Multi-domain text classification (MDTC) has obtained remarkable achievements
due to the advent of deep learning. Recently, many endeavors are devoted to
applying adversarial learning to extract domain-invariant features to yield
state-of-the-art results. However, these methods still face one challenge:
transforming original features to be domain-invariant distorts the
distributions of the original features, degrading the discriminability of the
learned features. To address this issue, we first investigate the structure of
the batch classification output matrix and theoretically justify that the
discriminability of the learned features has a positive correlation with the
Frobenius norm of the batch output matrix. Based on this finding, we propose a
maximum batch Frobenius norm (MBF) method to boost the feature discriminability
for MDTC. Experiments on two MDTC benchmarks show that our MBF approach can
effectively advance the performance of the state-of-the-art.

该研究探讨了最大批次 Frobenius 范数方法提高多领域文本分类的特征可辨识度，并在两个基准测试中展示了其成功地提升了最先进技术的表现。

多域文本分类的最大批次 Frobenius 范数

Maximum Batch Frobenius Norm for Multi-Domain Text Classification

Existing domain adaptation methods aim to reduce the distributional
difference between the source and target domains and respect their specific
discriminative information, by establishing the Maximum Mean Discrepancy (MMD)
and the discriminative distances. However, they usually accumulate to consider
those statistics and deal with their relationships by estimating parameters
blindly. This paper theoretically proves two essential facts: 1) minimizing the
MMD equals to maximize the source and target intra-class distances respectively
but jointly minimize their variance with some implicit weights, so that the
feature discriminability degrades; 2) the relationship between the intra-class
and inter-class distances is as one falls, another rises. Based on this, we
propose a novel discriminative MMD. On one hand, we consider the intra-class
and inter-class distances alone to remove a redundant parameter, and the
revealed weights provide their approximate optimal ranges. On the other hand,
we design two different strategies to boost the feature discriminability: 1) we
directly impose a trade-off parameter on the implicit intra-class distance in
MMD to regulate its change; 2) we impose the similar weights revealed in MMD on
inter-class distance and maximize it, then a balanced factor could be
introduced to quantitatively leverage the relative importance between the
feature transferability and its discriminability. The experiments on several
benchmark datasets not only prove the validity of theoretical results but also
demonstrate that our approach could perform better than the comparative
state-of-art methods substantially.

本研究通过理论证明了 MMD 对源域和目标域内类距离进行最大化，并连带减少它们的方差以降低特征可分性；同时分析了内类距离和间类距离的关系，提出了一种新的基于判别性 MMD 的方法，实验表明其在几个基准数据集上的效果优于现有方法。