Feature extraction from null and non-null spaces of kernel local discriminant embedding

Extracting discriminative features and reducing the dimensionality of data are two main objectives of manifold learning. Among different techniques, nonlinear manifold learning methods have been proposed in order to extract features from data which are not linearly distributed. Kernel trick is one of the famous nonlinear techniques which helps to project the data without an explicit mapping which can be used in combination with different linear techniques (e.g., Linear discriminant analysis and local discriminant embedding (LDE)). In this paper, we propose a Two Subspace-based Kernel Local Discriminant Embedding (TSKLDE) method which extract features from both non-null and null space of the within-class locality preserving scatter matrix of LDE in the kernel space. We evaluated the proposed algorithm using three publicly available face databases. The obtained results demonstrate that the use of both features in TSKLDE leads to more noise tolerant features compared to other kernel methods and to higher discriminant ability than many existing manifold learning techniques.