Supervised Dimension Reduction by Local Neighborhood Optimization for Image Processing

Subspace learning-based dimensionality reduction algorithms are important and have been popularly applied in data mining, pattern recognition and computer vision applications. They show the successful dimension reduction when data points are evenly distributed in the high-dimensional space. However, some may distort the local geometric structure of the original dataset and result in a poor low-dimensional embedding while data samples show an uneven distribution in the original space. In this paper, we propose a supervised dimension reduction method by local neighborhood optimization to disposal the uneven distribution of high-dimensional data. It extends the widely used Locally Linear Embedding (LLE) framework, namely LNOLLE. The method considers the class label of the data to optimize local neighborhood, which achieves better separability inter-class distance of the data in the low-dimensional space with the aim to abstain holding together the data samples of different classes while mapping an uneven distributed data. This effectively preserves the geometric topological structure of the original data points. We use the presented LNOLLE method to the image classification and face recognition, which achieves a good classification result and higher face recognition accuracy compared with existing manifold learning methods including popular supervised algorithms. In addition, we consider the reconstruction of the method to solve noise suppression for seismic image. To the best of our knowledge, this is the first manifold learning approach to solve high-dimensional nonlinear seismic data for noise suppression. The experimental results on forward model and real seismic data show that LNOLLE improves signal to noise ratio of seismic image compared with the widely used Singular Value Decomposition (SVD) filtering method.