  Kernel-based clustering algorithm can identify and capture the non-linear
structure in datasets, and thereby it can achieve better performance than
linear clustering. However, computing and storing the entire kernel matrix
occupy so large memory that it is difficult for kernel-based clustering to deal
with large-scale datasets. In this paper, we employ incomplete Cholesky
factorization to accelerate kernel clustering and save memory space. The key
idea of the proposed kernel $k$-means clustering using incomplete Cholesky
factorization is that we approximate the entire kernel matrix by the product of
a low-rank matrix and its transposition. Then linear $k$-means clustering is
applied to columns of the transpose of the low-rank matrix. We show both
analytically and empirically that the performance of the proposed algorithm is
similar to that of the kernel $k$-means clustering algorithm, but our method
can deal with large-scale datasets.
