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 cons
iders 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.
Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between samples w
hile ignore the intrinsic data structure within the whole data. To tackle this problem, this work develops a novel deep manifold embedding method(DMEM) for hyperspectral image classification. First, each class in the image is modelled as a specific nonlinear manifold and the geodesic distance is used to measure the correlation between the samples. Then, based on the hierarchical clustering, the manifold structure of the data can be captured and each nonlinear data manifold can be divided into several sub-classes. Finally, considering the distribution of each sub-class and the correlation between different subclasses, the DMEM is constructed to preserve the estimated geodesic distances on the data manifold between the learned low dimensional features of different samples. Experiments over three real-world hyperspectral image datasets have demonstrated the effectiveness of the proposed method.
In this paper, a novel statistical metric learning is developed for spectral-spatial classification of the hyperspectral image. First, the standard variance of the samples of each class in each batch is used to decrease the intra-class variance withi
n each class. Then, the distances between the means of different classes are used to penalize the inter-class variance of the training samples. Finally, the standard variance between the means of different classes is added as an additional diversity term to repulse different classes from each other. Experiments have conducted over two real-world hyperspectral image datasets and the experimental results have shown the effectiveness of the proposed statistical metric learning.
The load pick-up (LPP) problem searches the optimal configuration of the electrical distribution system (EDS), aiming to minimize the power loss or provide maximum power to the load ends. The piecewise linearization (PWL) approximation method can be
used to tackle the nonlinearity and nonconvexity in network power flow (PF) constraints, and transform the LPP model into a mixed-integer linear programming model (LPP-MILP model).However, for the PWL approximation based PF constraints, big linear approximation errors will affect the accuracy and feasibility of the LPP-MILP models solving results. And the long modeling and solving time of the direct solution procedure of the LPP-MILP model may affect the applicability of the LPP optimization scheme. This paper proposes a multi-step PWL approximation based solution for the LPP problem in the EDS. In the proposed multi-step solution procedure, the variable upper bounds in the PWL approximation functions are dynamically renewed to reduce the approximation errors effectively. And the multi-step solution procedure can significantly decrease the modeling and solving time of the LPP-MILP model, which ensure the applicability of the LPP optimization scheme. For the two main application schemes for the LPP problem (i.e. network optimization reconfiguration and service restoration), the effectiveness of the proposed method is demonstrated via case studies using a real 13-bus EDS and a real 1066-bus EDS.
