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Cross-channel degradation is one of the significant challenges facing speaker recognition systems. We study the problem for speaker recognition using support vector machines (SVMs). We perform channel compensation in SVM modeling by removing non-speaker nuisance 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. We apply our methods to a subset of the Switchboard 2 corpus. Experiments show dramatic improvement in performance for the cross-channel case.