Hybrid structure for robust dimensionality reduction

In recent years, dimensionality reduction has attracted a great deal of attention in the communities of machine learning and data mining. The basic goal of dimensionality reduction is to discover the low dimensional manifold embedded in a high dimensional space. Although some existing manifold learning algorithms (ISOMAP, LE, LLE, LTSA, etc.) can capture the local structure of data manifold, they have poor performance in some recognition tasks. This is mainly because that they cannot handle well with the "out of sample" problem. Moreover, these algorithms are sensitive to the choice of nearest neighbors, which is crucial in classification. To address these problems, this paper proposes a Robust Dimensionality Reduction Algorithm With Local and Global Structure (RLGS) based on a novel adaptive weighting mechanism. Hybrid structure of local and global structures is studied. By using the adaptive weight, RLGS has the capacity of adaptively exploiting non-linear structure of data manifold and is robust to parameters. Experiments demonstrate that RLGS performs better on public face databases compared with other reported algorithms.