Due to the difficulty of collecting labeled images for hundreds of thousands of visual categories, zero-shot learning, where unseen categories do not have any labeled images in training stage, has attracted more attention. In the past, many studies focused on transferring knowledge from seen to unseen categories by projecting all category labels into a semantic space. However, the label embeddings could not adequately express the semantics of categories. Furthermore, the common semantics of seen and unseen instances cannot be captured accurately because the distribution of these instances may be quite different. For these issues, we propose a novel deep semisupervised method by jointly considering the heterogeneity gap between different modalities and the correlation among unimodal instances. This method replaces the original labels with the corresponding textual descriptions to better capture the category semantics. This method also overcomes the problem of distribution difference by minimizing the maximum mean discrepancy between seen and unseen instance distributions. Extensive experimental results on two benchmark data sets, CU200-Birds and Oxford Flowers-102, indicate that our method achieves significant improvements over previous methods.

Robust principal component analysis (PCA) is one of the most important dimension-reduction techniques for handling high-dimensional data with outliers. However, most of the existing robust PCA presupposes that the mean of the data is zero and incorrectly utilizes the average of data as the optimal mean of robust PCA. In fact, this assumption holds only for the squared -norm-based traditional PCA. In this letter, we equivalently reformulate the objective of conventional PCA and learn the optimal projection directions by maximizing the sum of projected difference between each pair of instances based on -norm. The proposed method is robust to outliers and also invariant to rotation. More important, the reformulated objective not only automatically avoids the calculation of optimal mean and makes the assumption of centered data unnecessary, but also theoretically connects to the minimization of reconstruction error. To solve the proposed nonsmooth problem, we exploit an efficient optimization algorithm to soften the contributions from outliers by reweighting each data point iteratively. We theoretically analyze the convergence and computational complexity of the proposed algorithm. Extensive experimental results on several benchmark data sets illustrate the effectiveness and superiority of the proposed method.