Abstract The Delaunay triangulation learner (DTL), which is a new piecewise linear learner, is proposed for both regression and classification tasks. Based on the data samples in a p -dimensional feature space, the Delaunay triangulation algorithm provides a unique way of triangulating the space. 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. In the ensemble learning approaches, bagging DTLs, random crystal and the boosting DTL are introduced, where the DTLs are constructed on the subspaces of the features, and the feature interactions can be captured by Delaunay triangle meshes. Extensive numerical studies are conducted to compare the proposed DTL and its ensembles with tree-based counterparts, K-nearest neighbors and the multivariate adaptive regression spline. The DTL methods show competitive performances in various settings, and particularly the DTL demonstrates its superiority over others for smooth functionals.

中文翻译：

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Delaunay 三角剖分学习器及其集成

摘要 Delaunay三角学习器（DTL）是一种新的分段线性学习器，被提出用于回归和分类任务。Delaunay 三角剖分算法基于 ap 维特征空间中的数据样本，提供了一种独特的空间三角剖分方法。三角剖分将样本的凸包分成一系列不相交的 p -单纯形，其中样本是 p -单纯形的顶点。DTL 是通过在每个 Delaunay 单纯形上通过线性插值函数拟合响应来构建的，因此它通过分段线性函数来近似整个函数。在集成学习方法中，引入了 bagging DTL、随机晶体和 boosting DTL，其中 DTL 构建在特征的子空间上，并且特征交互可以通过 Delaunay 三角形网格捕获。进行了广泛的数值研究，以将所提出的 DTL 及其集成与基于树的对应项、K 近邻和多元自适应回归样条进行比较。DTL 方法在各种设置中都显示出有竞争力的性能，尤其是 DTL 展示了其在平滑泛函方面优于其他方法的优势。