In real-world applications, not all instances in multi-view data are fully represented. To deal with incomplete multi-view data, traditional multi-view algorithms usually throw away the incomplete instances, resulting in loss of available information. To overcome this loss, Incomplete Multi-view Learning (IML) has become a hot research topic. In this paper, we propose a general IML framework for unifying existing IML methods and gaining insight into IML. The proposed framework jointly performs embedding learning and low-rank approximation. Concretely, it approximates the incomplete data by a set of low-rank matrices and learns a full and common embedding by linear transformation. Several existing IML methods can be unified as special cases of the framework. More interestingly, some linear transformation based full-view methods can be adapted to IML directly with the guidance of the framework. This bridges the gap between full multi-view learning and IML. Moreover, the framework can provide guidance for developing new algorithms. For illustration, within the framework, we propose a specific method, termed as Incomplete Multi-view Learning with Block Diagonal Representation (IML-BDR). Based on the assumption that the sampled examples have approximate linear subspace structure, IML-BDR uses the block diagonal structure prior to learn the full embedding, which would lead to more correct clustering. A convergent alternating iterative algorithm with the Successive Over-Relaxation (SOR) optimization technique is devised for optimization. Experimental results on various datasets demonstrate the effectiveness of IML-BDR.
@cite_24: Real data are often with multiple modalities or coming from multiple channels, while multi-view clustering provides a natural formulation for generating clusters from such data. Previous studies assumed that each example appears in all views, or at least there is one view containing all examples. In real tasks, however, it is often the case that every view suffers from the missing of some data and therefore results in many partial examples, i.e., examples with some views missing. In this paper, we present possibly the first study on partial multiview clustering. Our proposed approach, PVC, works by establishing a latent subspace where the instances corresponding to the same example in different views are close to each other, and similar instances (belonging to different examples) in the same view should be well grouped. Experiments on two-view data demonstrate the advantages of our proposed approach.
PVC @cite_24 is originally designed for two-view data in the missing view setting. It learns a full representation from incomplete multi-view data based on the NMF. Denote @math as the examples presented in both views, and denote @math , @math as the examples only presented in the first view and the second view, respectively. The optimization problems of PVC is From codes (http: lamda.nju.edu.cn code .ashx) published by the authors, it can be known that the @math -norm in PVC @cite_24 is actually the @math -norm of matrix. where @math @math is the latent representation for the @math -th view, and @math is the basis matrix, @math is the dimension of the latent space, and @math is the trade-off parameter for the regularization terms.