A versatile ultra-fast spectral clustering method for single or multi-view data. 'Spectrum' uses a new type of adaptive density aware kernel that strengthens local connections in dense regions in the graph. For integrating multi-view data and reducing noise we use a recently developed tensor product graph data integration and diffusion system. 'Spectrum' contains two techniques for finding the number of clusters (K); the classical eigengap method and a novel multimodality gap procedure. The multimodality gap analyses the distribution of the eigenvectors of the graph Laplacian to decide K and tune the kernel. 'Spectrum' is suited for clustering a wide range of complex data.