Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Understanding the Generalization Performance of Spectral Clustering
  Algorithms   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.

0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org