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Predicting microRNA precursors with a generalized Gaussian components based density estimation algorithm
BMC Bioinformaticsvolume 11, Article number: S52 (2010)
Abstract
Background
MicroRNAs (miRNAs) are short noncoding RNA molecules, which play an important role in posttranscriptional regulation of gene expression. There have been many efforts to discover miRNA precursors (premiRNAs) over the years. Recently, ab initio approaches have attracted more attention because they do not depend on homology information and provide broader applications than comparative approaches. Kernel based classifiers such as support vector machine (SVM) are extensively adopted in these ab initio approaches due to the prediction performance they achieved. On the other hand, logic based classifiers such as decision tree, of which the constructed model is interpretable, have attracted less attention.
Results
This article reports the design of a predictor of premiRNAs with a novel kernel based classifier named the generalized Gaussian density estimator (G^{2}DE) based classifier. The G^{2}DE is a kernel based algorithm designed to provide interpretability by utilizing a few but representative kernels for constructing the classification model. The performance of the proposed predictor has been evaluated with 692 human premiRNAs and has been compared with two kernel based and two logic based classifiers. The experimental results show that the proposed predictor is capable of achieving prediction performance comparable to those delivered by the prevailing kernel based classification algorithms, while providing the user with an overall picture of the distribution of the data set.
Conclusion
Software predictors that identify premiRNAs in genomic sequences have been exploited by biologists to facilitate molecular biology research in recent years. The G^{2}DE employed in this study can deliver prediction accuracy comparable with the stateoftheart kernel based machine learning algorithms. Furthermore, biologists can obtain valuable insights about the different characteristics of the sequences of premiRNAs with the models generated by the G^{2}DE based predictor.
Background
MicroRNAs (miRNAs) are short RNAs (~2022 nt) that direct posttranscriptional regulation of target genes by arresting the translation of mRNAs or by inducing their cleavage [1]. Since the initial discovery of miRNAs in Caenorhabditis elegans, RNA molecules are regarded as not only a carrier of gene information, but also a mediator of gene expression [2, 3]. Currently, 9539 experimentally verified miRNAs have been collected in the miRBase database [4].
Experimental miRNA identification is accomplished by directional cloning of endogenous small RNAs [5]. Considering both the time and cost of experimental methods, many computational approaches have been proposed [6]. The mature miRNAs is cleaved from a 70120 nt precursor (premiRNA) with a stable hairpin structure. Identifying this specific structure has became an important step in analyzing miRNAs [1]. The earliest computational approaches for discovering premiRNAs are mainly based on comparative techniques and can only discover premiRNAs that are closely homologous to known miRNAs [7–10]. Alternatively, scientists have resorted to ab initio approaches to discover premiRNAs based on the characteristics of their secondary structures [11–15]. The ab initio approaches based predictors are more generally applicable than those that are based on homology searches, since the ab initio approaches do not rely on the existence of homologues. As a result, design of the ab initio approaches based predictors has attracted more attention in recent years.
The basis of the ab initio approaches is to design a coding scheme that maps the sequence and structure characteristics of premiRNAs into distinguishable patterns of feature vectors. Then, a supervised learning algorithm, also commonly referred to as data classification, is invoked to discover premiRNAs in the query RNA sequence based on the associated feature vectors. In recent years, the design of the coding scheme for characterizing premiRNAs has been extensively studied and several different schemes, including base pairing propensity [16], folding energy [17], base pair distance [18], and degree of compactness [19], have been proposed. On the other hand, most people working on this subject have employed the existing kernel based data classification algorithms such as the hidden Markov model (HMM) [20, 21], the support vector machine (SVM) [22, 23], and the kernel density estimator [15] to build the predictors due to the superior prediction performance delivered by these algorithms [24]. Nevertheless, conventional logic based data classification algorithms such as decision trees [25, 26] and decision rules [27, 28] continue to play a major role in some applications due to the interpretability of the logic rules identified by these algorithms. Such a summarized view of the characteristics and distribution of the data set further provides valuable insights about the relations among different features and is highly desirable for indepth analysis of premiRNAs.
Aiming to provide the desirable functionalities of both the kernel based and the logic based data classification algorithms, the study presented in this article has exploited the generalized Gaussian density estimator (G^{2}DE) that we have recently proposed [29]. The G^{2}DE identifies a small number of generalized Gaussian components to model the distribution of the data set in the vector space. As a result, the user can examine the parameter values associated with these of Gaussian components to obtain an overview picture of the distribution of the data set. Furthermore, through indepth analysis of the parameter values, the user can obtain valuable insights about the relations among different features.
Results and discussion
This section first describes the overall scheme of using G^{2}DE to analyze premiRNAs. Each step of the analysis procedure is further elaborated in the Methods section. Next, the prediction performance of the employed classification algorithm is evaluated and compared with four classification algorithms. A demonstrative analysis is also presented to investigate the interpretability of the employed classification algorithm.
