Mahalanobis kernel for the classification of hyperspectral images

Mathieu Fauvel (1) , Alberto Villa (2, 3) , Jocelyn Chanussot (4) , Jon Atli Benediktsson (2)

1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
2 University of Iceland [Reykjavik]
3 GIPSA-lab - Grenoble Images Parole Signal Automatique
4 GIPSA-SIGMAPHY - GIPSA - Signal Images Physique

The definition of the Mahalanobis kernel for the classification of hyperspectral remote sensing images is addressed. Class specific covariance matrices are regularized by a probabilistic model which is based on the data living in a subspace spanned by the p first principal components. The inverse of the covariance matrix is computed in a closed form and is used in the kernel to compute the distance between two spectra. Each principal direction is normalized by a hyperparameter tuned, according to an upper error bound, during the training of an SVM classifier. Results on real data sets empirically demonstrate that the proposed kernel leads to an increase of the classification accuracy by comparison to standard kernels.

Mots clés: Mahalanobis kernel; probabilistic principal component analysis; support vector machine; hyperspectral images; classification

Domaines: Traitement des images [eess.IV]

Mathieu Fauvel, Alberto Villa, Jocelyn Chanussot, Jon Atli Benediktsson. Mahalanobis kernel for the classification of hyperspectral images. IGARSS 2010 - IEEE International Geoscience and Remote Sensing Symposium, Jul 2010, Honolulu, Hawaii, United States. pp.3724-3727, ⟨10.1109/IGARSS.2010.5651956⟩. ⟨hal-00578952⟩