Classwise hyperspectral image classification with PerTurbo method

A new classification technique, PerTurbo, has been investigated in the context on hyperspectral remote sensing images context. In this framework, each class is characterised by its Laplace-Beltrami operator, then approximated by the spectrum of K(S), whose terms are derived from the Gaussian kernel. The method is very simple, easy to implement and involves few parameters to tune. It also allows the definition of a simple multi-class strategy, and, as a class-wise classification method, the addition of a new class does not requires the re-training of the pre-existing class models. We conducted experiments on two datasets: results for Pavia Centre dataset are encouraging, while results obtained on Pavia University show that SVM clearly outperforms PerTurbo. Nevertheless, we believe that this difference comes from a bad parametrization of the algorithm (for which we used a rule of thumb, contrarily to the SVM procedure which was fully optimized). Hence, a systematic search for the optimal value of the parameter would improve the results. Moreover, there are several other possible improvements coming from the fields of regularization methods of dimensionality reduction techniques which let us think that this first experiment is promising. In the near future, we also plan to investigate rules leading to a better choice of s. We are also interested in studying the behavior of PerTurbo when the classes are heterogeneous with only few training samples available, or when the classes in the training set are highly unbalanced.