Linear discriminant analysis (LDA) has been widely used as the technique of feature exaction. However, LDA may be invalid to address the data from different domains. The reasons are as follows: 1) the distribution discrepancy of data may disturb the linear transformation matrix so that it cannot extract the most discriminative feature and 2) the original design of LDA does not consider the unlabeled data so that the unlabeled data cannot take part in the training process for further improving the performance of LDA. To address these problems, in this brief, we propose a novel transferable LDA (TLDA) method to extend LDA into the scenario in which the data have different probability distributions. The whole learning process of TLDA is driven by the philosophy that the data from the same subspace have a low-rank structure. The matrix rank in TLDA is the key learning criterion to conduct local and global linear transformations for restoring the low-rank structure of data from different distributions and enlarging the distances among different subspaces. In doing so, the variations of distribution discrepancy within the same subspace can be reduced, i.e., data can be aligned well and the maximally separated structure can be achieved for the data from different subspaces. A simple projected subgradient-based method is proposed to optimize the objective of TLDA, and a strict theory proof is provided to guarantee a quick convergence. The experimental evaluation on public data sets demonstrates that our TLDA can achieve better classification performance and outperform the state-of-the-art methods.

中文翻译：

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可转移线性判别分析。

线性判别分析（LDA）已被广泛用作特征提取技术。但是，LDA可能无法处理来自不同域的数据。原因如下：1）数据的分布差异可能会干扰线性变换矩阵，从而无法提取出最有区别的特征； 2）LDA的原始设计未考虑未标记的数据，因此未标记的数据无法参与在培训过程中进一步提高LDA的性能。为了解决这些问题，在本文中，我们提出了一种新颖的可转移LDA（TLDA）方法，将LDA扩展到数据具有不同概率分布的情况下。TLDA的整个学习过程受以下哲学的驱使：来自同一子空间的数据具有低秩结构。TLDA中的矩阵等级是进行局部和全局线性变换的关键学习准则，以从不同分布还原数据的低等级结构并扩大不同子空间之间的距离。这样，可以减少同一子空间内分布差异的变化，即，可以很好地对齐数据，并且可以为来自不同子空间的数据实现最大分离的结构。提出了一种基于投影的基于梯度的简单方法来优化TLDA的目标，并提供了严格的理论证明来保证快速收敛。对公共数据集的实验评估表明，我们的TLDA可以实现更好的分类性能，并且胜过最新的方法。