A self-tuning spectral clustering method for single or multi-view data. 'Spectrum' uses a new type of adaptive density aware kernel that strengthens local connections in the graph. It uses a tensor product graph data integration and diffusion procedure to integrate different data sources and reduce noise. 'Spectrum' uses either the eigengap or multimodality gap heuristics to determine the number of clusters. The method is sufficiently flexible so that a wide range of Gaussian and non-Gaussian structures can be clustered with automatic selection of K.