B0277
Title: Hierarchical and stochastic crystallization learning with Delaunay triangulation
Authors: Guosheng Yin - Imperial College London (United Kingdom) [presenting]
Jiaqi Gu - The University of Hong Kong (Hong Kong)
Abstract: High dimensionality is known to be the bottleneck for both nonparametric regression and the Delaunay triangulation. To exploit the advantage of the Delaunay triangulation in a local feature space, the crystallization search is developed for the neighbour Delaunay simplices of the target point similar to crystal growth. The conditional expectation function is estimated by fitting a local linear model to the data points of the Delaunay simplices. Because the shapes and volumes of Delaunay simplices are adaptive to the density of feature data points, the proposed method selects neighbour data points more uniformly in all directions in comparison with Euclidean distance-based methods and thus it is more robust to the local geometric structure of the data. The stochastic approach is further developed for hyperparameter selection and the hierarchical crystallization learning is proposed for multimodal feature data densities, where an approximate global Delaunay triangulation is obtained by first triangulating the local centres and then constructing local Delaunay triangulations in parallel. Numerical experiments on both synthetic and real data demonstrate the advantages of the method over the existing ones.
