Modified LDE for Dimensionality Reduction of Hyperspectral Image

Hyperspectral image (HSI) has shown promising results in many fields because of its high spectral resolution. However, redundancy and noise in spectral dimension seriously affect the classification of HSI. For this reason, many popular dimensionality reduction (DR) methods are proposed to solve the problem. The local discriminant embedding (LDE) as an effective non-linear method for DR can be more discriminative by constructing two neighborhood graphs. However, HSI is very easy influenced by noise, and the LDE algorithm based on K nearest neighborhood is highly susceptible to interference from extreme point, which may lead to inaccurate graph construction and poor performance of classification. To overcome the problem and retain the advantages of LDE, a modified local discriminant embedding (MLDE) is firstly applied on HSI by constructing neighborhood graphs on a new spectral feature space instead of the original space. We use variance to characterize the pixels similarity of the same class and use covariance to characterize the separation of different classes of pixels. The combination of variance and covariance makes pixels in the same class to be closer and makes greater separation of pixels from different classes, which enhances classification performance of HSI. The way of representing data by using variance and covariance can attenuate the effects of noise. The Log-Euclidean metric is used to capture the similarity between spectral vectors, which can provide a more accurate similarity evaluation than euclidean distance. The experimental results of two hyperspectral datasets demonstrate the effectiveness of our proposed MLDE method.