Research Of Manifold Learning On Incomplete Data

Machine learning and data mining may involve high-dimensional data sets with arbitrary patterns of missing data in practical applications.For example,in video surveillance application,part of the target of the monitoring may be in the shade of other objects.The occluded images can be viewed as incomplete data.How to discover the intrinsic structure especially nonlinear features of incomplete data is increasingly becoming a focus.manifolds learning methods are proposed to learn the nonlinear low-dimensional manifolds from sample data points embedded in high-dimensional spaces as a non-linear dimensionality reduction method.They have been widely used in machine learning and data mining to tackle the curse of dimensionality problem.However,the effectiveness of manifold learning methods may be greatly limited when some values of the data are missing.So,this paper mainly focuses on selecting the neighbors of each sample point which can reflect the local geometric structure of the manifold and discovering the local geometric structure.More concretely,the main contributions of this paper are as follows:1.We propose an improved laplacian eigenmap algorithm for images with missing values.Considering the image with missing values as a vector,the algorithm measures the distances between these images by the cosine similarity to construct the local neighborhoods of the manifold.Meanwhile,a novel weight function is proposed to construct the weight matrix,and then nonlinearly map the points to a lower dimensional space preserving the discovered local geometries.Numerical experiments on multiple benchmark data sets show that the improved laplacian eigenmap algorithm can discover the intrinsic manifold structure of the images with missing values efficiently,and reduce the impact of missing values.2.A novel manifold learning approcach called Local Tangent Space Alignment via Nuclear Norm Regularization(LTSA-NNR)is proposed to discover the nonlinear features of the incomplete data.The neighbors of each sample point are selected using the cosine similarity measurement.A new nuclear norm regularization model is proposed to discover the local coordinate systems of the determined neighborhoods.Different with the traditional manifold learning approaches,the dimensions of local coordinate systems are various in a reasonable range.The global coordinates of the incomplete data are finally obtained by patching the local structure together.We demonstrate the effectiveness of LTSA-NNR by many visualization experiments and data classification experiments on incomplete data using real-world data sets.