Research On Linear Dimensionality Reduction Based On Topology Structure Remains And Its Application

Manifold learning and semi-supervised learning are the hot problems of patternrecognition and artificial intelligence,and attract more and more attention of relatedresearchers.As a kind of nonlinear dimensionality reduction methods,manifold learning caneffectively find the intrinsic geometry structure of high dimensional manifold data which arehighly nonlinear and strong attribute correlation,providing a basis for the further processing ofthe data sets.Manifold learning is a commonly used basic assumption in semi-supervisedlearning.It says that the samples in a small local neighborhood should have similarcharacteristics.This assumption is consistent with the local linear idea ofmanifold.Semi-supervised learning is a range of supervised learning and unsupervisedlearning method,it arms to get a good learning period form small quantities of labeled datasets and large unlabeled data sets.Based on analysis the state of the art and the existing problems of manifold learning andsemi-supervised learning,the thesis mainly investigates the dimensionality reduction andclassification using manifold assumption based semi-supervised learning.Based on the localtopology maintained manifold learning algorithm Locally Linear Embedding (the LLE,Locally-Linear Embedding) and Local Learning Projection (LLP, Local Learning Projectionis),the thesis proposed two semi-supervised dimensionality reduction algorithms whichbased on the local and the global structure(LGS3DR, and LLPPCA),these two algorithmswhich can integrate both local and global topological structures of the data as well as pairwiseconstraints.In order to reflect the effectiveness of the algorithm,first it compares the classificationperformance with the condition of different samples、K values、constraints on numbers anddifferent dimensions.Involved in the comparison algorithms have LGS3DR、LLPPCA、SSDR、NPSSDR、CLPP、PCA and BASELINE.Then applied the LLPPCA and LGS3DRalgorithms to image segmentation.Finally validate which have the most contribution toLGS3DR.Experiments on three popular face data sets and image segmentations show thatLGS3DR and LLPPCA are superior to many existing dimensionality reduction methods.