On the Spectral Property of Kernel-Based Sensor Fusion Algorithms of High Dimensional Data

We apply local laws of random matrices and free probability theory to study the spectral properties two kernel-based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) alternating diffusion (AD), for simultaneously recorded high dimensional datasets under null hypothesis. The matrix interest is product kernel associated with databsets, which may not be diagonalizable in general. prove that regime where dimensions both vectors are comparable sample size, if NCCA AD conducted using a smooth function, then first few nontrivial eigenvalues will converge real deterministic values provided independent Gaussian vectors. Toward claimed result, we also provide convergence rate affinity matrix.