Riemannian manifold learning based k-nearest-neighbor for hyperspectral image classification

The existence of nonlinear characteristics in hyperspectral data is considered as an influential factor curtailing the classification accuracy of canonical linear classifier like k-nearest neighbor (k-NN). To deal with the problem, we investigated approaches to combine manifold learning methods and the k-NN classifier to preserve nonlinear characteristics contained in hyperspectral imagery. Then we proposed a Riemannian manifold learning (RML) based k-NN classifier for hyperspectral image classification, which substitutes the Euclidean distances used in canonical kNN by geodesic distances yielded by RML. The experimental results on AVIRIS data show that in most cases, the RML-kNN Classifier accesses higher classification accuracies than canonical k-NN.

[1]  Thomas L. Ainsworth,et al.  Improved Manifold Coordinate Representations of Large-Scale Hyperspectral Scenes , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[2]  张振跃,et al.  Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment , 2004 .

[3]  D. Donoho,et al.  Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Hongbin Zha,et al.  Riemannian Manifold Learning , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Kilian Q. Weinberger,et al.  Unsupervised Learning of Image Manifolds by Semidefinite Programming , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[6]  Mikhail Belkin,et al.  Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering , 2001, NIPS.

[7]  Tian Han,et al.  Investigation of nonlinearity in hyperspectral remotely sensed imagery — a nonlinear time series analysis approach , 2007, 2007 IEEE International Geoscience and Remote Sensing Symposium.

[8]  Qing Wang,et al.  Using Diffusion Geometric Coordinates for Hyperspectral Imagery Representation , 2009, IEEE Geoscience and Remote Sensing Letters.

[9]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[10]  Thomas L. Ainsworth,et al.  Exploiting manifold geometry in hyperspectral imagery , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[11]  Jincheng Gao,et al.  The effect of solar illumination angle and sensor view angle on observed patterns of spatial structure in tallgrass prairie , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[12]  Li Ma,et al.  Local Manifold Learning-Based $k$ -Nearest-Neighbor for Hyperspectral Image Classification , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[13]  John F. Mustard,et al.  Spectral unmixing , 2002, IEEE Signal Process. Mag..

[14]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[15]  C. Mobley.  Light and Water: Radiative Transfer in Natural Waters , 1994 .

[16]  D. Roberts,et al.  Green vegetation, nonphotosynthetic vegetation, and soils in AVIRIS data , 1993 .

[17]  Hongbin Zha,et al.  Riemannian Manifold Learning for Nonlinear Dimensionality Reduction , 2006, ECCV.