Extracting the informative constraints for semi-supervised marginal projections in multimodal dimensionality reduction

This paper discusses the semi-supervised marginal projection problems learning from partial constrained data. Two effective multimodal dimensionality reduction (DR) algorithms, which we call semi-supervised marginal projections (SSMP) and orthogonal SSMP (OSSMP), are proposed. By specifying the types of similarity pairs with the pairwise constraints (PC), our techniques can preserve the global structures of all points as well as local geometrical and discriminant structures embedded in the PC. SSMP in singular case is also discussed. Because in all the PC guided methods, extracting the informative constraints is difficult and random constraints greatly affect the learning performance of techniques, this work also presents an effective and efficient methodology of optimally selecting the informative constraints for learning. The analytic form of the marginal projections can be effectively obtained by eigen-decomposition. The connections between this present work and the related semi-supervised algorithms are also detailed. The effectiveness of our proposed informative constraint selection method and algorithms are evaluated by benchmark problems. Results show our methods are capable of delivering competitive results with some widely used state-of-the-art semi-supervised algorithms.