Learning by Active Nonlinear Diffusion
Learning by Active Nonlinear Diffusion
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DOI：
10.3934/fods.2019012
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发表时间：
2019-05
期刊：
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通讯作者：
M. Maggioni;James M. Murphy
中科院分区：
文献类型：
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作者：
M. Maggioni;James M. Murphy
本文提出了一种主动学习方法，高维数据的基础上，通过扩散过程学习的内在数据几何图形的图。扩散距离用于参数化数据集上的低维结构，这允许仅使用少量精心选择的标签对数据集进行高准确度标记。数据的几何结构表明具有同质标签的区域，以及具有高标签复杂性的区域，应该查询标签。所提出的方法享有理论上的性能保证的一般几何数据模型，其中对应于语义有意义的类的集群被允许具有非线性的几何形状，高环境维数，并遭受显着的噪声和离群值腐败。该算法的实现方式是准线性的未标记的数据点的数量，并表现出竞争力的经验性能的合成数据集和真实的高光谱遥感图像。
This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the dataset, which allow for high-accuracy labelings of the dataset with only a small number of carefully chosen labels. The geometric structure of the data suggests regions that have homogeneous labels, as well as regions with high label complexity that should be queried for labels. The proposed method enjoys theoretical performance guarantees on a general geometric data model, in which clusters corresponding to semantically meaningful classes are permitted to have nonlinear geometries, high ambient dimensionality, and suffer from significant noise and outlier corruption. The proposed algorithm is implemented in a manner that is quasilinear in the number of unlabeled data points, and exhibits competitive empirical performance on synthetic datasets and real hyperspectral remote sensing images.