Figure 1
Classification by a support vector machine algorithm is performed by transforming the input variables data set by means of a mathematical function into a higher dimensional input space in which separation is much easier. The basis of this new heuristic is that classification of a seemingly chaotic input space is possible by increasing the dimensionality of that input space and thereby finding a separating boundary i.e. hyperplane. e.g.: (a) A two-dimensional training with positive examples as black circles and negative examples as white circles. The true decision boundary, (x1)2 +(x2)2 ≤ 1, is also shown. (b) The same data after mapping into a three-dimensional input space ((x1)2, (x2)2, √2(x1)(x2)). The circular decision boundary in (a) becomes a linear decision boundary in three dimensions (b). (copyright permission from Prentice Hall).