**2. Background**

Suppose D = [*x*1,..., *x*m] is a dataset of m samples, and each column is a sample of a d-dimensional vector. *φ*(*x*) is the mapping function induced by a kernel *k*, i.e., *k* - *xi*, *x<sup>j</sup>* = *φ*(*xi*) *Tφ* - *xj* . SVC used the nonlinear Gaussian kernel function *k* - *xi*, *x<sup>j</sup>* = exp- <sup>−</sup>*<sup>q</sup>* ∗ *x<sup>i</sup>* <sup>−</sup> *<sup>x</sup>j*<sup>2</sup> . Obviously, we have *k*(*x*, *x*) = 1. Both MDSVC and SVC aim to obtain the radius R of the sphere, center a of the hypersphere, and the radius of each point in feature space. Formally, we denote *X* the matrix whose *i*-th column is *φ*(*xi*), i.e., *x* = [*φ*(*x*1),..., *φ*(*x*m)]. In this paper, we use the Gaussian kernel as our nonlinear transformation approach to map data points to feature space.