Using G^{2}DE to analyze premiRNAs
This work uses only sequence information to identify premiRNAs from pseudo hairpins, which are RNA sequences with similar stemloop features to premiRNAs but containing no mature miRNAs. In this method, each RNA sequence is represented as a feature vector. The characteristics used to generate the feature vector, including sequence composition, folding energy and stemloop shape, have been shown to be useful for predicting premiRNAs in previous studies [17, 18, 30]. The main task carried out during the learning process of this method is to construct two mixture models of generalized Gaussian components for summarizing premiRNAs and pseudo hairpins in the vector space. We model this learning process as a largeparameteroptimization problem (LPOP) and employ an efficient optimization algorithm, Rankingbased Adaptive Mutation Evolutionary (RAME) [31], to decide the parameters associated with each generalized Gaussian component. Finally, the models learnt through the LPOP process are used to predict whether a query RNA sequence is a premiRNA. Furthermore, the constructed model of G^{2}DE comprises a small number of generalized Gaussian components and is capable of detecting the subclusters or subclasses of the data set. This study utilizes this feature of G^{2}DE to develop a twostage analysis where the first stage uses G^{2}DE to partition the data set while the second stage uses G^{2}DE to investigate each of the partitioned subsets.
Prediction performance
The present approach is evaluated using two datasets, HU920 and HU424, combined with four feature sets. See the Methods section for details of the datasets and the feature sets. The prediction performance is compared to two kernel based classifiers, SVM and RVKDE, and two logic based classifiers, C4.5 and RIPPER. The parameters for each classifier are determined by maximizing the prediction accuracy of tenfold crossvalidation on the HU920. A prediction is performed by using the HU920 dataset to predict the HU464 dataset with the selected parameters.
The employed G^{2}DE classifier is compared with two kernel based classifiers, SVM and the relaxed variable kernel density estimator (RVKDE) [32]. The SVM is a commonly used classifier because of its prevailing success in diverse bioinformatics problems [14, 33, 34], while the RVKDE has been shown to have advantages for predicting speciesspecific premiRNAs [15]. Two wellknown logic based classifiers, C4.5 [35] and RIPPER [36], are also included as representatives of logic based classification algorithms.
As shown in Table 1, the prediction accuracies of onestage G^{2}DE are 80.39%, 92.03%, 91.60% and 78.66% with different feature sets. The twostage G^{2}DE further improve the prediction accuracies and achieves the best average accuracy of 86.58%. Though the number of kernels increases from onestage to twostage G^{2}DE, it is still much less than the other kernel based classifiers. Table 1 also reveals that the kernel based classifiers generally outperform the logic based classifiers. As a result, the G^{2}DE is capable of delivering satisfactory performance using a smaller number of kernel functions than the other systems.
In addition to compare the alternative classification algorithms, the prediction performance of the proposed method is also compared to two existing premiRNA identification packages, miPred [14] and miRKDE [15]. A number (nf) of features from the four feature sets are selected with Wilcoxon rank sum test [37] are utilized as the feature set of G^{2}DE. In current implementation, nf is set to seven because that the feature set yielding the best performance in Table 1 contains seven features. In this experiment, a prediction is performed by using the HU920 dataset to predict the HU464 dataset with the parameters maximizing the prediction accuracy of tenfold crossvalidation on the HU920 dataset. The five indices for binary classification (Table 2) used in miPred and miRKDE are adopted. Table 3 shows the experimental results. G^{2}DE achieves comparable performance with those delivered by miPred and miRKDE. A notable difference between G^{2}DE and miPred and miRKDE is that G^{2}DE utilizes much less kernels. G^{2}DE2 yields the best %ACC, %SE, %Fm and %MCC, which are 93.32%, 90.09%, 93.10% and 87.16%, respectively. Although the number of kernels in G^{2}DE2 is five times larger than that in G^{2}DE, it is more acceptable to perform further analyses than that in miPred and miRKDE.
Interpretability of G^{2}DE
Though the twostage G^{2}DE achieves the best performance in Table 1, the small differences to other classifiers suggests that premiRNA prediction algorithms have reached the maximum with current feature sets. Hence, how to interpret the learnt model of machine learning techniques for users is crucial in premiRNA prediction. In this subsection, the second feature set is used as an example to explain how to interpret the models generated by the G^{2}DE based predictor. Figure 1 shows the parameters associated with the three Gaussian components used to summarize the premiRNAs in the HU920 dataset. To analyze these parameters, we compare them to the Pearson productmoment correlation coefficients (PMCC) [38] of the premiRNAs in the HU920 dataset (Figure 2). Parameters in the models generated by G^{2}DE that differ more from the corresponding elements obtained by PMCC are more of our interest. For instance, in Figure 2, the correlation between the first feature (mfe2) and the fifth feature (dQ) of this feature set is 0.36. See the 'Feature set' subsection for detailed explanations of these features. On the other hand, the correlations between the two features in the three Gaussian components (shown in Figure 1) are 0.12, 0.08 and 0.02, all of which are relatively lower than 0.36. As PMCC summarizes the distribution of all premiRNAs, this analysis suggests that the HU920 dataset is composed of multiple clusters of samples, where the relation between mfe2 and dQ varies in different clusters and causes the inconsistency of correlations.
