  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 two
sensors are modeled by a common low dimensional manifold embedded in a high
dimensional Euclidean space and the datasets are corrupted by high dimensional
noise. We establish the asymptotic limits and convergence rates for the
eigenvalues of the associated kernel matrices assuming that the sample
dimension and sample size are comparably large, where NCCA and AD are conducted
using the Gaussian kernel. It turns out that both the asymptotic limits and
convergence rates depend on the signal-to-noise ratio (SNR) of each sensor and
selected bandwidths. On one hand, we show that if NCCA and AD are directly
applied to the noisy point clouds without any sanity check, it may generate
artificial information that misleads scientists' interpretation. On the other
hand, we prove that if the bandwidths are selected adequately, both NCCA and AD
can be made robust to high dimensional noise when the SNRs are relatively
large.
