Discriminative Graph Embedding-based Dimension Reduction

In practical applications,high-dimensional data is growing rapidly,so how to deal with high-dimensional data has become a hot research field in pattern recognition and machine learning.On the one hand,in the real application system,the direct processing of high-dimensional data leads to high computational complexity and large storage space,and even brings potential "dimension curse" and over fitting problems;on the other hand,there are a large number of irrelevant,redundant features in the highdimensional data,which will affect the classification of data.The above two aspects show that it is necessary to reduce the dimension of high-dimensional data.The purpose of dimensionality reduction is to find the low-dimensional representation of highdimensional data.In this thesis,three feature extraction methods are proposed to process high-dimensional data.The main research work and innovation are as follows:In graph embedding,the existing graph constructions hardly directly consider the geometrical distribution of each point to assign the weights to edges of the adjacent graphs.In fact,each point in the feature space of data has different geometrical distribution.Thus,two points of each edge have their own geometrical contributions to determining the weights of the edge.In order to overcome the shortcomings of existing methods,a novel method called Discriminative Globality and Locality Preserving Graph Embedding(DGLPGE)dimensionality reduction method is proposed.In the DGLPGE,the discrimination information and the geometrical distributions of data are fully considered to construct the global and local adjacency graph.To further enhance the pattern discrimination among the different classes,the adjacent weights of edges in the intra-class and inter-class constructed graphs are discriminatively defined.Through characterizing the geometry preserving scatters with the adjacent weights,we use maximum margin criterion to formulate the objective function,in order to keep the global and local geometry preserving scatters to be more discriminative.Inspired by the representation based graph embedding dimension reduction method,Collaborative Representation-based Locality Preserving Projections(CRLPP)and Probabilistic Collaborative Representation-based Geometry Preserving Graph Embedding(PCRGPGE)separately are presented.In the CRLPP,they assume that the similar samples should have similar reconstructions by collaborative representation and the similar reconstructions should also have the similar low-dimensional representations in the projected subspace.CRLPP first reconstructs each training sample using the collaborative representation of the other remaining training samples,at the same time,the adjacency graph including the local structure of samples is constructed,finally establishes the objective function of graph embedding,so as to obtain the low-dimensional representation of high dimensional data.In the PCRGPGE,a new graph construction is employed for considering the geometric and discriminant information of data and the probabilistic collaborative representation(PCR)is used for data reconstruction is combined to get the objective function,so that the intrinsic structure information of high-dimensional data is preserved in subspace.The experimental results of CRLPP and PCRGPGE show that they are effective dimension reduction methods.A prototype system of image classification based on discriminative graph embedding is designed and implemented.The system consists of three stages: requirement analysis,outline design and detailed design and implementation,and is developed by Java and its series of open source frameworks.The system mainly consists of login,algorithm selection and execution,ands algorithm result display page.