Dimensionality reduction method based on a tensor model

Abstract. Dimensionality reduction is a preprocessing step for hyperspectral image (HSI) classification. Principal component analysis reduces the spectral dimension and does not utilize the spatial information of an HSI. Both spatial and spectral information are used when an HSI is modeled as a tensor, that is, the noise in the spatial dimension is decreased and the dimension in a spectral dimension is reduced simultaneously. However, this model does not consider factors affecting the spectral signatures of ground objects. This means that further improving classification is very difficult. The authors propose that the spectral signatures of ground objects are the composite result of multiple factors, such as illumination, mixture, atmospheric scattering and radiation, and so on. In addition, these factors are very difficult to distinguish. Therefore, these factors are synthesized as within-class factors. Within-class factors, class factors, and pixels are selected to model a third-order tensor. Experimental results indicate that the classification accuracy of the new method is higher than that of the previous methods.

[1]  Russell M. Mersereau,et al.  On the impact of PCA dimension reduction for hyperspectral detection of difficult targets , 2005, IEEE Geoscience and Remote Sensing Letters.

[2]  Liangpei Zhang,et al.  Tensor Discriminative Locality Alignment for Hyperspectral Image Spectral–Spatial Feature Extraction , 2013, IEEE Transactions on Geoscience and Remote Sensing.

[3]  Salah Bourennane,et al.  Denoising and Dimensionality Reduction Using Multilinear Tools for Hyperspectral Images , 2008, IEEE Geoscience and Remote Sensing Letters.

[4]  Fang Liu,et al.  Dimensionality reduction for hyperspectral image classification based on multiview graphs ensemble , 2016 .

[5]  Andrzej Cichocki,et al.  Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis , 2014, IEEE Signal Processing Magazine.

[6]  Caroline Fossati,et al.  Dimensionality reduction and coloured noise removal from hyperspectral images , 2015 .

[7]  Joos Vandewalle,et al.  On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors , 2000, SIAM J. Matrix Anal. Appl..

[8]  Zach DeVito,et al.  Opt , 2017 .

[9]  Jun Huang,et al.  Hyperspectral image denoising using the robust low-rank tensor recovery. , 2015, Journal of the Optical Society of America. A, Optics, image science, and vision.

[10]  Jason A. Cole,et al.  Hyperspectral Remote Sensing and Its Applications , 2005 .

[11]  L. Tucker,et al.  Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.

[12]  Jianxun Li,et al.  Data field modeling and data description for hyperspectral target detection , 2016 .

[13]  Salah Bourennane,et al.  Improvement of Target Detection Methods by Multiway Filtering , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[14]  Shiming Xiang,et al.  Discriminant Tensor Spectral–Spatial Feature Extraction for Hyperspectral Image Classification , 2015, IEEE Geoscience and Remote Sensing Letters.

[15]  Peng Li,et al.  Compressive Hyperspectral Imaging via Sparse Tensor and Nonlinear Compressed Sensing , 2015, IEEE Transactions on Geoscience and Remote Sensing.

[16]  Yang Gao,et al.  Dimensionality Reduction for Hyperspectral Data Based on Class-Aware Tensor Neighborhood Graph and Patch Alignment , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[17]  M. Borengasser,et al.  Hyperspectral Remote Sensing: Principles and Applications , 2007 .

[18]  Salah Bourennane,et al.  Nonorthogonal Tensor Matricization for Hyperspectral Image Filtering , 2008, IEEE Geoscience and Remote Sensing Letters.

[19]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..