To verify the above analysis, this study depicts the HU920 dataset with their mfe2 and dQ values (Figure 3). In Figure 3, the red squares and green circles represent the premiRNAs and the pseudo hairpins, respectively. The red ellipses, named GGC_{1}, GGC_{2} and GGC_{3}, are the generalized Gaussian components shown in Figure 1, and the black ellipse is the Gaussian distribution shown in Figure 2. Figure 3 reveals that there are potentially two clusters of premiRNAs in this dataset and form a shape of a mirrored 'L' in the feature space of mfe2 and dQ. mfe2 measures the energy of folding while dQ measures the arrangement of base paring. Table 4 shows the detailed descriptions of these features. Figure 3 suggests that if a RNA sequence has low folding energy, it is probably a premiRNA regardless of the arrangement of its base paring. On the other hand, there is another cluster of premiRNAs that have similar folding energies to those of pseudo hairpins. No obvious correlation exists in both clusters of premiRNAs. These findings coincide with the analysis based on the models generated by G^{2}DE. In this example, the Gaussian components learnt by G^{2}DE help users to identify features of interest without plotting all pairs of features along with the relations between them.
Another useful analysis provided by the learnt model of the G^{2}DE based predictor is subclass detection. By defining that a sample belongs to the Gaussian component reporting the maximum function value at the location of that sample, the learnt Gaussian components of G^{2}DE suggests that "a sample that belongs to GGC_{2} is a premiRNA." This statement is similar to the normal decision rule "a sample that has mfe2 < 0.4 is a premiRNA," except that the conditions (belong vs. mfe2 < 0.4) within the rule inferred by G^{2}DE is nonlinear. This nonlinearity of a single rule is an important feature of G^{2}DE to describe more complicated model than traditional logic based classifiers when the number of kernels of G^{2}DE is limited to the number of rules of logic based algorithms. One immediate application of the subclass detection is to group samples into clusters and then construct a classifier for each of the clusters. The performance improved by applying such twostage framework has been shown in the previous subsection.
Conclusion
Software predictors that identify premiRNAs in genomic sequences have been exploited by biologists to facilitate molecular biology research in recent years. However, design of advanced predictors of premiRNAs has focused mostly on coding the distinguishable sequence as well as structure characteristics of miRNAs. The study presented in this article addresses this issue from the aspect of exploiting advanced machine learning algorithms. The G^{2}DE employed in this study has been designed to deliver prediction accuracy comparable with the stateoftheart kernel based machine learning algorithms, while providing the user with good interpretability. As demonstrated by the experiments reported in this study, the models generated by the G^{2}DE based classifier provide the user with crucial clues about the different characteristics of the sequences of premiRNAs.
Methods
Feature set
This work adopts 33 characteristic features which have been shown to be useful for miRNA detection in previous studies [16–19, 30, 39–41]. To investigate how alternative classifiers perform when using different features, these features are grouped as four different sets according to their biochemical properties. The first feature set includes 17 sequence composition variables, which comprise frequencies of 16 dinucleotide pairs and proportion of G and C in the RNA molecule. The second feature set includes seven folding measures: Minimum Free Energy (MFE) and two of its variants [17, 18, 39], base pairing propensity [16], Shannon entropy [18], base pair distance [18, 40] and degree of compactness [19, 41]. The third feature set uses the Zscore [42] to normalize the features in the second feature set except the two MFE variants. The fourth feature set includes four stemloop features: hairpin length [15], loop length [15], consecutive basepairs [15] and the ratio of loop length to hairpin length [15]. Table 4 shows a summary of these features.
Dataset
The process of data preparation is the same as that in the compared premiRNA identification packages [14, 15] for a fair comparison. 692 human miRNA precursors are collected from the miRBase registry database [43] (release 12.0) as the positive set. For the negative set, 8494 pseudo hairpins collected from the proteincoding regions (CDSs) according to RefSeq [44] and UCSC refGene [45] annotations are analyzed. These RNA sequences are extracted from genomic regions where no experimentally validated splicing event has been reported [12]. The secondary structures of the 8494 RNA sequences are obtained by executing RNAfold [46]. RNA sequences with <18 base pairs on the stem, MFE > 25 kcal/mol and multiple loops are excluded. As a result, 3988 pseudo hairpins, which are similar to genuine premiRNAs in terms of length, stemloop structure, and number of bulges but not have been reported as premiRNAs, are used as the negative set.
