Regularized Difference Criterion for Computing Discriminants for Dimensionality Reduction

Hyperspectral data classification has shown potential in many applications. However, a large number of spectral bands cause overfitting. Methods for reducing spectral bands, e.g., linear discriminant analysis, require matrix inversion. We propose a semidefinite programming for linear discriminants regularized difference (SLRD) criterion approach that does not require matrix inversion. The paper establishes a classification error bound and provides experimental results with ten methods over six hyperspectral datasets demonstrating the efficacy of the proposed SLRD technique.

[1]  T. Poggio,et al.  The Mathematics of Learning: Dealing with Data , 2005, 2005 International Conference on Neural Networks and Brain.

[2]  LinLin Shen,et al.  Unsupervised Band Selection for Hyperspectral Imagery Classification Without Manual Band Removal , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[3]  Erik Blasch,et al.  Dynamic Data-driven Application System (DDDAS) for Video Surveillance User Support , 2015, ICCS.

[4]  Chein-I Chang,et al.  Constrained band selection for hyperspectral imagery , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[5]  Tao Jiang,et al.  Efficient and robust feature extraction by maximum margin criterion , 2003, IEEE Transactions on Neural Networks.

[6]  Antonio J. Plaza,et al.  Hyperspectral Image Segmentation Using a New Bayesian Approach With Active Learning , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[7]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[8]  Arkadi Nemirovski,et al.  Non-euclidean restricted memory level method for large-scale convex optimization , 2005, Math. Program..

[9]  Aleksandra Pizurica,et al.  Classification of Hyperspectral Data Over Urban Areas Using Directional Morphological Profiles and Semi-Supervised Feature Extraction , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[10]  Uwe Weidner,et al.  Classification in High-Dimensional Feature Spaces—Assessment Using SVM, IVM and RVM With Focus on Simulated EnMAP Data , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[11]  Rama Chellappa,et al.  Discriminant Analysis for Recognition of Human Face Images (Invited Paper) , 1997, AVBPA.

[12]  Terence Sim,et al.  Discriminant Subspace Analysis: A Fukunaga-Koontz Approach , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Anastasios Tefas,et al.  Weighted Piecewise LDA for Solving the Small Sample Size Problem in Face Verification , 2007, IEEE Transactions on Neural Networks.

[14]  Keinosuke Fukunaga,et al.  Introduction to Statistical Pattern Recognition , 1972 .

[15]  Jieping Ye,et al.  A two-stage linear discriminant analysis via QR-decomposition , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  J. Friedman.  Regularized Discriminant Analysis , 1989 .

[17]  Jing Peng,et al.  Discriminant Learning Analysis , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  Chein-I Chang,et al.  Automatic spectral target recognition in hyperspectral imagery , 2003 .

[19]  Haesun Park,et al.  Generalizing discriminant analysis using the generalized singular value decomposition , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Alex J. Aved,et al.  Multi-INT Query Language for DDDAS Designs , 2015, ICCS.

[21]  Mikhail F. Kanevski,et al.  A Survey of Active Learning Algorithms for Supervised Remote Sensing Image Classification , 2011, IEEE Journal of Selected Topics in Signal Processing.

[22]  Kuldip K. Paliwal,et al.  A Gradient Linear Discriminant Analysis for Small Sample Sized Problem , 2008, Neural Processing Letters.

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

[24]  Adolfo Martínez Usó,et al.  Comparison of Unsupervised Band Selection Methods for Hyperspectral Imaging , 2007, IbPRIA.

[25]  Dapeng Wu,et al.  A RELIEF Based Feature Extraction Algorithm , 2008, SDM.

[26]  David A. Landgrebe,et al.  Hyperspectral Image Data Analysis as a High Dimensional Signal Processing Problem , 2002 .

[27]  Erik Blasch,et al.  Hyperspectral imagery throughput and fusion evaluation over compression and interpolation , 2008, 2008 11th International Conference on Information Fusion.

[28]  Qian Du,et al.  Automatic target recognition for hyperspectral imagery using high-order statistics , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[29]  K. Etemad,et al.  Discriminant analysis for recognition of human face images , 1997 .

[30]  Yurii Nesterov,et al.  Smooth minimization of non-smooth functions , 2005, Math. Program..

[31]  S. Smale,et al.  Shannon sampling II: Connections to learning theory , 2005 .

[32]  Witold Malina,et al.  On an Extended Fisher Criterion for Feature Selection , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[33]  Jing Peng,et al.  Computing Linear Discriminants for Idiomatic Sentence Detection , 2009 .

[34]  Stephen P. Boyd,et al.  Semidefinite Programming , 1996, SIAM Rev..

[35]  Larry A. Rendell,et al.  A Practical Approach to Feature Selection , 1992, ML.

[36]  Jing Peng,et al.  Weighted Additive Criterion for Linear Dimension Reduction , 2007, Seventh IEEE International Conference on Data Mining (ICDM 2007).

[37]  Chein-I Chang,et al.  Kalman filtering approach to multispectral/hyperspectral image classification , 1999 .

[38]  Guna Seetharaman,et al.  Chernoff distance and Relief feature selection , 2012, 2012 IEEE International Geoscience and Remote Sensing Symposium.

[39]  Tao Wang,et al.  Bio-Inspired Adaptive Hyperspectral Imaging for Real-Time Target Tracking , 2010, IEEE Sensors Journal.