Research On Image Processing Algorithms Based On Manifold Learning And Tensor Representation

Demands for manipulating big data have grown higher and higher with the rapidly developed technologies.Data are usually vectorized before processed by computers,no matter they are image data,text data,voice data,or whatever other kinds.Such kind of data calls for high computational complexity due to their massive and high-dimensional feature,which makes the process hard.Various algorithms have been proposed to avoid this disadvantage.Manifold learning is a group of methods of studying machine learning problems under the manifold assumption,which realizes dimensionality reduction by learning the spatial structure information of data.In this paper,we improve the performance of conventional non-negative matrix factorization and conventional sparse coding algorithms by taking the advantages of manifold learning and tensor representation,respectively.We propose novel algorithms and perform them on real data set.Nonnegative matrix factorization(NMF)is one of classical techniques in pattern recognition and computer vision.The performance of the standard NMF can be significantly improved by incorporating with the manifold regularization.However,most existing manifold methods fail to take the extrinsic geometry into account.We propose a novel algorithm,named curvatureaware nonnegative matrix factorization(CANMF),to explicitly consider the extrinsic geometrical structures of the data distribution.We use an affinity graph and an anisotropic diffusion process to encode the intrinsic geometrical structure of the data and the extrinsic curvature,respectively.With the extrinsic geometrical structures,the weights from different classes can be compressed,and the discriminative ability of the proposed CANMF can be enhanced.The experimental results on several real-world datasets show the effectiveness and discriminative ability of our algorithm.Sparse coding(SC)is an automatic feature extraction and selection technique that is widely used in unsupervised learning.However,conventional sparse coding vectorizes the input images,which breaks apart the local proximity of pixels and destructs the object structures of images.We propose a novel two-dimensional sparse coding(2DSC)model that represents gray images as the tensor-linear combinations.2DSC learns much more concise dictionaries because of the circular convolution operator,since the shifted versions of the learned atoms by conventional SC is treated the same.We apply 2DSC to natural images and demonstrate that 2DSC returns meaningful dictionaries for large patches,which is not true for conventional SC.