sentences:  Spectral clustering has been successfully applied on large graphs by first identifying their community structure, and then clustering communities.Spectral clustering is closely related to nonlinear dimensionality reduction, and dimension reduction techniques such as locally-linear embedding can be used to reduce errors from noise or outliers.Free software to implement spectral clustering is available in large open source projects like Scikit-learn  using LOBPCG with multigrid preconditioning, or ARPACK, MLlib for pseudo-eigenvector clustering using the power iteration method, and R.
  
  The kernel "k"-means problem is an extension of the "k"-means problem where the input data points are mapped non-linearly into a higher-dimensional feature space via a kernel function formula_20.