Semi-supervised Learning for Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix Vector Products

We generalize a graph-based multiclass semi-supervised classification technique based on diffuse interface methods to multilayer graphs allowing for a very high number of layers. Besides the treatment of various applications with an inherent multilayer structure, we present a very flexible approach that interprets high-dimensional data in a low-dimensional multilayer graph representation. Highly efficient numerical methods involving the spectral decomposition of the corresponding differential graph operators as well as fast matrix-vector products based on the nonequispaced fast Fourier transform (NFFT) enable the rapid treatment of very large data sets and make the algorithm independent of specialized hardware as well as scalable to even larger problems. We test the performance of our method on a variety of large and high-dimensional data sets.