To investigate the adversarial perturbations to twin support vector machines (TWSVMs) and hence increase the deviation of separating hyperplanes, we establish an optimization framework for adversarial perturbations of linear TWSVMs by taking the minimal perturbation that may cause the original label changes into account. By transforming the problem into a distance problem from point to intersecting hyperplane, we respectively obtain the explicit solutions to the model for the sample-adversarial perturbations case and for the class-universal adversarial perturbations case. The explicit solution obtained, it increases the interpretability of the conclusion and provides great convenience for calculation. Some numerical experiments are conducted on datasets MNIST and CIFAR-10 with Gaussian noise and trained SVM perturbations, which shows the efficiency of our proposed adversarial perturbations model.

As a classical supervised dimensionality reduction (DR) method, linear discriminant analysis (LDA) has been developed for many variants. However, it is not applicable to the case that labeled samples are scarce and unlabeled samples are in large quantity, which always happens in the real world. In this letter, we propose a novel technique format termed semisupervised LDA based on pairwise constraint propagation (SLDA-PCP) for hyperspectral images (HSIs). The basic idea of this method is to use a specially designed PCP technique to propagate label information from the labeled samples to the unlabeled samples. In addition, an extended LDA format to learn the optimal projection vectors according to the newly obtained label information is also created. Comprehensive experiments on two HSIs show that our SLDA-PCP performs better than some state-of-the-art semisupervised DR methods.

In this mymargin letter, we propose a novel supervised dimensionality reduction (DR) method termed linear discriminant analysis based on kernel-based possibilistic c-means (LDA-KPCM) for hyperspectral images (HSIs). The basic idea of this method is to use KPCM algorithm to generate different weights for different samples so that the newly-proposed method can learn the optimal transformation directions according to the relative importance of samples. The weights generated by KPCM are relatively higher for important samples but relatively lower for outliers. The experimental results on two HSI benchmark data sets demonstrate that LDA-KPCM can achieve better performance than the other state-of-the-art DR methods.