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Eigenvoice-based methods have been shown to be effective for fast speaker adaptation when only a small amount of adaptation data, say, less than 10 s, is available. At the heart of the method is principal component analysis (PCA) employed to find the most important eigenvoices. In this paper, we postulate that nonlinear PCA using kernel methods may be even more effective. The eigenvoices thus derived will be called kernel eigenvoices (KEV), and we will call our new adaptation method kernel eigenvoice speaker adaptation. However, unlike the standard eigenvoice (EV) method, an adapted speaker model found by the kernel eigenvoice method resides in the high-dimensional kernel-induced feature space, which, in general, cannot be mapped back to an exact preimage in the input speaker supervector space. Consequently, it is not clear how to obtain the constituent Gaussians of the adapted model that are needed for the computation of state observation likelihoods during the estimation of eigenvoice weights and subsequent decoding. Our solution is the use of composite kernels in such a way that state observation likelihoods can be computed using only kernel functions without the need of a speaker-adapted model in the input supervector space. In this paper, we investigate two different composite kernels for KEV adaptation: direct sum kernel and tensor product kernel. In an evaluation on the TIDIGITS task, it is found that KEV speaker adaptation using both forms of composite Gaussian kernels are equally effective, and they outperform a speaker-independent model and adapted models found by EV, MAP, or MLLR adaptation using 2.1 and 4.1 s of speech. For example, with 2.1 s of adaptation data, KEV adaptation outperforms the speaker-independent model by 27.5%, whereas EV, MAP, or MLLR adaptation are not effective at all.