On Inner-Product Kernels of High Dimensional Data

In this article we investigate the eigenspectrum of inner-product kernel matrices of the type √pK={f(xi
^T
xj/√p)}i,j=1
ⁿ
. Under a two-class mixture modeling of the input data xi ∈ \mathbbR
^p
, we position ourselves in the regime where the number of data n and their dimension p are both large and comparable, and show, for a wide range of kernel functions f, that the spectrum of K only depends on f via three key parameters, with only two of them useful in extracting the statistical structure from the data. By carefully balancing these two parameters, a significant gain in classification performance is observed on real-world datasets.