Research On Unsupervised 2D Dimensionality Reduction Algorithms With Adjacency Graph Learning

Dimensionality reduction for high dimensional data has always been a key topic in computer vision,image content retrieval and pattern recognition.In recent years,unsupervised two-dimensional(2D)dimensionality reduction methods for unlabeled large-scale data have made great progress.Usually,similarity matrix is used to reveal the underlying geometry structure of data in these methods.However,because of noise data,performance of these degrades when the learning of similarity matrix is at the beginning of the dimensionality reduction process.It is difficult to learn the optimal similarity matrix.Instead of using a predetermined similarity matrix to characterize the underlying geometry structure of the original 2D image space,in this thesis,we propose a new dimensionality reduction model for 2D image matrices: unsupervised 2D dimensionality reduction with adaptive structure learning(DRASL).Our proposed DRASL approach involves the learning of similarity matrix into the procedure of dimensionality reduction.To realize a desirable neighbors assignment after dimensionality reduction,we add a constraint to DRASL model such that there are exact c connected components in the final subspace.To accomplish these goals,we propose a unified objective function to integrate dimensionality reduction,the learning of the similarity matrix,and adaptive neighbors assignment into it.In addition,consider the over-emphasis of local structures of data may lead to overfitting and degrade the clustering performance.After transforming the 2-dimensional data matrices to the corresponding 1-dimensional vectors,we incorporated the global discriminative information of data distribution into DRASL and proposed a more robust unsupervised 2D dimensionality reduction method: discriminative unsupervised 2D dimensionality reduction with graph embedding(DUGE).The basic idea of DUGE is proposed based on the preservation of local geometry structure and global structure of data.It is helpful to obtain representative projection matrices.Two iterative algorithms are proposed to solve the objective function of DRASL and DUGE respectively.We compare the proposed methods with several 2-dimensional unsupervised dimensionality reduction methods and 1-dimensional unsupervised dimensionality reduction methods and evaluate the clustering performance by Kmeans on several benchmark data sets.The experimental results show that the proposed DRASL and DUGE outperform the state-of-the-art methods.