Dimensionality Reduction Based On Data Representations And Affinity Learning

As science and technology energetically develop,high-dimensional data such as behavioral characteristic data,space remote sensing data,medical data,financial market transaction data and etc,spring up and their complex,high-dimensional and unstructured characteristics resulted in the situation that the inner relationships and rules behind the raw data are difficult to be intuitively discovered.Therefore,data reduction become the main way to understand and deal with high-dimensional data.Because graph is a powerful tool that can describe the similarity relation between data and excavate the essential structure of high-dimensional data,the graph based data dimensionality reduction technology has emerged and become one of the important research directions in machine learning,pattern recognition and other more fields.How to construct the high-quality graph which can reflect the intrinsic structure of high-dimensional data has become a significant problem in dimensionality reduction based graph embedding.In this thesis,we propose a novel dimensionality reduction algorithm named Dimensionality Reduction based on Data Representations and Affinity Learning(DRDRAL)for data dimensionality reduction technology based on graph embedding.Compared with traditional graph-based dimensionality reduction algorithms,the proposed DRDRAL algorithm has the following advantages: First of all,we use the idea of linear reconstruction,simultaneously learns the data representations and their affinity matrix,avoids the problem of parameter selection in the traditional k nearest neighbors or ?-ball neighborhood criterions;Secondly,after obtaining the adaptive graph structure,the DRDRAL algorithm effectively takes advantage of the locality preserving projection(LPP)model,learned the projection matrix which can effectively describe the high-dimensional data's intrinsic structural;Finally,the DRDRAL method gives the solution of the objective function,namely,iterative updating strategy and calculating generalized eigenvalue problem.In order to evaluate the performance of the proposed algorithm,we perform a large number of classification and clustering experiments on six image databases(Yale,Extended YaleB,CMU PIE,AR,COIL 20 and ORL),the experimental results show that the proposed algorithm outperforms other compared methods.At the same time,we also analyzed the convergence and regularization parameters of the DRDRAL algorithm,the results show the feasibility,effectiveness and stability of our method.