Images Understanding Research Based On Manifold Learning

Recently, manifold learning has been increasingly attracted close attention in exploring the underlying structure of the nonlinear data. Most of the manifold learning methods, such as isometric feature mapping (Isomap), locally linear embedding (LLE), Laplacian-eigenmaps (LE), and local tangent space alignment (LTSA) have demonstrated excellent results to find the embedding manifolds that best describe the samples with minimum reconstruction error, so they are suboptimal from the classification viewpoint. At the same time, these kinds of methods confront many commen problems such as small samples, out of samples, nonlinear distribution of samples, high computational complexity and robust problem like short circuits etc. In addition, these methods can't effectively deal with some large-scale images and large image sequences. Based on these issues, the contributions of this paper are as follows:1. A novel method called KIMD-ISOMAP for dimensionality reduction is presented. Firstly, a modified Image Euclidean Distance is proposed and used to find the suitable neighborhood. Then, Direct Linear Discriminant Analysis (Direct LDA) is used to replace Multi-Dimensional Scaling (MDS), which aims to enhance the ability of classification. KIMD-ISOMAP is robust for small geometrical deformation and slight noise, and extends the range of the neighborhood.2. This paper presents a novel linear subspace learning algorithm called Linear Fisher Discriminant Analysis via linear local tangent space alignment (LDA-LLTSA). Globally, LDA-LLTSA uses the Fisher criterion to maximize the between-class objective function while minimizing the between-class objective function, and then the global optimal projection matrix is obtained. At the same time, in order to get a better classification of LDA-LLTSA, similar to local LDA, LDA-LLTSA also has the Fisher analysis in local tangent space based on reformulating LLTSA.3. This paper presents a novel framework, called Adaptive Hierarchical Neighbourhood Technique (AHNT), in order to obtain a'safe'neighborhood for resolving the "abnormal" phenomenon including short-circuit and sensitiveness to critical outliers widely existing in manifold learning. Under the AHNT framework, firstly we can continuously enlarge the range of stable neighbourhood through the ordered accumulation of robust and relatively small one; then, a local Gaussian model is used for enhancing the ability of discrimination in image visualization.4. A novel method is proposed to express the typhoon image sequences using manifold learning features and a framework is presented for typhoon tracking and prediction. Manifold learning methods can preserve the intrinsic structure from high-dimensionality space to embedding space, so a novel similarity maching method in low-dimensionality space can be developed to establish the prediction model based on history data.