Dimensionality Reduction Based On Multiple Locality Constrained Graph Optimization

With the development of science and technology,it is easier for people to obtain the high-dimensional data(such as face images,medical images and video sequences,etc.).The continuous accumulation of high-dimensional data makes dimensionality reduction become a main way to understand and analyze the high-dimensional data.Recently,graph-based dimensionality reduction techniques have received increasingly concern in the relevant fields such as pattern recognition and machine learning,the reason is that the graph is a powerful tool which can characterize the similarity between data and capture the underlying structural information hidden in the high-dimensional data.In recent years,studies have shown that most of the existing dimensionality reduction methods can be unified into the graph embedding framework,hence,how to construct the high-quality graph which can reflect the intrinsic structure(e.g.subspace manifold structure)of high-dimensional data has become a significant problem in dimensionality reduction based graph embedding.In this paper,we propose a novel dimensionality reduction algorithm named Dimensionality Reduction based on Multiple Locality Constrained Graph Optimization,(DRMLCGO).Compared with other graph-based dimensionality reduction algorithms,the proposed DRMLCGO algorithm has the following characteristics: firstly,we adopt the reconstruction coefficients between high-dimensional data to construct the graph structure adaptively and our DRMLCGO algorithm avoids the problem of parameter selection in the traditional k nearest neighbors or ?-ball neighborhood criterions;Secondly,unlike most of graph-based dimensionality reduction methods in which the graphs are constructed in advance and kept unchanged during dimensionality reduction,the DRMLCGO unifies the graph construction and projection matrix learning into a joint model,the graph in the proposed algorithm can be automatically updated during the procedure of dimensionality reduction.Finally,we integrate and weight local constraints based on the various distance measurements so that the local information of input data can be discovered and well preserved,moreover,the graph constructed by our DRMLCGO algorithm can describe the intrinsic structure of high-dimensional data comprehensively and accurately.In order to evaluate the performance of the proposed algorithm,we perform a large number of classification and clustering experiments on four image databases(AR,Extended YaleB,CMU PIE and COIL20)and four UCI datasets,the experimental results show that the proposed algorithm outperforms other compared methods.In addition,we also compare the multiple local constraints with the single local constraints in DRMLCGO algorithm,which verify the feasibility and effectiveness of the proposed algorithm.