Volume 11 Supplement 2
Predicting gene function using few positive examples and unlabeled ones
© Li et al; licensee BioMed Central Ltd. 2010
Published: 02 November 2010
A large amount of functional genomic data have provided enough knowledge in predicting gene function computationally, which uses known functional annotations and relationship between unknown genes and known ones to map unknown genes to GO functional terms. The prediction procedure is usually formulated as binary classification problem. Training binary classifier needs both positive examples and negative ones that have almost the same size. However, from various annotation database, we can only obtain few positive genes annotation for most offunctional terms, that is, there are only few positive examples for training classifier, which makes predicting directly gene function infeasible.
We propose a novel approach SPE_RNE to train classifier for each functional term. Firstly, positive examples set is enlarged by creating synthetic positive examples. Secondly, representative negative examples are selected by training SVM(support vector machine) iteratively to move classification hyperplane to a appropriate place. Lastly, an optimal SVM classifier are trained by using grid search technique. On combined kernel ofYeast protein sequence, microarray expression, protein-protein interaction and GO functional annotation data, we compare SPE_RNE with other three typical methods in three classical performance measures recall R, precise P and their combination F: twoclass considers all unlabeled genes as negative examples, twoclassbal selects randomly same number negative examples from unlabeled gene, PSoL selects a negative examples set that are far from positive examples and far from each other.
In test data and unknown genes data, we compute average and variant of measure F. The experiments showthat our approach has better generalized performance and practical prediction capacity. In addition, our method can also be used for other organisms such as human.
One of the important challenges in the post-genome era is determining the functional role of all genes in the cell although about one-third of the genes have been annotated and deposited in database such GO(gene ontology) . With the recent invention of several large-scale experimental methods, a wealth of functional genomic data was accumulated, including sequence, micro-array expression profile and protein-protein interaction data. These large data-sets have fueled an interest in computational approaches to gene function prediction, which promises to harness the information present in these large collections of data to automatically deduce accurate gene annotations [2, 3]. Furthermore, many works have shown that integration of different kinds of data sources can considerably improve prediction results [4, 5]. GO is a widely-used set of functional terms with which some genes are annotated, we also call functional terms as functional classes in related to classification problem from machine learning. GO functional annotation associates each gene or gene product to some functional terms. For an unknown gene, predicting its functions will assign some GO functional terms to it, which is called multi-label classification problem in machine learning community. The mainstream approach is to transform it into a binary classification task for each functional class, which focuses on training a classifier such as SVM (support vector machine) with some labeled positive and negative examples. However, the available information from the annotation databases, such as GO , is only about positive examples, i.e. for a functional class, we only know which gene is assigned to it, but we are not sure that a gene has no this function except for too few genes. As a result, when training classifier for a functional class, we can only obtain labeled positive examples and many unlabeled ones. In other words, for a functional class, we need to learn a classifier from positive and unlabeled examples. Thus, an important step is to select a suitable set of negative examples from unlabeled examples before training classifier.
Some approaches to select negative examples have been proposed. For example, Lanckriet et. al labeled the annotated genes as positive examples and the remaining ones as negative ones for each functional class . Carter et.al randomly selected the negative examples with the same size as the positive examples from the unlabeled examples . We call these two methods twoclass and twoclassbal algorithm respectively. Chunlin Wang et.al selected a set of negative examples in two steps: firstly, identifying genes which are far from each other and the most dissimilar to positive examples as initial negative examples set. Then, using iteratively SVM to expanse negative examples and stopping while the remaining unlabeled examples are less than given threshold. Their method is called PSoL(Positive Sample only learning) and its detail can be found in .
Above approaches can be divided into two categories and some problems can occur when only few positive examples and major unlabeled ones are given: 1. Regarding all unlabeled examples as negative examples . On the one hand, it may lead to class imbalance problem because of few positive examples . on the other hand, the false negative noise may seriously decrease the prediction accuracy. 2. Selecting negative examples with same size as positive examples [6, 7]. These methods eliminate the impact of imbalanced problem, but, only few negative examples can be selected, as a result, the classifier is trained on a small training set and easily leads to over-fitting. When we use GO annotation, many functional classes have few annotated genes, which will lead to a lower prediction accuracy and need to be solved . In this paper, aiming at both imbalance and over-fitting problem for genes function prediction with only few positive examples and unlabeled examples, we propose a novel strategy for predicting genes function using SVM. Firstly, we create some synthetic positive examples with few negative noises to enlarge positive examples set P. Secondly, we extract a representative negative example set RN from unlabeled genes U using SVM iteratively. Finally, an optimal SVM classifier with RBF (Radial Basis Function) is trained by using Grid-search technique. This method is called SPE_RNE(Learning classifier by Synthetic Positive Examples and Representative Negative Examples).
Results and discussion
Four groups of function terms and number of term
number of terms
The protein sequence of all of the Yeast genes were downloaded from SGD .We applied the Smith-Waterman pairwise sequence alignment algorithm  to these sequences. Each protein is represented as a vector of Smith-Waterman log E-values, and computed with respect to all 5,873 Yeast genes. A 5873*5873 similar matrix is obtained.
