Feature extraction based on multifractal spectrum for hyperspectral data

Considering the fractal dimension deficiency to process hyperspectral data, a singularity feature extraction method was proposed, and the multifractal spectrum was used to characterize the singularity feature of spectra. In this method, the spectral curves were divided to several segments according to fractal measure, and the partition function was generated with the spectral probability measure. The multifractal spectrum was extracted with the Legendre transformation of scale exponent. Effective features of multifractal spectrum were selected based on discriminable rule of Bhattacharyya distance. Classification experiments of hyperspectral data are carried out to prove the value of multifractal spectrum, and the classification accuracy reaches 95.2%. With 10% of the original spectra's dimension, the accuracy reaches 82.2%. The fractal dimension of spectral subset with the same singularity exponent is characterized by multifractal spectrum, and the singularity distribution of spectra are is expressed sufficiently. As a conclusion, the method is appropriate to extract the features of hyperspectral data.