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We study the behavior of two kernel based sensor fusion algorithms,nonparametric canonical correlation analysis (NCCA) and alternating diffusion(AD), under the nonnull setting that the clean datasets collected from twosensors are modeled by a common low dimensional manifold embedded in a highdimensional Euclidean space and the datasets are corrupted by high dimensionalnoise. We establish the asymptotic limits and convergence rates for theeigenvalues of the associated kernel matrices assuming that the sampledimension and sample size are comparably large, where NCCA and AD are conductedusing the Gaussian kernel. It turns out that both the asymptotic limits andconvergence rates depend on the signal-to-noise ratio (SNR) of each sensor andselected bandwidths. On one hand, we show that if NCCA and AD are directlyapplied to the noisy point clouds without any sanity check, it may generateartificial information that misleads scientists' interpretation. On the otherhand, we prove that if the bandwidths are selected adequately, both NCCA and ADcan be made robust to high dimensional noise when the SNRs are relativelylarge.

How do kernel-based sensor fusion algorithms behave under high dimensional noise?