Due to the domain discrepancy in visual domain adaptation, the performance of
source model degrades when bumping into the high data density near decision
boundary in target domain. A common solution is to minimize the Shannon Entropy
to push the decision boundary away from the high density area. However, entropy
minimization also leads to severe reduction of prediction diversity, and
unfortunately brings harm to the domain adaptation. In this paper, we
investigate the prediction discriminability and diversity by studying the
structure of the 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 Frobenius-norm and rank of the
batch output matrix. The nuclear-norm is an upperbound of the former, and a
convex approximation of the latter. Accordingly, we propose Batch Nuclear-norm
Maximization and Minimization, which performs nuclear-norm maximization on the
target output matrix to enhance the target prediction ability, and nuclear-norm
minimization on the source batch output matrix to increase applicability of the
source domain knowledge. We further approximate the nuclear-norm by
L_{1,2}-norm, and design multi-batch optimization for stable solution on large
number of categories. The fast approximation method achieves O(n^2)
computational complexity and better convergence property. Experiments show that
our method could boost the adaptation accuracy and robustness under three
typical domain adaptation scenarios. The code is available at
this https URL

本文提出了一种通过最大化目标输出矩阵的核范数和最小化源输出矩阵的核范数来提高区分能力和多样性的方法，以增强目标预测能力并提高源领域知识的适用性。这种方法可以在三种典型的领域适应方案下提高适应的准确性和稳健性。