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

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.