Incremental Multi-manifold Out-of-Sample Data Prediction

A lot of manifold learning algorithms have been developed, which are used to learn a low dimensional model on a manifold representing large numbers of data in high dimensionality. Multi-manifold learning algorithms have also been put forward to provide a compact representation when these data come from different classes, with different intrinsic dimensionalities. However, when unseen data samples are added to the data set, the necessity of retraining becomes a barrier to the application of multi-manifold learning algorithms as preprocessing step in predictive modeling. In this paper, an incremental out-of-sample data low dimensional coordinates prediction approach is proposed to solve the out-of-sample data problem for multi-manifold. The algorithm can learn a global low dimensional structure with randomly sampled data from each class in the first step, and can compute the low dimensional coordinates on the corresponding manifold for each new coming data effectively. The algorithm is evaluated using both synthetic and real-world datasets and the results are shown both qualitatively and quantitatively.