Microarray expression profile
Microarray datasets are real-valued matrices measuring gene expression levels under different experimental conditions. We use gene expression microarray data from the Stanford Microarray Database(SMD)  containing results from several publications, providing a total of 294 real-valued features for all 5,873 genes. Microarray entries typically include missing values due to experimental imperfections. We estimate such entries using the widely accepted KNNimpute algorithm  with default k value. Then, we computed similarity between two genes using Gauss kernel with γ = 2. The second 5873*5873 gene similar matrix is generated.
We downloaded the protein-protein interaction data from BioGRID2.0.30 . Protein-protein interaction data is described as a graph in which nodes denote protein and edges denote interaction and diffusion kernel  with diffusion constant β = 2 is used to measure the similarity between two proteins. Each gene is also represented as a vector of similarity with respect to all 5,873 genes. The third gene similar matrix is computed.
Several previous researches have shown that integrating various genomic data to predict gene function can improve prediction accuracy [4, 5]. In this paper, we add three similar matrices and obtain a sum matrix. It is noticeable that each matrix should be centralized and normalized to eliminate the effect from major data before adding them . While training SVM classifier, this pre-computed kernel matrix is used.
Experiment setting and evaluation
where TP,FP and FN denote the number of true positive, false positive and false negative respectively. Then, using 2,077 unknown genes released in April 2007 as test examples, we predict their functions and evaluate ROC (Receiver operating characteristics) score with gene function association released in December 2008 as annotation standard.
Performance comparison on known genes
For each functional class, 3796 genes are in two categories: genes assigned to this functional class and unlabeled genes. we randomly select 20 percent from these two categories as validation set, the others are training set. SVM classifiers are learned on training set and used to predict genes functions on validation set to evaluate generalized performance of algorithms.
The number of functional class whose F 1 = NaN for four algorithms and four functional groups
As shown by table 2, twoclass has the most serious imbalance and PSoL has more serious imbalance, but our method SPE-RNE, like twoclassbal, doesn’t suffer from imbalanced problem at all because we select reasonable quantity of negative examples after enlarging the positive examples set. In addition, functional classes with few annotated genes have more serious imbalance.
The mean of F 1 for four algorithms and four functional groups
The variance of F 1 for four algorithms and four functional groups
Predicting performance on unknown genes
The average ROC score for four algorithms and four functional groups
Predicting result on unknown genes
The ten genes with the most predicted functions and their predicted functions
In this paper, We propose a novel approach to predicting gene function for genes with few positive examples and unlabeled ones SPE-RNE: creating synthetic examples to enlarge the set of positive examples, extracting representative negative examples from unlabeled examples and training SVM classifier using Grid-search technique. For SPE-RNE, the validation on known gene data set shows its best F 1 value and good stability. Prediction on unknown genes set illustrates its higher ROC scores and better prediction performance than several classic algorithms. All the algorithms run in a sum matrix which is obtained by adding simply several similarity matrixes from heterogeneous data sources, which may loss some information. How to integrate effectively these heterogeneous data to predict gene function is our next research subject in future. In addition, our method can also be used for other organisms such as human.
Creating synthetic examples to enlarge the positive examples set
The problem about learning classifier with few positive examples can be found in text classification domain. An intuitive idea is to enlarge the positive examples set. Li et al  assume that positive examples in P and likely positive examples from U have common underlying feature dimensions (or subspaces) as they belong to the same class. The representative words (RW) extracted from P are used to identify more hidden positive examples from U. Fung et al  firstly identified feature words in P and select a set of reliable negative examples from U, then, all negative examples are divided into some clusters due to the diversity of negative examples, for an example from U, computing similarity d P between it and centroid of positive examples and similarity d U between it and cluster centroid of negative examples, if d U – d P is greater than a given threshold, it is added to P.
Due to sparse and discrete features of text vectors, Li and Fung’s method can not be used for continuous feature vector of gene. We can not find so-called feature words in gene vectors to identify hidden positive examples. We can only use some distance, such as Euclidean distance, to measure the similarity between genes . Fung’s method enlarges the positive examples set after selecting the reliable negative examples, but, if we use Euclidean distance or cosine distance, a better positive example centroid can not be found due to irregularity of positive examples distribution, which has been validated by our many experiments. Our experiments also show that enlarging the P by identifying hidden positive examples from U generates easily false positive noise because of few hidden positive examples in U.
The following propositions convinces us of likely positive examples of .
is a likely positive example.
Let the classification hyperplane be
f(x) = w T x + b
According to Vapnik’s theory minimizing empiric risk , following two inequalities are correct with probability close to 1:
w T e + b > 0
w T e′ + b > 0
Further f(α e + (1 – α)e′)
= w T (α e + (1 – α)e′) + b
= α w T e + (1 – α)w T e′ + b
= α(w T e + b) + (1 – α)(w T e′ + b)
f (α e +(1 – α)e′) > 0
That is, = α e + (1 – α)e′ is a positive example with probability close to 1.
