Research On Algorithm Analysis And Applications Of Manifold Learning

Dimension reduction is one of the important techniques to deal with high dimensional data and there exist a lot of research works in this field.With the precondition that the geometrical relationship and the distance measurement among data can be kept unchanged, the main purpose of dimension reduction is that manifold corresponding to the original data in high dimension space can be mapped into low dimension space so that not only the data quantity can be reduced in future calculation but also the redundant information will be removed. The precision and efficiency will be highly improved.The linear manifold learning algorithms such as PCA have the advantages of substantial mathematical foundation and simple implementation, but these methods can't show complex nonlinear manifold structure with their linear essence. Because of this disadvantage, nonlinear manifold learning algorithms such as principal curves, ISOMAP, LLE, LE etc. come into being. Experiments show that dimension reduction of manifold learning won't cause obvious loss in precision while the efficiency is remarkably improved.Firstly, some typical manifold learning algorithms are discussed and the performance of these algorithms is deeply investagated. Secondly, through visible analysis of manifold learning algorithm, the algorithm of constructing principal curves is mainly researched. The problem of morbidity hypothesis of speech frames is solved by using the feature that neighborhood of datasets can be kept after reducing their dimensions through principal curves. Using principal curves algorithms, a double-phoneme trajectory subspace model is constructed.Considering the wide applications of manifold learning algorithms, manifold learning algorithms can be used in the pretreatment of mass image datasets, a method of dealing with the retrieval of web images using manifold learning is proposed. For RGB color spaces can't match with the apperceiving of people's eyes, a method of reducing the dimensions and classification of those images based on HSV color space is presented. Experiments show that this method has better performance in content-based image retrieval (CBIR).