Spectral clustering has been shown to be more effective in finding clusters than some traditional 
clustering methods. Spectral clustering methods make use of the spectrum (eigenvalues) of the similarity 
matrix to reveal the data cluster structure. To perform spectral clustering on big data, we investigate 
representative way of approximating the dense similarity matrix as sparse similarity matrix. Spectral 
clustering is considered as an application of eigenvalue problems with large-scale sparse matrices. We 
propose similarity measure methods to construct large-scale sparse similarity matrix for spectral 
clustering, with the goal to develop a new direction of our high performance eigensolver and improve the 
accuracy of spectral clustering.