Although Neural networks could achieve state-of-the-art performance while recongnizing images, they often suffer a tremendous defeat from adversarial examples–inputs generated by utilizing imperceptible but intentional perturbations to samples from the datasets. How to defense against adversarial examples is an important problem which is well worth to research. So far, only two well-known methods adversarial training and defensive distillation have provided a significant defense. In contrast to existing methods mainly based on model itself, we address the problem purely based on the adversarial examples itself. In this paper, a novel idea and the first framework based Generative Adversarial Nets named AE-GAN capable of resisting adversarial examples are proposed. Extensive experiments on benchmark datasets indicate that AE-GAN is able to defense against adversarial examples effectively. …

Dual Principal Component Pursuit (DPCP)
We extend the theoretical analysis of a recently proposed single subspace learning algorithm, called Dual Principal Component Pursuit (DPCP), to the case where the data are drawn from of a union of hyperplanes. To gain insight into the properties of the $\ell_1$ non-convex problem associated with DPCP, we develop a geometric analysis of a closely related continuous optimization problem. Then transferring this analysis to the discrete problem, our results state that as long as the hyperplanes are sufficiently separated, the dominant hyperplane is sufficiently dominant and the points are uniformly distributed inside the associated hyperplanes, then the non-convex DPCP problem has a unique global solution, equal to the normal vector of the dominant hyperplane. This suggests the correctness of a sequential hyperplane learning algorithm based on DPCP. A thorough experimental evaluation reveals that hyperplane learning schemes based on DPCP dramatically improve over the state-of-the-art methods for the case of synthetic data, while are competitive to the state-of-the-art in the case of 3D plane clustering for Kinect data. …

CORrelation Differences (CORD)
Given a zero mean random vector X=:(X1,…,Xp) ∈ R^p, we consider the problem of defining and estimating a partition G of {1,…,p} such that the components of X with indices in the same group of the partition have a similar, community-like behavior. We introduce a new model, the G-exchangeable model, to define group similarity. This model is a natural extension of the more commonly used G-latent model, for which the partition G is generally not identifiable, without additional restrictions on X. In contrast, we show that for any random vector X there exists an identifiable partition G according to which X is G-exchangeable, thereby providing a clear target for community estimation. Moreover, we provide another model, the G-block covariance model, which generalizes the G-exchangeable model, and can be of interest in its own right for defining group similarity. We discuss connections between the three types of G-models. We exploit the connection with G-block covariance models to develop a new metric, CORD, and a homonymous method for community estimation. We specialize and analyze our method for Gaussian copula data. We show that this method recovers the partition according to which X is G-exchangeable with a G-block copula correlation matrix. In the particular case of Gaussian distributions, this estimator, under mild assumptions, identifies the unique minimal partition according to the G-latent model. The CORD estimator is consistent as long as the communities are separated at a rate that we prove to be minimax optimal, via lower bound calculations. Our procedure is fast and extensive numerical studies show that it recovers communities defined by our models, while existing variable clustering algorithms typically fail to do so. This is further supported by two real-data examples. …