This paper presents a support vector machine based method (SVMHC) to predict peptides that bind MHC class I molecules. Support vector machines are a class of machine learning methods that recently has been applied for classification of microarray data, protein structure prediction and other biological problems [14–16]. In preliminary studies, it was indicated that support vector machines performed better than neural networks for MHC-peptide predictions. SVMHC is based on the support vector machine package SVM-LIGHT [17].
Support vector machines
A full coverage of the use of SVM for pattern recognition is given by Vapnik [18], but some basic concepts are introduced here. Lets assume that we have a series of examples (or input vectors) 
∈ Rd (i = 1, 2 ..., N) with corresponding labels y
i
∈ {+1, -1} (i = 1, 2, ..., N). In the case of MHC class I binding peptides, corresponds to the amino acid sequence of the peptide and y
i
(+1 or -1) represents binder/non-binder. The amino acid sequence of a peptide is represented by sparse encoding [9].
This task is carried out by (i) mapping of the input vectors
into a high dimensional feature space 
and (ii) construction of an optimal separating hyperplane (OSH) in the new feature space. The OSH is the hyperplane with the maximum distance to the nearest data points of each class in the feature space H. One of the most central points in using SVM is the choice of mapping φ (·), which is defined by a kernel function K(,
). The decision function used by SVM can be written:
The coefficients α
i
are given by the solution of the quadratic programming task: Maximize
subject to
c in equation (2) is a parameter controlling the trade off between the margin and and the training error. It is the kernel function that determines the dimension of the feature space, meaning that different kernels will represent the input vectors in different ways. The aim of the SVM is then to find an OSH without loosing the ability of generalization, often referred to as over-training. The kernels tested for MHC class I peptide predictions were linear, polynomial and radial basis function.
Equation (3) is an example of the radial basis function and equation (4) shows the polynomial kernel function.
The problem of choosing the most suitable kernel for a SVM is analogous to the problem of choosing the architecture for a neural network [15]. One main feature of SVM is that the quadratic programming task is a convex optimization problem, which ensure a global optimum. This can be compared to ANN that uses gradient based training functions with the risk of getting stuck in a local minimum.
SVMHC performance and parameter optimization
A central part of the process of developing a prediction method is to have a good measure of the prediction performance. The main goal is to have a prediction method that can generalize and correctly classify unseen data. Therefore, four-fold cross validation was used to verify SVM performance [19]. Further we have used redundancy reduction, such that no two peptides share more than four amino acids, see below. The main measure of performance used for SVMHC parameter optimization was Matthews Correlation coefficients (Mc) [20].
For each MHC-type the optimal kernel and trade off c was optimized by a systematic variation of the parameters and evaluation of prediction performance using Matthews Correlation coefficients. For the linear kernel the parameters j, a cost factor between errors on binding and non-binding peptides was also optimized. In the case of a polynomial and radial basis kernel the parameters describing the form of the function were optimized as well. The parameters chosen for each MHC class I type, were the ones that gave the best Matthews Correlation coefficient. For a more detailed explanation of the parameters, see the SVM-LIGHT documentation at http://svmlight.joachims.org/.
MHC databases
In this study we have used two databases SYFPEITHI [6] and MHCPEP [21] to create MHC class I predictors for different alleles. MHCPEP is a curated database comprising over 13000 peptide sequences known to bind MHC molecules. Entries are compiled from published reports as well as from direct submissions of experimental data. SYFPEITHI is supposed to be of a higher quality and is restricted to published data and only contain sequences that are natural ligands to T-cell epitopes. The two databases have different advantages, MHCPEP contains signicantly more data (13000 vs 3500), while the quality of the data in SYFPEITHI is assumed to be higher. Therefore, using MHCPEP data for SVM training, it is possible to make predictions for 26 different MHC types. This can be compared with only 6 MHC types when SYFPEITHI data is used for SVM training. However, the predictions from SYFPEITHI might be more reliable and should therefore be used when enough data exists.
Peptide sequences known to bind a MHC class I alleles were extracted from one of the databases. All peptides from the two databases are considered as binding peptides, i.e. no difference between strong and weak binders is considered. Unfortunately, there are very few experimentally verified examples of peptides that do not bind to a particular MHC. Therefore, the non-binding training examples were extracted randomly from the ENSEMBL database of human proteins [22]. Protein sequences from the ENSEMBL database were chopped up into the length of interest and known MHC-peptides were removed. Obviously, there is a risk that some of the non-binders actually binds, but since less than 1% of the peptides are expected to bind to a MHC molecule, we do not expect this to cause any major problems. The ratio of binder/non-binders was kept to 1:2 for all MHC types.
Redundancy reduction
When utilizing machine learning methods it is important that the training data reproduces well what can be expected for unseen data. If the training data only contains a subset of what can be expected there is a risk for over-training, i.e. that the obtained performance is not representative for unseen data. One method to avoid over-training is to use a "redundancy reduced" test-set. To understand the risk of over-training the data we used two alleles to study the change in performance using different reduction levels. We examined the performance on cross validated test-sets using different reduction levels for two different MHC alleles. For HLA-A*0201 the performance is not dependent on the reduction level, while a small increase is seen for HLA-A3 (from Mc = 0.60 to 0.74) when a looser cutoff is used, see figure 3. Using a stricter redundancy reduction might improve future predictions but as the dataset is limited it makes less alleles available for prediction. Therefore, in all studied below we choose to include a restriction that no two peptides in the dataset should share more than 4 identical residues.
Comparison of different prediction methods
The performance of SVMHC was compared to the performance of two public prediction servers, SYFPEITHI and HLA_BIND. The prediction performances were measured using Matthews Correlation coefficients (Mc) [20], Specificity-Sensitivity plots [23] and the percentage correct predictions. For SYFPEITHI and HLA_BIND the cutoff distinguishing between binders and non-binders was optimized, while for SVMHC it was kept constant and 0. There are six MHC types common between the three methods and all of these were used for comparing the performance. Each binding and non-binding peptide tested was submitted to the public prediction servers and the different prediction performances were calculated. The threshold for binder/non-binder for the public prediction servers, were chosen to give the maximum Mc on the test set.
and (ii) construction of an optimal separating hyperplane (OSH) in the new feature space. The OSH is the hyperplane with the maximum distance to the nearest data points of each class in the feature space H. One of the most central points in using SVM is the choice of mapping φ (·), which is defined by a kernel function K(
). The decision function used by SVM can be written:
