HIGH PERFORMANCE SPECTRAL METHODS FOR GRAPH-BASED MACHINE LEARNING

Graphs play a critical role in machine learning and data mining fields. The success of graph-based machine learning algorithms highly depends on the quality of the underlying graphs. Desired graphs should have two characteristics: 1) they should be able to well-capture the underlying structures of the data sets. 2) they should be sparse enough so that the downstream algorithms can be performed efficiently on them. This dissertation first studies the application of a two-phase spectrum-preserving spectral sparsification method that enables to construct very sparse sparsifiers with guaranteed preservation of original graph spectra for spectral clustering. Experiments show that the computational challenge due to the eigen-decomposition procedure in spectral clustering can be fundamentally addressed. We then propose a highly-scalable spectral graph learning approach GRASPEL. GRASPEL can learn high-quality graphs from high dimensional input data. Compared with prior state-of-the-art graph learning and construction methods , GRASPEL leads to substantially improved algorithm performance