Research On Manifold Learning And Sparse Regression Algorithm In Image Supervised Classification

With the development of multimedia technology and the improvement of storage technology,a large number of high-dimensional data have been generated.Computer's data processing capability and the clssification accuracy will be affected by the existence of high-dimensional characteristics of the data.In recent years,how to get the low dimensional representation of high-dimensional data has become an important research direction.The traditional dimensionality reduction algorithm is linear.But in many case,the distribution of the data is manifold,which is nolinear and not separable by the traditional methods.To assume that the distribution of data is globally nonlinear or local linear is the core idea of manifold learning.By minimizing the loss function,the internal nonlinear structure of the data can be learned.So the original data structure can still be maintained in the low-dimensional space.The sparse regression algorithm is instructed to make the mapping matrix low rank.In this thesis,the ideas of manifold learning and sparse regression are discussed from many aspects.Firstly,in the construction of neighborhood graph,the algorithm of KNN Graph is improved.The original samples are mapped to the regenerated kernel Hilbert space?RKHS?by the idea of kernel,so the neighborhood graph is constructed in the feature space.At the same times,the unbiased estimator l_2,1 is introduced to make the matrix sparse.The algorithm not only have no need to initializaes the value of nearest neighbor parameter K,but also effectively reduce the over fitting phenomenon.Secondly,the feature mapping algorithm is constructed and some comparative algorithms are introduced.The basic ideas,steps and characteristics of the algorithm are analyzed and compared respectively.In addition,the nonlinear embedding algorithm of manifold learning and sparse regression is studied deeply.It is combined with the improved neighborhood graph.So a nonlinear embedding algorithm is constructed by using the adjustment factor ?.The algorithm not only reduce the over dependence of the previous mapping algorithm on the neighborhood graph,but also makes the projection matrix P a sparse matrix,which improves the robustness and noise resistance of the algorithm.Finally,the algorithm is applied to supervised learning and the compared with the four algorithms introducedThe experimental results show the nonlinear graph embedding algorithm of manifold learning and the sparse regression studied in this thesis has high stability and superiority in complex data sets and simple data set.It has better performance on both ORL Face and Coil-20 data sets.Compared with other dimensionality reduction methods,it has the advantages of less input parameters,higher algorithm stability and higher recognition accuracy.