Therefore, the synthetic example is probably positive example and the enlarged set of positive examples, has few negative noise. In fact, from the point of view of algebra, is convex combination of e and e′, and from the point of view of geometry, is a random point in line segment from e to e′. We have following algorithm 1 for creating synthetic examples.
The enlarging times for different functional groups
function MAKE SYN EXPS(P,n,k)
P is positive examples set;
n is amount of enlarging
k is number of nearest neighbors
pnum=size of P
nnarray=array of nearest neighbor with size k
synexps=array of synthetic examples
making syntheticpositive examples
for all e ? P do
nnarray=k nearest neighbors of e from P
selnn=n nearest neighbors randomly selected from nnarray
for all e' ? selnn do
generating a random number a ? (0, 1)
= a * e + (1 – a) * e'
adding e into synexps
Extracting the representative negative examples
After enlarging the positive examples set P, we need to train SVM on new positive examples set and unlabeled examples set U . To learn a better classifier, we should extract a subset of the most probably negative examples from unlabeled data U so that it can best recover the positive examples hidden in U . This extracted negative examples subset can represent the whole negative set well and should have suitable size to avoid the class imbalance problem. To achieve this goal, our algorithm extracts representative negative examples and consists of three steps.
Step 1, identifying a reliable initial negative examples set. For gene vectors, only distance-based similarity can be used and the most dissimilar genes to positive examples are assumed as reliable negative examples. In PSoL, initial negative set N met two conditions: all elements in N are most dissimilar to positive example set . elements in N are far from each other. Since this problem is NP-hard, an approximate solution was used. In our algorithm, one-class SVM  is utilized to extract efficiently initial negative examples. Give a percentage of negative examples, such as 10 percent, it can draw an initial decision boundary to cover most of the positive and unlabeled examples. The data points not covered by the decision boundary can be regarded as negative example points because these data points are far from the positive set in the feature space.
Step 2, learning SVM iteratively to move classification hyperplane to an appropriate place. In this iteration process, a set of classifier, C S and corresponding set of negative example set, N S are obtained. In i th iteration, we obtain not only SVM classifier C i but also negative example set N i +1 to be used to train next SVM
N i +1 = N pred ∪ N SVs (5)
Step 3, selecting the best representative negative set. The representative negative set should have best classification performance, therefore, we use each SVM from Cs to classify a validation set V that is selected randomly form and U with 10 percent of total respectively at the start of algorithm. The discrimination ability of the trained classifiers is evaluated with F 1 . Accordingly, the negative set corresponding to the best classifier is returned as the representative negative samples RN. In stead PSoL selects final classifier to classify remaining examples, our algorithm selects best classifier according to classification performance on validation set and corresponding negative set is regarded as representative negative set, final classifier is trained in the third stage. The algorithm for extracting representative negative examples is displayed in Algorithm 2.
function SEL NEG EXPS( , U)
randomly selecting 10 percent of and U respectively as validation set V
= – V, U' = U – V;
identifying the initial reliable negative examples
Training one-class SVM classifier C0 based on and U';
Classify U' using C0. The predicted negative set N1 is used as the initial negative training set
U' = U' – N1
Training iteratively SVMs.
Classifier set Cs;
negative set Ns
i = 1
while |U'| = 4 *| | do
Training two-class SVM classifier C i based on and N1;
Cs(i) = C i , Ns(i) = N1;
Classify U' by C i , N2 is the predicted reliable negative set, where |N2| = m| |;
N1 = N2 + N SV , where N SV is the negative SVs of C i ;
U' = U' – N2.
i = i + 1;
selecting representive negative examples set
for all C ? Cs do
computing the F 1 on V
return RN from Ns with maximum F 1
Training the SVM for predicting genes function
After enlarging the positive examples set and extracting the representative negative examples, we merge these two kinds of examples into a training set ∪ RN. A SVM classifier with RBF kernel is trained on it. Grid-search technique  is used to search the optimal parameters c and g and an optimal SVM classifier can be successfully obtained.
This work is supported in part by the National Science Foundation NSF CCF 0905291, NSF IIS 0448023, NSF IIP 0934197, Natural Science Foundation in China with grant No 60573057 ”Research on Key Technology of Data Minging” and grant No 90920005 ”Chinese Language Semantic Knowledge Acquisition and Semantic Computational Model Study”. We would like to thank Prof. Chih-Jen Lin from National Taiwan University for using SVM matlab toolkit. Publication of this supplement was made possible with support from the International Society of Intelligent Biological Medicine (ISIBM).
This article has been published as part of BMC Genomics Volume 11 Supplement 2, 2010: Proceedings of the 2009 International Conference on Bioinformatics & Computational Biology (BioComp 2009). The full contents of the supplement are available online at http://www.biomedcentral.com/1471-2164/11?issue=S2.
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