Tensor Based Hyperspectral Images Dimensionality Reduction And Classification

The hyperspectral images are characterized by hundreds of spectral bands with nanometer spectral resolution.The rich information supplied by hyperspectral makes it possible to make a more precise analysis of land covers.With the development of sensor,the number of spectral bands is increasing day by day.On the other hand,the high feature dimensionality also causes the huge cost of storage and computation.What’s worse,for high dimensionality dataset,the classification performance may decrease dramatically due to the curse of dimensionality especially when there are not enough training samples.So,it is an essential and important task to extract instinct information of hyperspectral images and reduce the feature dimensionality.It has been proved that,spatial information is important for hyperspectral images dimensionality reduction.The traditional vector based dimensionality reduction methods may destroy the spatial information which may decrease the performances of dimensionality reduction methods.To fully explore the intrinsic structure information of hyperspectral images and achieve dimensionality reduction,this thesis analyzed the intrinsic structure information of hyperspectral images and proposed a tensor based dimensionality reduction and classification method for hyperspectral images.The main work of this thesis can be summarized as follows:(1)A group based low rank tensor decomposition dimensionality reduction method for hyperspectral images is proposed.The hyperspectral images have the local and nonlocal spatial structure similarity,but most of the available tensor based methods are only consider the local structure information.Also,a complex calculation method is needed to compute the best rank in low rank tensor based methods.To fully explore the local and nonlocal spatial structure information of hyperspectral images,the tensor samples are grouped into some clusters,thus the samples within a cluster have the local and nonlocal similarity.Then,the low rank tensor approximation is employed to decompose each cluster.It is noted that,with a appropriate spatial size of tensor samples,the rank along each mode of tensor samples can be set directly without estimation and calculation.At last,the Tucker decomposition is employed to achieve dimensionality reduction.(2)A compact feature representation based tensor discriminative analysis method of dimensionality reduction for hyperspectral images is proposed.Hyperspectral images have the characters of high spectral resolution and large spectral bands.On the other hand,the corre-lation between different bands is strong and there is much redundancy information between different bands,so the feature distribution is dispersed among different spectral bands which may decrease the ability of representation.So a compact feature representation method is proposed by employing tensor low rank decomposition,which makes the feature representation more compact and expressive.What’s more,in order to enhance the discriminative of reduced dataset,the linear discriminative analysis is generalized to tensor space and the factor matrices are calculated by the scatter difference criterion.At last,the dimensionality is achieved by the Tucker decomposition with the obtained factor matrices.(3)A tensor based low rank and sparse graph is proposed for hyperspectral images dimensionality reduction.As two important data representation methods,low rank representation can preserve the global structure information while the sparse representation can preserve the local structure information of original dataset.But the two representation methods are usually considered separated in available methods which may degrade the performance of corresponding methods.To jointly utilize the advantages of these two representations,the tensor based low rank representation and sparse representations are unified within a framework.After calculating the sparse and low rank factor matrices along each mode of tensor data,a graph is constructed with these factor matrices.In addition a clustering algorithm is employed to enhance the low rank and sparse constraints and reduce the computational cost.At last,the dimensionality reduction is achieved with framework of graph based dimensionality reduction.(4)A tensor-based low rank graph with multi-manifold regularization for dimensionality reduction of hyperspectral images is proposed.With the advantage of preserving original intrinsic structure information,manifold learning methods have been applied to many fields,such as dimensionality reduction and land covers classification and so on,and achieved promising performance.Based on the analysis of manifold learning,the concepts of submanifold and multi-manifold are generalized to tensor space.By exploiting the sub-manifolds information of the original dataset,multi-manifold learning is effective in enhancing the discriminative ability of the processed dataset.In addition,the low rank constraint is integrated into the framework which can exploit the global structure of original dataset.At last,the dimensionality reduction is achieved under the graph embedding framework which is constructed by the obtained factor matrices.In T-LGMR,the low rank constraint is imposed to keep the global data structures whilst tensor analysis is employed to preserve the spatial neighborhood information.Multi-manifold is utilized to preserve the local geometrical property and enhance the discriminability.In general,the proposed method can preserve thelocal and globe data structure simultaneously and enhance the discrimination.(5)A multi-scale low rank analysis method for hyperspectral images reduction is proposed.In available tensor-and low rank-based methods,how to obtain appropriate tensor samples and determine the optimal rank of hyperspectral images are still challenging issues.To address these problems,a tensor-based multi-scale low rank decomposition method for hyperspectral images dimensionality reduction is proposed.The proposed method treats the raw cube hyperspectral image as the only tensor sample which avoids the complex processing of constructing tensor samples and need no label information.In addition,a novel multi-scale low rank decomposition method is employed to acquire the multiple low rank representation of the original hyperspectral image with a novel rank estimation method.Finally,the multiscale low rank feature representation is fused and the achieve dimensionality reduction is achieved by low rank tensor approximation analysis model.