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Similarity matrix is critical to the performance of spectral clustering.  Mercer kernels have become popular largely due to its successes in applying  kernel methods such as kernel PCA. A novel spectral clustering method is  proposed based on local neighborhood in kernel space (SC-LNK), which assumes  that each data point can be linearly reconstructed from its neighbors. The  SC-LNK algorithm tries to project the data to a feature space by the Mercer  kernel, and then learn a sparse matrix using linear reconstruction as the  similarity graph for spectral clustering. Experiments have been performed on  synthetic and real world data sets and have shown that spectral clustering  based on linear reconstruction in kernel space outperforms the conventional  spectral clustering and the other two algorithms, especially in real world  data sets.

An improved spectral clustering algorithm based on local neighbors in kernel space