VC dimension of ellipsoids
  We will establish that the VC dimension of the class of d-dimensional ellipsoids is (d^2+3d)/2, and that maximum likelihood estimate with N-component d-dimensional Gaussian mixture models induces a geometric class having VC dimension at least N(d^2+3d)/2.   Keywords: VC dimension; finite dimensional ellipsoid; Gaussian mixture model 
Yohji Akama and Kei Irie
math.CO cs.LG stat.ML