Research On The Application Of Manifold Learning Algorithms In Image Processing

With the development of information technology, the data processing has been becoming more and more complex. The inner structure of the data is usually high-dimensional, so that people can hardly understand it by direct-viewing cognition. Dimension reduction is one of the important techniques to deal with high—dimensional data. It has the original data in a higher dimensional space mapped into a lower dimensional space that the geometrical relationship and the distance measurement among data can be kept unchanged. Thus, the data quantity in future relative calculation can be reduced, also the mainly feature of the data can be availed.The dimensional reduction can be divided into two classes - linear and nonlinear. Linear methods, represented by Principal Component Analysis (PCA), Multi -dimensional Scaling (MDS), etc, with their substantial mathematical foundation and simple implementation, has been developed maturely. However, it can not show the inner structure of the data in linear methods. Manifold learning, such as Isometric Mapping (Isomap), Locally Linear Embedding (LLE), Laplacian Eigenmaps (LE), Local Tangent Space Alignment (LTSA), is a kind of nonlinear method, the research on it is a focus these days. Compared with traditional linear method, manifold learning can discover the intrinsic dimensions of nonlinear high dimensional data effectively, helping researchers to reduce dimensionality and analyze data better.This thesis studies the image processing with the method of manifold learning algorithm, conducts simulation to prove the three kinds of non-linear dimensionality reduction technologies (Isomap, LLE, LE), and analysis the features and conclusions of each method; Also, this thesis gives a corresponding improvement analysis on three manifold learning algorithms from the aspects as differences of algorithm ideological, Computational complexity and the effect of dimensional reduction.Having analyzed the disadvantage of disable to the classification of samples by LLE, this paper has introduced a theory of Supervised Locally Linear Embedding (SLLE). Through the simulation work, SLLE algorithm proves its stronger ability to classify the different samples. Besides, the method of original LLE and SLLE are too sensitive for the number of nearest neighbors. This thesis uses a method to improve algorithm which changes the way to measure the distance between two samples. As the result shows, the improved algorithms are not so sensitive to the number of he nearest neighbors. Also, SLLE is applied in the face recognition in this thesis. The result shows that compare to the original LLE, using SLLE concludes a higher recognition rate.