Bilevel Multiview Latent Space Learning

Different kinds of features describe different aspects of image data, and each feature can be treated as a view when we take it as a particular understanding of images. Leveraging multiple views provides a richer and comprehensive description than using only a single view. However, multiview data are often represented by high-dimensional heterogeneous features, so it is meaningful to find a low-dimensional consensus representation from multiple views. In this paper, we propose an unsupervised multiview dimensionality reduction method for images based on bilevel latent space learning. As different views have different physical meanings and statistical properties, they are not directly comparable. Therefore, we learn the comparable representation for each view in the first level. The shared and the private nature of multiview data are exploited to accurately preserve the information of each view. Then, we fuse different views into a low-dimensional representation by conducting joint matrix factorization in the second level. To guarantee the low-dimensional representation to be compact and discriminative, the intrinsic geometric structure of data is utilized. Besides, our method considers resisting the outliers and noise contained in multiview data, which may influence the learned representation and deteriorate its semantic consistency. We design appropriate optimization objectives to learn the latent spaces in different levels. Compared with the existing methods, our method could provide a more flexible multiview learning strategy that not only accurately captures the information of each view but also is robust to outliers and noise, which can obtain a more discriminative and compact low-dimensional representation. Experiments on two real-world image data sets demonstrate the advantages of our method over the existing multiview dimensionality reduction methods.