Research Announcement: Di use Interface Methods for Multiclass Segmentation of High-Dimensional Data
Ekaterina Merkurjev, Cristina García–Cardona, Andrea Louise Bertozzi, Arjuna Flenner, Allon G. Percus · 2014
We present two graph-based algorithms for multiclass segmentation of high-dimensional data, motivated by the binary di use interface model. One algorithm generalizes Ginzburg-Landau (GL) functional minimization on graphs to the Gibbs simplex. The other algorithm uses a reduction of GL minimization, based on the Merriman-Bence-Osher scheme for motion by mean curvature. These yield accurate and e cient algorithms for semi-supervised learning. Our algorithms outperform existing methods, including supervised learning approaches, on the benchmark data sets that we used. We refer to (1) for a more detailed illustration of the methods, as well as di erent experimental examples.