Zero-shot learning (ZSL) refers to the design of predictive functions on new classes (unseen classes) of data that have never been seen during training. In a more practical scenario, generalized zero-shot learning (GZSL) requires predicting both seen and unseen classes accurately. In the absence of target samples, many GZSL models may overfit training data and are inclined to predict individuals as categories that have been seen in training. To alleviate this problem, we develop a parameter-wise adversarial training process that promotes robust recognition of seen classes while designing during the test a novel model perturbation mechanism to ensure sufficient sensitivity to unseen classes. Concretely, adversarial perturbation is conducted on the model to obtain instance-specific parameters so that predictions can be biased to unseen classes in the test. Meanwhile, the robust training encourages the model robustness, leading to nearly unaffected prediction for seen classes. Moreover, perturbations in the parameter space, computed from multiple individuals simultaneously, can be used to avoid the effect of perturbations that are too extreme and ruin the predictions. Comparison results on four benchmark ZSL data sets show the effective improvement that the proposed framework made on zero-shot methods with learned metrics.

Support vector machines (SVM) are state-of-the-art classifiers. Typically L 2 -norm or L 1 -norm is adopted as a regularization term in SVMs, while other norm-based SVMs, for example, the L 0 -norm SVM or even the L ∞ -norm SVM, are rarely seen in the literature. The major reason is that L 0 -norm describes a discontinuous and nonconvex term, leading to a combinatorially NP-hard optimization problem. In this letter, motivated by Bayesian learning, we propose a novel framework that can implement arbitrary norm-based SVMs in polynomial time. One significant feature of this framework is that only a sequence of sequential minimal optimization problems needs to be solved, thus making it practical in many real applications. The proposed framework is important in the sense that Bayesian priors can be efficiently plugged into most learning methods without knowing the explicit form. Hence, this builds a connection between Bayesian learning and the kernel machines. We derive the theoretical framework, demonstrate how our approach works on the L 0 -norm SVM as a typical example, and perform a series of experiments to validate its advantages. Experimental results on nine benchmark data sets are very encouraging. The implemented L 0 -norm is competitive with or even better than the standard L 2 -norm SVM in terms of accuracy but with a reduced number of support vectors, − 9.46% of the number on average. When compared with another sparse model, the relevance vector machine, our proposed algorithm also demonstrates better sparse properties with a training speed over seven times faster.