Spectral clustering is widely used in modern data analysis. Spectral clustering methods speed up the computation and keep useful information by reducing dimensionality. Recently, graph signal filtering (GSF) has been introduced to further speed up the dimensionality reduction process by avoiding solving eigenvectors.

Spectral clustering (SC) is an important data mining method in bioinformatics due to the collection of big datasets. Calculating the number of clusters and feature vectors are two main steps of SC, both of which are related to eigenproblem. We propose a novel SC method using an adaptive filter which accelerates the SC and completely sidestepping the eigensolver. Results: We are inspired by two theories of different disciplines. The first theory is Density of State (DOS), a concept of solid-state physics. DOS roughly represents the distribution of eigenvalues. We propose a more accurate DOS and integrate it to obtain the number of clusters. The second theory is Graph Signal Processing (GSP) in irregular graph. Based on existing dimension reduction method, we use GSP to compute the feature vectors. We use Chebyshev polynomials to compute DOS and GSP and let them share the polynomials. Both the computational complexity and storage complexity are low.