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Extending out-of-sample manifold learning via meta-modelling techniques

机译:通过元建模技术扩展样本外流形学习

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Unsupervised manifold learning has become accepted as an important tool for reducing dimensionality of a data set by finding its meaningful low dimensional representation lying on an unknown nonlinear subspace. Most manifold learning methods only embed an existing data set, but do not provide an explicit mapping function for novel out-of-sample data, thereby potentially resulting in an ineffective tool for classification purposes. To address this issue, out-of-sample extension methods have been introduced to generalize an existing embedding to new samples. In this work, a meta-modelling method called High Dimensional Model Representation (HDMR) is firstly implemented as a nonlinear multivariate regression for the out-of-sample problem for non-parametric unsupervised manifold learning algorithms. Several experiments show that the proposed method outperforms several state-of-the-art out-of-sample extension methods in terms of generalization to new samples for classification experiments on two remote sensing hyperspectral data sets.
机译:通过发现位于未知非线性子空间上的有意义的低维表示形式,无监督流形学习已成为减少数据集维数的重要工具。大多数流形学习方法仅嵌入现有数据集,而没有为新颖的样本外数据提供显式映射功能,从而可能导致无效的分类工具。为了解决这个问题,引入了样本外扩展方法,以将现有的嵌入泛化为新样本。在这项工作中,针对非参数无监督流形学习算法的样本外问题,首先将称为高维模型表示(HDMR)的元建模方法实现为非线性多元回归。多个实验表明,在针对两个遥感高光谱数据集进行分类实验的新样本的泛化方面,该方法优于几种最新的样本外扩展方法。

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