The remedy employed by the programmer to separate them is to go into the third dimension, as it were. With the aid of a mathematical algorithm—a kernel function that can be chosen at will—he raises or lowers the points in the two-dimensional level so that they now float at different heights in three-dimensional space. »As a control value for the height, one can for example take one third of the weight plus four times the size,« Bauer explains. A skillful selection of this kernel function makes it possible subsequently to use a plane to separate the points floating in three-dimensional space. With regard to three-dimensional space, the plane represents a linear solution. This procedure can be enhanced at will. The points (vectors) can also be transformed into a multidimensional space (or even an infinitely dimensional one). The linear ›separating hyperplane‹ is then in each case one dimension lower.
Every separating plane is defined by several selected vectors, i.e., by those that are nearest to it. For this reason they are also called ›support vectors.‹ You can visually imagine them as stilts that support the separating
plane from both sides (without actually touching it). Referring back to the previous sample system, if a pair
of values for size and weight is now fed from an unknown source, the support vector machine compares the vector derived from these values with the support vectors that identify the male–female border, in this way quickly determining the sex.
A support vector machine represents men and women whose height and weight has been entered as points in a 2-D level. The clouds of points representing men and women cannot be separated linearly using a separating line but only with a wavy line.Remedy is provided by a mathematical algorithm (kernel function) with which the points that were previously in the 2D level are raised varying amounts in 3D space. There it is possible to cleanly separate them using a 2D separating plane (blue) that—relative to the 3D space—represents a linear solution.