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_32: Nowadays multi-modal visual data are much easier to access as the technology develops. Nevertheless, there is an underlying problem hidden behind the emerging multi-modality techniques: What if one more modal data fail? Motivated by this question, we propose an unsupervised method which well handles the incomplete multimodal data by transforming the original and incomplete data to a new and complete representation in a latent space. Different from the existing efforts that simply project data from each modality into a common subspace, a novel graph Laplacian term with a good probabilistic interpretation is proposed to couple the incomplete multi-modal samples. In such a way, a compact global structure over the entire heterogeneous data is well preserved, leading to a strong grouping discriminability. As a non-trivial contribution, we provide the optimization solution to the proposed model. In experiments, we extensively test our method and competitors on one synthetic data, two RGB-D video datasets and two image datasets. The superior results validate the benefits of the proposed method, especially when multimodal data suffer from large incompleteness.
The Incomplete Multi-modality Grouping (IMG) approach can be regarded as an enhanced version of PVC. Differently, IMG gets rid of the nonnegative constraint and considers the global structure in the latent space @cite_32 . Using the same notations with PVC, the latent representation of all samples can be denoted as @math . With a Laplacian graph regularization (LGR) to capture the global structure, the objective function of IMG is where @math is the Laplacian matrix of similarity matrix @math , @math , @math and @math are positive parameters.