Belief Functions
The theory of belief functions provides a non-Bayesian way of using mathematical probability to quantify subjective judgements. Whereas a Bayesian assesses probabilities directly for the answer to a question of interest, a belief-function user assesses probabilities for related questions and then considers the implications of these probabilities for the question of interest. …

Maucha Diagrams
This diagram was proposed by Rezso Maucha in 1932 as a way to vizualise the relative ionic composition of water samples. …

Cycle-Consistent Adversarial GAN (CycleAdvGAN)
In image classification of deep learning, adversarial examples where inputs intended to add small magnitude perturbations may mislead deep neural networks (DNNs) to incorrect results, which means DNNs are vulnerable to them. Different attack and defense strategies have been proposed to better research the mechanism of deep learning. However, those research in these networks are only for one aspect, either an attack or a defense, not considering that attacks and defenses should be interdependent and mutually reinforcing, just like the relationship between spears and shields. In this paper, we propose Cycle-Consistent Adversarial GAN (CycleAdvGAN) to generate adversarial examples, which can learn and approximate the distribution of original instances and adversarial examples. For CycleAdvGAN, once the Generator and are trained, can generate adversarial perturbations efficiently for any instance, so as to make DNNs predict wrong, and recovery adversarial examples to clean instances, so as to make DNNs predict correct. We apply CycleAdvGAN under semi-white box and black-box settings on two public datasets MNIST and CIFAR10. Using the extensive experiments, we show that our method has achieved the state-of-the-art adversarial attack method and also efficiently improve the defense ability, which make the integration of adversarial attack and defense come true. In additional, it has improved attack effect only trained on the adversarial dataset generated by any kind of adversarial attack. …

Deep Multiset Canonical Correlation Analysis (dMCCA)
We propose Deep Multiset Canonical Correlation Analysis (dMCCA) as an extension to representation learning using CCA when the underlying signal is observed across multiple (more than two) modalities. We use deep learning framework to learn non-linear transformations from different modalities to a shared subspace such that the representations maximize the ratio of between- and within-modality covariance of the observations. Unlike linear discriminant analysis, we do not need class information to learn these representations, and we show that this model can be trained for complex data using mini-batches. Using synthetic data experiments, we show that dMCCA can effectively recover the common signal across the different modalities corrupted by multiplicative and additive noise. We also analyze the sensitivity of our model to recover the correlated components with respect to mini-batch size and dimension of the embeddings. Performance evaluation on noisy handwritten datasets shows that our model outperforms other CCA-based approaches and is comparable to deep neural network models trained end-to-end on this dataset. …