Sparsity preserving projections (SPP) has drawn more and more attention recently. However, the SPP only focuses on the sparse structure but ignores the discriminant information of labeled samples. We proposed a new sparse manifold learning method, called sparse discriminant embedding (SDE), for hyperspectral image (HSI) classification. The SDE utilizes the merits of both sparsity property and manifold structure. It not only preserves the sparse reconstructive relations but also explicitly boosts the discriminant manifold structure of the data, and the discriminating power of the SDE is further improved than the SPP. Experiments on the Flightline C1, Washington DC Mall, and Botswana HSI datasets are performed to demonstrate the effectiveness of the proposed SDE method.
We present a novel feature extraction algorithm for face recognition called the uncorrelated and discriminative graph embedding (UDGE) algorithm, which incorporates graph embedding and local scaling method and obtains uncorrelated discriminative vectors in the projected subspace. An optimization objective function is herein defined to make the discriminative projections preserve the intrinsic neighborhood geometry of the within-class samples while enlarging the margins of between-class samples near to the class boundaries. UDGE efficiently dispenses with a prespecified parameter which is data-dependent to balance the objective of the within-class locality and the between-class locality in comparison with the linear extension of graph embedding in a face recognition scenario. Moreover, it can address the small sample-size problem, and its classification accuracy is not sensitive to neighbor samples size and weight value, as well. Extensive experiments on extended YaleB, CMU PIE, and Indian face databases demonstrate the effectiveness of UDGE.