNA are mapped into its associated stem-loop (generated by the mfold program 29) and then features are extracted as described below. Similarly, we used sliding 21 nt windows along each stem-loop strand to extract features for the negative (non-miRNA) class.

For the structural features, 62 features are derived from three parts of the associated hairpin (stem-loop) (See Fig. 3) – foot, mature, and head – and include the following for each of these parts: (1) the total number of base pairs(bp), (2) the number of bulges, (3) the number of loops, (4) the number of asymmetric loops, (5) eight features representing the number of bulges of lengths 1–7 and greater than 7, (6) eight features representing the number of symmetric loops of length 1–7 and greater than 7, (7) the distance from the mature miRNA candidate to the first paired base of the foot and head part.

For the sequence features, we define "words" as sequences having lengths equal to or less than 3. The frequency of each word in the first 9 nt of the 21 nt putative mature miRNA is extracted to form a representation in the vector space. For justification of the use of first 9 nt and the 1- 2- and 3-mers ("words"), a comparison study between different "words" lengths was conducted as presented in Table A and Table B [Additional file 1]. More detailed information can be found in 13. When using a two-class method, we chose values for features of the negative class which lie outside the distributions of values for those features which characterized the positive class 13. For one-class methods this required arbitrary choice is unnecessary since there is no need to describe a negative class.

In general a binary learning (two-class) approach to miRNA discovery considers both positive (miRNA) and negative (non-miRNA) classes by providing examples for the two classes to a learning algorithm in order to build a classifier that will attempt to discriminate between them. The most common term for this kind of learning is supervised learning where the labels of the two-classes are known before hand. One-class uses only the information for the target class (positive class) building a classifier which is able to recognize the examples belonging to its target and rejecting others as outliers.

Among the many classification algorithms available, we chose five one-class algorithms to compare for miRNA discovery. We give a brief description of each one-class classifier and we refer references 3031 for additional details including a description of parameters and thresholds. The LIBSVM library 32 was used as implementation of the SVM (both one-class and two-class using the RBF kernel function) and the DDtools 33 for the other one-class methods. See Table D [Additional file 1] for optimal parameter selections and used parameter value.

Each classifier returns a score which is a measure of the likelihood that the candidate being tested belongs to the positive class. The highest score determines the preferred candidate associated with a given hairpin structure, see Fig. 1

Support Vector Machines (SVMs) are a learning machine developed as a two-class approach 3435. The use of one-class SVM was originally suggested by Scholkopf et al. 31. One-class SVM is an algorithmic method that produces a prediction function trained to "capture" most of the training data. For that purpose a kernel function is used to map the data into a feature space where the SVM is employed to find the hyper-plane with maximum margin from the origin of the feature space. In this use, the margin to be maximized between the two classes (in two-class SVM) becomes the distance between the origin and the support vectors which define the boundaries of the surrounding circle, (or hyper-sphere in high-dimensional space) which encloses the single class.

The Gaussian model is considered as a density estimation model. The assumption is that the target samples form a multivariate normal distribution, therefore for a given test sample z in n-dimensional space, the probability density function can be calculated as:

p ( z ) = 1 ( 2 Π ) n / 2 | Σ | 1 / 2 e ( − 1 / 2 ( z − μ ) T Σ − 1 ( z − μ ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGaemiCaaNaeiikaGIaemOEaONaeiykaKIaeyypa0tcfa4aaSaaaeaacqaIXaqmaeaacqGGOaakcqaIYaGmcqqHGoaucqGGPaqkdaahaaqabeaacqWGUbGBcqGGVaWlcqaIYaGmaaWaaqWaaeaacqqHJoWuaiaawEa7caGLiWoadaahaaqabeaacqaIXaqmcqGGVaWlcqaIYaGmaaaaaOGaemyzau2aaWbaaSqabeaacqGGOaakcqGHsislcqaIXaqmcqGGVaWlcqaIYaGmcqGGOaakcqWG6bGEcqGHsisliiGacqWF8oqBcqGGPaqkdaahaaadbeqaaiabdsfaubaaliabfo6atnaaCaaameqabaGaeyOeI0IaeGymaedaaSGaeiikaGIaemOEaONaeyOeI0Iae8hVd0MaeiykaKcaaaaa@591F@

where μ and Σ are the mean and covariance matrix of the target class estimated from the training samples.

