  Dimensionality reduction is an important operation in information
visualization, feature extraction, clustering, regression, and classification,
especially for processing noisy high dimensional data. However, most existing
approaches preserve either the global or the local structure of the data, but
not both. Approaches that preserve only the global data structure, such as
principal component analysis (PCA), are usually sensitive to outliers.
Approaches that preserve only the local data structure, such as locality
preserving projections, are usually unsupervised (and hence cannot use label
information) and uses a fixed similarity graph. We propose a novel linear
dimensionality reduction approach, supervised discriminative sparse PCA with
adaptive neighbors (SDSPCAAN), to integrate neighborhood-free supervised
discriminative sparse PCA and projected clustering with adaptive neighbors. As
a result, both global and local data structures, as well as the label
information, are used for better dimensionality reduction. Classification
experiments on nine high-dimensional datasets validated the effectiveness and
robustness of our proposed SDSPCAAN.
