Two approaches are presented for non-linear PLDA to be used in speaker verification. In NIST 2010 speaker recognition evaluation (SRE) tests under DET-5 conditions, the two methods and particularly their combination provided significant improvements in equal error rates and minDCF values over a standard PLDA scheme. The proposed schemes were also applied within a speaker verification system that employs DNN-based sufficient statistics calculation resulting in a 45% reduction in minDCF relative to a conventional GMM based system.