  The theoretical analysis of spectral clustering mainly focuses on
consistency, while there is relatively little research on its generalization
performance. In this paper, we study the excess risk bounds of the popular
spectral clustering algorithms: \emph{relaxed} RatioCut and \emph{relaxed}
NCut. Firstly, we show that their excess risk bounds between the empirical
continuous optimal solution and the population-level continuous optimal
solution have a $\mathcal{O}(1/\sqrt{n})$ convergence rate, where $n$ is the
sample size. Secondly, we show the fundamental quantity in influencing the
excess risk between the empirical discrete optimal solution and the
population-level discrete optimal solution. At the empirical level, algorithms
can be designed to reduce this quantity. Based on our theoretical analysis, we
propose two novel algorithms that can not only penalize this quantity, but also
cluster the out-of-sample data without re-eigendecomposition on the overall
sample. Experiments verify the effectiveness of the proposed algorithms.
