EducationSupport Vector Machines and Kernels for ComputationalBiologyAsa Ben-Hur1., Cheng Soon Ong2,3.¤, So¨ren Sonnenburg4, Bernhard Scho¨lkopf3, Gunnar Ra¨tsch2*1 Department ofComputer Science,Colorado State University,Fort Collins,Colorado,United States of America,2 Friedrich Miescher Laboratory,Max Planck Society,Tu¨bingen,Germany,3 Max Planck Institute for BiologicalCybernetics,Tu¨bingen,Germany,4 Fraunhofer Institute FIRST,Berlin,GermanyIntroductionThe increasing wealth of biological datacoming from a large variety ofplatformsand the continued developmentof newhigh-throughputmethodsforprobingbiologicalsystemsrequire increasinglymore sophisticatedcomputationalap-proaches.Putting allthese data in sim-ple-to-usedatabasesisa first step;butrealizingthe full potentialof the datarequiresalgorithmsthat automaticallyextractregularitiesfrom the data,whichcan then lead to biologicalinsight.Many ofthe problems in computationalbiology are in the form of prediction: startingfrom predictionofagene’sstructure,prediction ofits function,interactions,androle in disease.Supportvectormachines(SVMs)and related kernelmethodsareextremely good at solving such problems [1–3]. SVMs are widely used in computationalbiology due to theirhigh accuracy,theirability to dealwith high-dimensionalandlarge datasets,and their flexibility in mod-eling diverse sources of data [2,4–6].Thesimplestform ofapredictionproblem is binary classification:trying todiscriminate between objectsthatbelongto one oftwo categories—positive (+1)ornegative (21). SVMs use two key conceptstosolve this problem:large marginseparation and kernelfunctions.The ideaof large margin separation can be moti-vated by classification ofpointsin twodimensions (see Figure 1). A simple way toclassify the points is to draw a straight lineand callpoints lying on one side positiveand on the other side negative.If the twosetsare wellseparated,one would intui-tively draw the separating line such that itis as far as possible away from the points inboth sets(seeFigures2and 3). Thisintuitive choice capturesthe idea oflargemargin separation,which ismathematicallyformulated in thesection Classificationwith Large Margin.Instead of the abstract idea of points inspace,one can think of our data points asrepresenting objects using a setof featuresderived from measurements performed oneach object.For instance,in the case ofFigures 1–5,there are two measurementsfor each object,depicted aspointsin atwo-dimensionalspace.For large marginseparation,it turns out that not the exactlocation butonly the relative position orsimilarityofthe pointsto each otherisimportant.In the simplestcase oflinearclassification,the similarity oftwo objectsiscomputed bythe dot-product(a.k.a.