The objective in eqn. 6 is to minimize, by tuning c, R, and slack variables in ξ ξ ξ, the squared radius of the sphere R 2 plus a mean, weighted by hyperparameter ν -1 > 0, of the slack variables. The former term seeks a minimum-size sphere; the latter term penalizes constraint violations. Each response vector m i is associated with a non-negative (imposed by constraint in eqn. 8) slack variable ξ i ≥ 0. Eqn. 7 expresses a soft constraint that each response vector m i falls inside the hypersphere; a nonzero slack variable ξ i > 0 allows m i to fall outside the hypersphere, but this is penalized by the second term in the objective function. Te hyperparameter ν controls how much to penalize such nonzero slack variables.