Orthogonal subspace based nonlinear correlation learning for supervised dimensionality reduction

Many problems in intelligent data analysis involve some forms of dimensionality reduction. The paper discusses a new supervised dimensionality reduction method where samples are accompanied with class labels. We also show that it can be easily extended to the non-linear dimensionality reduction scenarios by the kernel tricks, and then we proposes an effective orthogonal feature subspace and correlation learning based non-linear dimensionality reduction called OSNCL, which is a way of measuring the nonlinear relationships between two multidimensional datasets and aims to find two sets of orthogonal bases, one for each dataset. In this setting, pairwise constraints are adopted to specify whether the pairs of instances belong to the same class or not. OSNCL can project the multivariate data into a set of more useful features and preserve the intrinsic structure of the data and the pairwise constraints defined in the orthogonal feature subspaces, under which the projections of the data are easier to be effectively partitioned from each other. We also demonstrate the practical usefulness and high scalability of OSNCL method in many data visualization tasks and experimental results on a broad range of datasets show that OSNCL method is superior to many established dimensionality reduction methods. After dimensions of the samples are reduced, few of the clusters with different class labels lying in the orthogonal subspaces constructed by OSNCL are mixed with each other.