The Study Of Manifold Learning Algorithms And Their Application

With the progress of technology,the complexity of data can be reflected in its form.Faced with the massive high-dimensional nonlinear data,in the fields of Applied Mathematics,Information Science and other fields,a hot topic has emerged that how to process the characteristic information speedily and effectively.Since the internal structure of the data is generally not directly obtained through analysis,the manifold learning method can effectively describe the internal laws of high-dimensional data,and ensure that the local structure of the data is unchanged when the data is maps into the low-dimensional space.Therefore,this method has been widely used in the field of nonlinear dimensionality reduction.Traditional manifold learning methods are mostly based on the local characteristics of the data,and it is easy to ignore the global nature of the data,resulting the unclear relationship between the distant points when constructing the global low-dimensional embedding.Since most manifold learning algorithms depict the geometric structure of data by creating a neighbor graph,and need to adjust parameters based on experience,which has a tremendous influence for the performance of the algorithm.To solve such issues,the present thesis proposes two novel manifold learning methods.Considering the local characteristics of the data and obtaining parameters adaptively,we avoid the impact of manually setting approach on the performance of the algorithm,and ensure the reliability and efficiency of the algorithm.Specifically,the main studies of our thesis are as follows:1.An adaptive manifold learning algorithm has been put forward to investigate the problem of parameter selection.Manual selection of the neighborhood size and the best embedding dimension is required in the traditional local tangent space alignment(LTSA)algorithm.In the article,self-organizing mapping algorithm has been utilized so that describing the geometric structure of the sample points and adaptively selecting the size of the neighborhood.Simultaneously,by application of Cao's method of solving the minimum embedding dimension,the optimal embedding dimension has been calculated,which avoids the limitation of the traditional methods on manually adjusting parameters based on experience,and improves the classification performance of the algorithm.2.The PCA-LPP algorithm is proposed to deal with the limitations of local algorithms.The Local Preserving Projection(LPP)algorithm is a traditional method to reduce the dimensionality based on the local characteristics of the sample,and ignores the global characteristics of the sample,while the Principal Component Analysis(PCA)is a global feature extraction algorithm,and the local features of the sample cannot be considered.Therefore,in the present thesis,canonical correlation analysis method is used to fuse the feature information obtained by the above two algorithms,so that the obtained feature information not only retains the local feature information,but also has the global feature information.Compared with a single feature extraction algorithm,it has better effect.3.The two improved manifold learning algorithms proposed in this thesis are applied to the field of fault diagnosis,and the feasibility of the algorithm is verified by comparative experiments on the fault data of rolling bearings.At first,the fault data is preprocessed by applying the overall average empirical mode decomposition and bispectrum analysis to remove the Gaussian and non-Gaussian noise,and the gray-level co-occurrence matrix is used to generate a high-dimensional texture feature matrix.Then the two improved manifold learning algorithms proposed in this thesis are used to reduce the dimensionality,and the low-dimensional embedding matrix is obtained.Finally,by the way of support vector machine,we derive the recognition accuracy.It is proved by experiments in both the identification of fault types and the degree of fault damage,the proposed algorithms have fairly performance.