Kmeans is a simple and well-known unsupervised machine learning algorithm used in order to partition the data into k clusters. Using the OC-Kmeans we describe the data as k clusters, or more specifically as k centroids, one derived from each cluster. For a new sample, z, the distance d(z) is calculated as the minimum distance to each centroid. Then based on a user threshold, the classification decision is made. If d(z) is less than the threshold the new sample belongs to the target class, otherwise it is rejected.

One-class principal component analysis (OC-PCA). Principal component analysis (PCA) is a classical statistical method known as a linear transform that has been widely used in data analysis and compression. Mainly PCA is a projection method used for reducing dimensionality in a given dataset by capturing the most variance by a few orthogonal subspaces called principal components (PCs). For the one-class approach (OC-PCA) one needs to build the PCA model based on the training set and then for a given test example z the distance to the PCA(z) model is calculated and used as a decision factor for acceptance or rejection.

The one-class nearest neighbor classifier (OC-KNN) is a modification of the known two-class nearest neighbor classifier which learns from positive examples only. The algorithm operates by storing all the training examples as its model, then for a given test example z, the distance to its nearest neighbor y (y = NN(z)) is calculated as d(z, y). The new sample belongs to the target class when:

d ( z , y ) d ( y , N N ( y ) ) < δ MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWGKbazcqGGOaakcqWG6bGEcqGGSaalcqWG5bqEcqGGPaqkaeaacqWGKbazcqGGOaakcqWG5bqEcqGGSaalcqWGobGtcqWGobGtcqGGOaakcqWG5bqEcqGGPaqkcqGGPaqkaaGccqGH8aapiiGacqWF0oazaaa@4129@

where NN(y) is the nearest neighbor of y, in other words, it is the nearest neighbor of the nearest neighbor of z. The default value of δ is 1. The average distance of the k nearest neighbors is considered for the OC-KNN implementation.

To evaluate classification performance, we used the data generated from the positive class and 1,000 negative examples chosen at random from the negative class pool (candidates which failed one of four initial criteria, as previously described 13). The negative class is not used for training of the one-class classifiers, but merely for estimating the specificity performance.

The positive class data includes 117 miRNAs from C. elegans, 224 miRNAs from Mouse, 243 miRNAs from Human, and all 1,359 known miRNAs from other species, called All-miRNA 13. In All-miRNA, 100 homologous precursors were removed from the dataset to avoid bias, but this had little effect on accuracy (compare Table F with Table G [Additional file 1]). See 13 for more details.

The two-class naïve Bayes classifier and two-class SVM were trained with 90% of the positive miRNA data and with a negative class ranging from 50 examples to 900 chosen randomly from the pool of 1,000 negative examples. The test was done with the remaining 10% from the miRNA class and the remaining negative examples. The evaluation procedure was repeated 100 times and the results are reported in Table 1 under the title "Two-Class." For the naïve Bayes test with the set All-miRNA, the number of negative examples was extended to 55,000.

Each one-class algorithm was trained using 90% of the positive class and the remaining 10% was used for sensitivity evaluation. The randomly selected 1,000 negative examples were used for the evaluation of specificity. The whole process was repeated 100 times in order to evaluate the stability of the methods. Additionally, the Matthews Correlation Coefficient (MCC) 36 measurement is used to take into account both over-prediction and under-prediction in imbalanced data sets. It is defined as:

M C C = ( T p T n − F p F n ) ( T p + F p ) ( T p + F n ) ( T n + F n ) ( T n + F p ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGaemyta0Kaem4qamKaem4qamKaeyypa0tcfa4aaSaaaeaacqGGOaakcqWGubavcqWGWbaCcqWGubavcqWGUbGBcqGHsislcqWGgbGrcqWGWbaCcqWGgbGrcqWGUbGBcqGGPaqkaeaadaGcaaqaaiabcIcaOiabdsfaujabdchaWjabgUcaRiabdAeagjabdchaWjabcMcaPiabcIcaOiabdsfaujabdchaWjabgUcaRiabdAeagjabd6gaUjabcMcaPiabcIcaOiabdsfaujabd6gaUjabgUcaRiabdAeagjabd6gaUjabcMcaPiabcIcaOiabdsfaujabd6gaUjabgUcaRiabdAeagjabdchaWjabcMcaPaqabaaaaaaa@5C7D@

The MCC score is in the interval (-1, 1), where one shows a perfect separation, and zero is the expected value for random scores.

In Table 1, we present the performance for each one-class classifier (The performance using secondary structural features without any sequence information is shown separately in Table H [Additional file 1]). The performance for the two-class methods is presented as well. The results for a specific number of negative examples with the highest MCC only are shown.