A new algorithm for preserving global and local structures in supervised dimensionality reduction

Previous research on dimensionality reduction has shown that global and local information is both important for capturing the crucial features of data sets. In this paper, we develop a new approach that can effectively retain both global and local features of a dataset for supervised dimensionality reduction. A new quadratic measure is developed to accurately describe the local features of a dataset and a composite objective is used to balance the global and local features in the dimensionality reduction of labeled datasets. The directions along which the composite objective can be maximized are computed to reduce the dimensionality of the dataset. Testing results on benchmark data sets show that this approach is able to efficiently capture features crucial for classification and generate more accurate results than a few other approaches for dimensionality reduction.