Cross-channel degradation is one of the significant challenges facing speaker recognition systems. We study this problem in the support vector machine (SVM) context and nuisance variable compensation in high-dimensional spaces more generally. We present an approach to nuisance variable compensation by removing nuisance attribute-related dimensions in the SVM expansion space via projections. Training to remove these dimensions is accomplished via an eigenvalue problem. The eigenvalue problem attempts to reduce multisession variation for the same speaker, reduce different channel effects, and increase "distance" between different speakers. Experiments show significant improvement in performance for the cross-channel case.