IEEE Trans Image Process. 2015 Dec;24(12):5812-25. doi: 10.1109/TIP.2015.2490539. Epub 2015 Oct 13.
One underlying assumption of the conventional multi-view learning algorithms is that all examples can be successfully observed on all the views. However, due to various failures or faults in collecting and pre-processing the data on different views, we are more likely to be faced with an incomplete-view setting, where an example could be missing its representation on one view (i.e., missing view) or could be only partially observed on that view (i.e., missing variables). Low-rank assumption used to be effective for recovering the random missing variables of features, but it is disabled by concentrated missing variables and has no effect on missing views. This paper suggests that the key to handling the incomplete-view problem is to exploit the connections between multiple views, enabling the incomplete views to be restored with the help of the complete views. We propose an effective algorithm to accomplish multi-view learning with incomplete views by assuming that different views are generated from a shared subspace. To handle the large-scale problem and obtain fast convergence, we investigate a successive over-relaxation method to solve the objective function. Convergence of the optimization technique is theoretically analyzed. The experimental results on toy data and real-world data sets suggest that studying the incomplete-view problem in multi-view learning is significant and that the proposed algorithm can effectively handle the incomplete views in different applications.
传统的多视图学习算法有一个基本假设，即所有示例都可以在所有视图上成功观察到。然而，由于在不同视图上收集和预处理数据时会出现各种故障或错误，我们更有可能面临一个不完整视图设置，其中一个示例可能在一个视图上缺少其表示（即缺失视图），或者在该视图上只能部分观察到（即缺失变量）。低秩假设通常用于恢复特征的随机缺失变量，但它被集中的缺失变量禁用，对缺失视图没有影响。本文提出，处理不完整视图问题的关键是利用多个视图之间的连接，通过完整视图的帮助来恢复不完整视图。我们提出了一种有效的算法，通过假设不同的视图是从共享子空间生成的，从而实现具有不完整视图的多视图学习。为了处理大规模问题并获得快速收敛，我们研究了一种连续超松弛方法来求解目标函数。从理论上分析了优化技术的收敛性。在玩具数据和真实数据集上的实验结果表明，在多视图学习中研究不完整视图问题是有意义的，并且所提出的算法可以有效地处理不同应用中的不完整视图。
