Robust Joint and Individual Variance Explained

Discovering the common (joint) and individual subspaces is crucial for analysis of multiple data sets, including multi-view and multi-modal data. Several statistical machine learning methods have been developed for discovering the common features across multiple data sets. The most well studied family of the methods is that of Canonical Correlation Analysis (CCA) and its variants. Even though the CCA is a powerful tool, it has several drawbacks that render its application challenging for computer vision applications. That is, it discovers only common features and not individual ones, and it is sensitive to gross errors present in visual data. Recently, efforts have been made in order to develop methods that discover individual and common components. Nevertheless, these methods are mainly applicable in two sets of data. In this paper, we investigate the use of a recently proposed statistical method, the so-called Joint and Individual Variance Explained (JIVE) method, for the recovery of joint and individual components in an arbitrary number of data sets. Since, the JIVE is not robust to gross errors, we propose alternatives, which are both robust to non-Gaussian noise of large magnitude, as well as able to automatically find the rank of the individual components. We demonstrate the effectiveness of the proposed approach to two computer vision applications, namely facial expression synthesis and face age progression in-the-wild.