  Generalized matrix approximation plays a fundamental role in many machine
learning problems, such as CUR decomposition, kernel approximation, and matrix
low rank approximation. Especially with today's applications involved in larger
and larger dataset, more and more efficient generalized matrix approximation
algorithems become a crucially important research issue. In this paper, we find
new sketching techniques to reduce the size of the original data matrix to
develop new matrix approximation algorithms. Our results derive a much tighter
bound for the approximation than previous works: we obtain a $(1+\epsilon)$
approximation ratio with small sketched dimensions which implies a more
efficient generalized matrix approximation.
