A novel logistic multi-class supervised classification model based on multi-fractal spectrum parameters for hyperspectral data

Abstract

A novel logistic multi-class supervised classification model based on multi-fractal spectrum parameters is proposed to avoid the error that is caused by the difference between the real data distribution and the hypothetic Gaussian distribution and avoid the computational burden working in the logistic regression classification directly for hyperspectral data. The multi-fractal spectra and parameters are calculated firstly with training samples along the spectral dimension of hyperspectral data. Secondly, the logistic regression model is employed in our work because the logistic regression classification model is a distribution-free nonlinear model which is based on the conditional probability without the Gaussian distribution assumption of the random variables, and the obtained multi-fractal parameters are applied to establish the multi-class logistic regression classification model. Finally, the Newton–Raphson method is applied to estimate the model parameters via the maximum likelihood algorithm. The classification results of the proposed model are compared with the logistic regression classification model based on an adaptive bands selection method by using the Airborne Visible/Infrared Imaging Spectrometer and airborne Push Hyperspectral Imager data. The results illuminate that the proposed approach achieves better accuracy with lower computational cost simultaneously.

Keywords:

• hyperspectral remote sensing
• supervised classification
• logistic regression model
• multi-fractal spectrum parameters

2010 AMS Subject Classification::

• 68W40

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 61177008 and 61008047), China Geological Survey (Grant No. 1212011120227), the National High Technology Research and Development Program (863 Program) (Grant No. 2012AA12A30801 and 2012YQ05250) and Program for Changjiang Scholars and Innovative Research Team (Grant No.IRT0705). The authors would like to thank Prof. Zhang Bing, Prof. Zheng Lanfen and Dr Gao Lianru at Center for Earth Observation and Digital Earth, Chinese Academy of Science, for providing the PHI hyperspectral data used in the experiments.