Class-preserving manifold learning for detection and classification

This paper proposes a supervised approach for analysis of high-dimensional data using low-dimensional submanifolds. This method offers many useful properties. Using first order approximation for the given nonlinear mapping, we introduce a locally linear model. This model is such that it minimizes the local approximation error resulted by mapping to a local subspace during the learning. Additionally, the proposed method preserves local data energy to conserve local topology. Finally, this method guarantees the separability of the mapped data for different data classes. Two different approaches used for this aim, Linear Discriminant Analysis (LDA) and Regularized Maximum Margin Criterion (RMMC). Having those local feature-domain data, the whole feature domain data can be estimated in MMSE sense. The performance of this method is demonstrated on a sonar imagery dataset for classification of underwater objects.