Support Vector Machines
Simon Foucart
Abstract
This chapter studies binary classification from a non-statistical viewpoint. For data that are linearly separable, the perceptron algorithm is presented first. It is followed by an optimization program, known as the hard support vector machine (SVM), consisting in maximizing the margin. For data that are not exactly linearly separable, this optimization program is relaxed into soft SVM. Finally, for data that are linearly separable only after applying a feature map, the representer theorem is used to validate the so-called kernel trick.
Topics & Concepts
Support vector machineSeparable spacePerceptronMargin (machine learning)Kernel (algebra)Binary numberKernel methodComputer scienceFeature (linguistics)Artificial intelligenceHyperplanePattern recognition (psychology)Feature vectorVector optimizationBinary classificationAlgorithmMathematicsOptimization problemMachine learningArtificial neural networkDiscrete mathematicsCombinatoricsArithmeticMulti-swarm optimizationLinguisticsMathematical analysisPhilosophyNeural Networks and Applications