Nowadays, deep learning methods, especially the convolutional neural networks (CNNs), have shown impressive performance on extracting abstract and high-level features from the hyperspectral image. However, general training process of CNNs mainly considers the pixel-wise information or the samples correlation to formulate the penalization while ignores the statistical properties especially the spectral variability of each class in the hyperspectral image. These samples-based penalizations would lead to the uncertainty of the training process due to the imbalanced and limited number of training samples. To overcome this problem, this work characterizes each class from the hyperspectral image as a statistical distribution and further develops a novel statistical loss with the distributions, not directly with samples for deep learning. Based on the Fisher discrimination criterion, the loss penalizes the sample variance of each class distribution to decrease the intra-class variance of the training samples. Moreover, an additional diversity-promoting condition is added to enlarge the inter-class variance between different class distributions and this could better discriminate samples from different classes in hyperspectral image. Finally, the statistical estimation form of the statistical loss is developed with the training samples through multi-variant statistical analysis. Experiments over the real-world hyperspectral images show the effectiveness of the developed statistical loss for deep learning.
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