The Delaunay Triangulation Learner
时间：2018-07-03
阅读量：410次
- 演讲人： Professor Guosheng Yin
- 时间：2018年07月03日 周二下午1:30
- 地点：玉泉校区工商管理楼一楼105报告厅
摘要： We propose a new piecewise linear learner, called the Delaunay triangulation learner (DTL), which is a smoother duality of the 1-nearest neighbor (1-NN) leaner. Based on the data samples in a p-dimensional feature space, the Delaunay triangulation algorithm provides a unique triangulation of the space, which yields a dual graph of the 1-NN Voronoi diagram. The triangulation separates the convex hull of the samples into a series of disjoint p-simplices, where the samples are the vertices of the p-simplices. The DTL is constructed by fitting the responses through linear interpolation functions on each of the Delaunay simplices, and thus it approximates the whole functional by a piecewise linear function. We study the theoretical properties of the DTL and compare its performances with the 1-NN learner on multi-dimensional random smooth functionals. Furthermore, we propose two appropriate regularization functions to penalize the roughness of the DTL and improve its predictability on the testing data. In ensemble learning approaches, we propose the bagging DTLs, random crystal and the boosting DTL, where the DTLs are constructed on the subspaces of the features, and the feature interactions are captured by Delaunay triangle meshes. Extensive numerical studies are conducted to compare the proposed DTL and its ensembles with 1-NN and tree-based counterparts. The DTL methods show competitive performances in various settings, and particularly for smooth functionals the DTL demonstrates its superiority over other methods.