u2032 u2062 w u2062 u2062 s t u2062 d u2061 aw u2147 u03b3 y u2265 u2147 y u2265 0 1 and u03b3 determines their location relative to the origin the first plane above bounds the class 1 points and the second plane bounds the class u2212 1 points when the two classes are strictly linearly separable that is when the slack variable y 0 the linear separating surface is the plane midway between the bounding planes of eq 2 if the classes are linearly inseparable then the two planes bound the two classes with a u201c soft margin u201d determined by a nonnegative slack variable y that is the 1 norm of the slack variable y is minimized with weight u03bd in eq 1 the quadratic term in eq 1 which is twice the reciprocal of the square of the 2 norm distance between the two bounding planes of eq 2 in the n dimensional space of w u00d7 r n for a fixed u03b3 maximizes that distance often called the u201c margin u201d fig1 depicts the points represented by a and a u2212 the bounding planes defined by eq 2 with margin and the separating plane of eq 3 which separates a the points represented by rows of a with d ii 1 from a u2212 the points represented by rows of a with d ii u2212 1 methods of solving quadratic support vector machines are known in the art according to an embodiment of the invention a newton lagrangian svm nsvm was used an algorithm based on an essentially equivalent formulations of this classification task in this formulation the square of 2 norm of the slack variable y is minimized with weight u03bd 2 instead of the 1 norm of y as in eq 1 in.