The learning of the deep networks largely relies on the data with human-annotated labels. In some label insufficient situations, the performance degrades on the decision boundary with high data density. A common solution is to directly minimize the Shannon Entropy, but the side effect caused by entropy minimization, i.e., reduction of the prediction diversity, is mostly ignored. To address this issue, we reinvestigate the structure of classification output matrix of a randomly selected data batch. We find by theoretical analysis that the prediction discriminability and diversity could be separately measured by the Frobeniusnorm and rank of the batch output matrix. Besides, the nuclear-norm is an upperbound of the Frobenius-norm, and a convex approximation of the matrix rank. Accordingly, to improve both discriminability and diversity, we propose Batch Nuclear-norm Maximization (BNM) on the output matrix. BNM could boost the learning under typical label insufficient learning scenarios, such as semi-supervised learning, domain adaptation and open domain recognition. On these tasks, extensive experimental results show that BNM outperforms competitors and works well with existing well-known methods. The code is available at https: //github.com/cuishuhao/BNM .

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We address the unsupervised open domain recognition (UODR) problem, where categories in labeled source domain S is only a subset of those in unlabeled target domain T . The task is to correctly classify all samples in T including known and unknown categories. UODR is challenging due to the domain discrepancy, which becomes even harder to bridge when a large number of unknown categories exist in T . Moreover, the classification rules propagated by graph CNN (GCN) may be distracted by unknown categories and lack generalization capability.To measure the domain discrepancy for asymmetric label space between S and T , we propose Semantic-Guided Matching Discrepancy (SGMD), which first employs instance matching between S and T , and then the discrepancy is measured by a weighted feature distance between matched instances. We further design a limited balance constraint to achieve a more balanced classification output on known and unknown categories. We develop Unsupervised Open Domain Transfer Network (UODTN), which learns both the backbone classification network and GCN jointly by reducing the SGMD, enforcing the limited balance constraint and minimizing the classification loss on S. UODTN better preserves the semantic structure and enforces the consistency between the learned domain invariant visual features and the semantic embeddings. Experimental results show superiority of our method on recognizing images of both known and unknown categories.

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Semi-supervised domain adaptation (SSDA) aims to solve tasks in target domain by utilizing transferable information learned from the available source domain and a few labeled target data. However, source data is not always accessible in practical scenarios, which restricts the application of SSDA in real world circumstances. In this paper, we propose a novel task named Semi-supervised Source Hypothesis Transfer (SSHT), which performs domain adaptation based on source trained model, to generalize well in target domain with a few supervisions. In SSHT, we are facing two challenges: (1) The insufficient labeled target data may result in target features near the decision boundary, with the increased risk of mis-classification;(2) The data are usually imbalanced in source domain, so the model trained with these data is biased. The biased model is prone to categorize samples of minority categories into majority ones, resulting in low prediction diversity. To tackle the above issues, we propose Consistency and Diversity Learning (CDL), a simple but effective framework for SSHT by facilitating prediction consistency between two randomly augmented unlabeled data and maintaining the prediction diversity when adapting model to target domain. Encouraging consistency regularization brings difficulty to memorize the few labeled target data and thus enhances the generalization ability of the learned model. We further integrate Batch Nuclearnorm Maximization into our method to enhance the discriminability and diversity. Experimental results show that our method outperforms existing SSDA methods and unsupervised model adaptation methods on DomainNet, Office-Home and Office-31 datasets. The code is available at https://github.com/Wang-xd1899/SSHT.