With the tremendous generation of data, there are more and more situations where observations are described by more than one view. This is for example the case with multilingual documents that convey the same information in different languages or images that are naturally described according to different set of features (for example SIFT, HOG, CNN etc). In this paper, we study the related machine learning problem that consists in finding an efficient classification model from different information sources that describe the observations. This topic, called multiview learning Atrey et al. [2010], Sun [2013], has been expanding over the past decade, spurred by the seminal work of Blum and Mitchell on co-training Blum and Mitchell [1998] (with only two views). The aim is to learn a classifier which performs better than classifiers trained over each view separately (called view-specific classifier).

We tackle the issue of classifier combinations when observations have multiple views. Our method jointly learns view-specific weighted majority vote classifiers (i.e. for each view) over a set of base voters, and a second weighted majority vote classifier over the set of these view-specific weighted majority vote classifiers. We show that the empirical risk minimization of the final majority vote given a multiview training set can be cast as the minimization of Bregman divergences. This allows us to derive a parallel-update optimization algorithm for learning our multiview model. We empirically study our algorithm with a particular focus on the impact of the training set size on the multiview learning results. The experiments show that our approach is able to overcome the lack of labeled information.

We study a two-level multiview learning with more than two views under the PAC-Bayesian framework. This approach, sometimes referred as late fusion, consists in learning sequentially multiple view-specific classifiers at the first level, and then combining these view-specific classifiers at the second level. Our main theoretical result is a generalization bound on the risk of the majority vote which exhibits a term of diversity in the predictions of the view-specific classifiers. From this result it comes out that controlling the trade-off between diversity and accuracy is a key element for multiview learning, which complements other results in multiview learning. Finally, we experiment our principle on multiview datasets extracted from the Reuters RCV1/RCV2 collection.

We address the problem of learning classifiers when observations have multiple views, some of which may not be observed for all examples. We assume the existence of view generating functions which may complete the missing views in an approximate way. This situation corresponds for example to learning text classifiers from multilingual collections where documents are not available in all languages. In that case, Machine Translation (MT) systems may be used to translate each document in the missing languages. We derive a generalization error bound for classifiers learned on examples with multiple artificially created views. Our result uncovers a trade-off between the size of the training set, the number of views, and the quality of the view generating functions. As a consequence, we identify situations where it is more interesting to use multiple views for learning instead of classical single view learning. An extension of this framework is a natural way to leverage unlabeled multi-view data in semi-supervised learning. Experimental results on a subset of the Reuters RCV1/RCV2 collections support our findings by showing that additional views obtained from MT may significantly improve the classification performance in the cases identified by our trade-off.