Semi-Supervised Nonlinear Dimensionality Reduction with Pairwise Constraints

The problem of semi-supervised dimensionality reduction with kernels called (KSDR)-D-2 is considered for semi-supervised learning. In this setting, domain knowledge in the form of pair constraints is adopted to specify whether pairs of instances belong to the same class or not. (KSDR)-D-2 can project the samples data onto a set of 'useful' features and preserve the structure of unlabeled samples data as well as both similar and dissimilar constraints defined in the feature space, under which the samples with different class labels are easier to be effectively partitioned from each other. We demonstrate the practical usefulness and high scalability of (KSDR)-D-2 algorithms in data visualization and classification tasks through extensive simulation studies. Experimental results show the proposed methods can almost always achieve the highest accuracy when the dimension is reduced. And (KSDR)-D-2 methods outperform some established dimensionality reduction methods no matter how many numbers of constraints, dimensions are used.