Narrow Results

Subspace-based face recognition method aims to find a low-dimensional subspace of face appearance embedded in a high-dimensional image space. The differences between different methods lie in their different motivations and objective functions. The objective function of the proposed method is formed by combining the ideas of linear Laplacian eigenmaps and linear discriminant analysis. The actual computation of the subspace reduces to a maximum eigenvalue problem. Major advantage of the proposed method over traditional methods is that it utilizes both local manifold structure information and discriminant information of the training data. Experimental results on the AR face databases demonstrate the effectiveness of the proposed method.

The high spectral resolution of hyperspectral data allows us to solve important applied tasks with improved accuracy, but the costs of transmission, storage, processing, and recognition of such data are high. However, hyperspectral data contain substantial redundancy, so the important problem is to reduce the dimensionality of such data while preserving the improved quality of the solution of applied tasks.

In this chapter, to solve the above problem, we focus on a well-known nonlinear mapping technique, which is based on the principle of preserving pairwise Euclidean distances between vectors. We compare this technique to other dimensionality reduction techniques. To address the problem of the high computational complexity, we use a variety of methods, including stochastic gradient descent, interpolation, and space partitioning.

Next, we extend the considered technique in a natural way to use it with different spectral dissimilarity measures, such as spectral angle, spectral correlation, and spectral information divergence. In particular, several dimensionality reduction techniques based on the principle of preserving the selected pairwise dissimilarity measures are described in this chapter.

Finally, for hyperspectral images, we consider how the spatial information contained in images can be used in nonlinear mapping. In particular, we modify the dissimilarity measures to take into account the spatial context of image pixels using the order statistics.

All the experiments in this chapter are conducted using well-known open hyperspectral images.

Laplacian Eigenmaps (LE) is a widely used dimensionality reduction and data reconstruction method. When the data has multiple connected components, the LE method has two obvious deficiencies. First, it might reconstruct each component as a single point, resulting in loss of information within the component. Second, it only focuses on local features but ignores the location information between components, which might cause the reconstructed components to overlap or to completely change their relative positions. To solve these two problems, this paper first modifies the optimization objective of the LE method, proposes to describe the relative position between different components of data by using the similarity between high-density core points, and solves optimization problem by using gradient descent method to avoid the over-compression of data points in the same connected component. A series of experiments on synthetic data and real-world data verify the effectiveness of the proposed method.