Based on the positive and negative sets, one training set and one testing set are built to evaluate the premiRNA predictors. The training set, HU920, comprises 460 human premiRNAs and 460 pseudo hairpins randomly selected from the positive and negative sets, respectively. The HU920 dataset is used for parameter selection and model construction of the premiRNA predictors. The testing set, HU464, comprises the remaining 232 human premiRNAs and 232 randomly selected pseudo hairpins. Care has been taken to ensure that no pseudo hairpin is included in both datasets. Before performing any experiments on these datasets, the features are rescaled linearly by the svmscale program [47] to the interval of [1.0, 1.0].
Generalized Gaussian density estimator
This work transforms samples into feature vectors and then uses them to construct a generalized Gaussian density estimator (G^{2}DE) [29]. A density estimator is in fact an approximate probability density function. With the G^{2}DE algorithm, one approximate probability density function of the following form is generated for each class of samples:
where d is the dimension of the vector space and w_{ i }, μ_{ i }, and Σ_{ i }are the weight, mean vector, and the covariance matrix of the ith Gaussian component. Let denote the approximate probability density function for the jth class of samples. Then, a query sample located at v is predicted to belong to the class of which the corresponding likelihood function defined in the following gives the maximum value:
where S_{ j }is the set of classj training samples and S_{ j } is the number of classj training samples.
In current G^{2}DE implementation, the user can specify the maximum number of generalized Gaussian components that can be incorporated to generate the approximate probability density function for one class of samples. If the user sets this number to k and the total number of features of the data set is d, then the learning algorithm of G^{2}DE needs to figure out the optimal combination of the values of the following k(d+2)(d+1)/2 parameters in order to generate one approximate probability density function: k ddimensional vectors as the means of the generalized Gaussian components; k sets of d(d+1)/2 coefficients with each corresponding to the covariance matrix of one generalized Gaussian components; k weights. The optimal combination of parameter values are figured out using the Rankingbased Adaptive Mutation Evolutionary (RAME) algorithm [31].
In the evolutionary optimization algorithm, the objective function to be maximized is as follows:
where

(1)
Z is the vector formed by concatenating all the k(d+2)(d+1)/2 parameters associated with the approximate probability density function of one class of samples;

(2)
#Correct is the number of correctly classified training samples;

(3)
θ is a userdefined parameter;

(4)
, where s_{ i }is the ith training sample of class j.
The objective function adopted in the learning process of G^{2}DE consists of two terms. Both terms have specific mathematical meanings. Maximizing term #Correct implies that the number of training samples of which the class can be correctly predicted with the decision model is maximized. Meanwhile, maximizing the second term implies that the mixture models give the maximum likelihood with the training samples.
Twostage G^{2}DE
The learnt model of G^{2}DE is composed of a small number of Gaussian components. In this study, a sample is defined as belonging to the Gaussian component reporting the maximum function value at the location of that sample. The twostage classification framework is performed by first grouping samples belonging to the same Gaussian component into clusters and then constructing a classifier for each of the clusters. In the first stage, all training samples would be submitted to G^{2}DE for constructing a mixture model of generalized Gaussian components. Suppose that the learnt model contains n_{1} generalized Gaussian components, essentially dividing the training dataset into n_{1} clusters. Each training sample would then be assigned to the Gaussian component to which it belongs. In the second stage, G^{2}DE is invoked n_{1} times to construct n_{1} mixture models for each cluster. If each of the learnt models in the second stage contains n_{2} generalized Gaussian components, the final classifier will contain n_{1} × n_{2} generalized Gaussian components.
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Acknowledgements
The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under Contract Nos NSC 972627P001002, NSC 962320B006027MY2 and NSC 962221E006232MY2.
This article has been published as part of BMC Bioinformatics Volume 11 Supplement 1, 2010: Selected articles from the Eighth AsiaPacific Bioinformatics Conference (APBC 2010). The full contents of the supplement are available online at http://www.biomedcentral.com/14712105/11?issue=S1.
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Authors' contributions
Author C.H. Hsieh performed all calculations and analysis and drafted the manuscript. Author D. T.H. Chang aided in design of the methodology, interpretation of the data and manuscript preparation. Author C.H. Hsueh and C.Y. Wu participated in the data preparation. Author Y.J. Oyang conceived the design of G^{2}DE classifier. All authors have read and approved this manuscript.
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Keywords
 Support Vector Machine
 Prediction Performance
 Gaussian Component
 Kernel Density Estimator
 Folding Energy