用源任务知识增强小样本目标数据的PCA，提升降维效果
TL-PCA: Transfer Learning of Principal Component Analysis
- 通过引入源任务的主成分或数据，改进目标域的PCA优化目标
- 在图像数据上验证，无论降维维度是否超过样本数，表征性能均提升
- 适合数据稀缺场景下的降维与表示学习，如小样本分类
当目标数据样本过少时，主成分分析（PCA）性能会显著受限。本文提出一种迁移学习型PCA方法（TL-PCA），利用相关源任务的知识弥补目标数据不足的问题。该方法有两种版本：一使用源任务预训练的PCA解，二使用源任务原始数据。通过在目标子空间与源子空间间添加距离惩罚项，扩展了标准PCA的优化目标。该优化可通过特征分解求解，其可学习的主方向数量不再受目标样本数限制——这是传统PCA性能受限的根本原因。实验表明，在图像数据集上，当降维维度低于或高于目标样本数时，TL-PCA均能有效提升测试数据的表示质量。
原文摘要 · Abstract (English)
Principal component analysis (PCA) can be significantly limited when there is too few examples of the target data of interest. We propose a transfer learning approach to PCA (TL-PCA) where knowledge from a related source task is used in addition to the scarce data of a target task. Our TL-PCA has two versions, one that uses a pretrained PCA solution of the source task, and another that uses the source data. Our proposed approach extends the PCA optimization objective with a penalty on the proximity of the target subspace and the source subspace as given by the pretrained source model or the source data. This optimization is solved by eigendecomposition for which the number of data-dependent eigenvectors (i.e., principal directions of TL-PCA) is not limited to the number of target data examples, which is a root cause that limits the standard PCA performance. Accordingly, our results for image datasets show that the representation of test data is improved by TL-PCA for dimensionality reduction where the learned subspace dimension is lower or higher than the number of target data examples.
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