Nearest Regularized Subspace for Hyperspectral Classification

A classifier that couples nearest-subspace classification with a distance-weighted Tikhonov regularization is proposed for hyperspectral imagery. The resulting nearest-regularized-subspace classifier seeks an approximation of each testing sample via a linear combination of training samples within each class. The class label is then derived according to the class which best approximates the test sample. The distance-weighted Tikhonov regularization is then modified by measuring distance within a locality-preserving lower-dimensional subspace. Furthermore, a competitive process among the classes is proposed to simplify parameter tuning. Classification results for several hyperspectral image data sets demonstrate superior performance of the proposed approach when compared to other, more traditional classification techniques.

[1]  Trac D. Tran,et al.  Discriminative graphical models for sparsity-based hyperspectral target detection , 2012, 2012 IEEE International Geoscience and Remote Sensing Symposium.

[2]  James E. Fowler,et al.  Block-Based Compressed Sensing of Images and Video , 2012, Found. Trends Signal Process..

[3]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[4]  Lei Zhang,et al.  Sparse representation or collaborative representation: Which helps face recognition? , 2011, 2011 International Conference on Computer Vision.

[5]  Masashi Sugiyama,et al.  Dimensionality Reduction of Multimodal Labeled Data by Local Fisher Discriminant Analysis , 2007, J. Mach. Learn. Res..

[6]  Trac D. Tran,et al.  Hyperspectral Image Classification Using Dictionary-Based Sparse Representation , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[7]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[8]  Lorenzo Bruzzone,et al.  Classification of Hyperspectral Images With Regularized Linear Discriminant Analysis , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[9]  Trac D. Tran,et al.  Exploiting Sparsity in Hyperspectral Image Classification via Graphical Models , 2013, IEEE Geoscience and Remote Sensing Letters.

[10]  Saurabh Prasad,et al.  Decision Fusion With Confidence-Based Weight Assignment for Hyperspectral Target Recognition , 2008, IEEE Transactions on Geoscience and Remote Sensing.

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

[12]  Jon Atli Benediktsson,et al.  Spectral–Spatial Classification of Hyperspectral Imagery Based on Partitional Clustering Techniques , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[13]  Trac D. Tran,et al.  Hyperspectral Image Classification via Kernel Sparse Representation , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[14]  Ralph Bernstein,et al.  Gaussian Maximum Likelihood and Contextual Classification Algorithms for Multicrop Classification , 1987, IEEE Transactions on Geoscience and Remote Sensing.

[15]  David A. Landgrebe,et al.  Hyperspectral image data analysis , 2002, IEEE Signal Process. Mag..

[16]  Rick Archibald,et al.  Feature Selection and Classification of Hyperspectral Images With Support Vector Machines , 2007, IEEE Geoscience and Remote Sensing Letters.

[17]  Shigeo Abe DrEng.  Pattern Classification , 2001, Springer London.

[18]  Guillermo Sapiro,et al.  Discriminative sparse representations in hyperspectral imagery , 2010, 2010 IEEE International Conference on Image Processing.

[19]  R. Tibshirani,et al.  Regression shrinkage and selection via the lasso: a retrospective , 2011 .

[20]  Kilian Q. Weinberger,et al.  Distance Metric Learning for Large Margin Nearest Neighbor Classification , 2005, NIPS.

[21]  Xiaofei He,et al.  Locality Preserving Projections , 2003, NIPS.

[22]  David G. Stork,et al.  Pattern Classification (2nd ed.) , 1999 .

[23]  Ye Zhang,et al.  Robust Hyperspectral Classification Using Relevance Vector Machine , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[24]  Lorenzo Bruzzone,et al.  Classification of hyperspectral remote sensing images with support vector machines , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[25]  Gustavo Camps-Valls,et al.  Learning Relevant Image Features With Multiple-Kernel Classification , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[26]  James E. Fowler,et al.  Locality-Preserving Discriminant Analysis in Kernel-Induced Feature Spaces for Hyperspectral Image Classification , 2011, IEEE Geoscience and Remote Sensing Letters.

[27]  Luis Samaniego,et al.  Supervised Classification of Remotely Sensed Imagery Using a Modified $k$-NN Technique , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[28]  James E. Fowler,et al.  Locality-Preserving Dimensionality Reduction and Classification for Hyperspectral Image Analysis , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[29]  Shuzhi Sam Ge,et al.  $k$-NS: A Classifier by the Distance to the Nearest Subspace , 2011, IEEE Transactions on Neural Networks.

[30]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[31]  Fuchun Sun,et al.  A Fast and Robust Sparse Approach for Hyperspectral Data Classification Using a Few Labeled Samples , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[32]  James E. Fowler,et al.  Video Compressed Sensing with Multihypothesis , 2011, 2011 Data Compression Conference.

[33]  Peter Bühlmann.  Regression shrinkage and selection via the Lasso: a retrospective (Robert Tibshirani): Comments on the presentation , 2011 .

[34]  Vincent Lepetit,et al.  Are sparse representations really relevant for image classification? , 2011, CVPR 2011.

[35]  Allen Y. Yang,et al.  Robust Face Recognition via Sparse Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[36]  Kai Feng,et al.  L1-graph semisupervised learning for hyperspectral image classification , 2012, 2012 IEEE International Geoscience and Remote Sensing Symposium.