  In real-world applications, not all instances in multi-view data are fully
represented. To deal with incomplete data, Incomplete Multi-view Learning (IML)
rises. In this paper, we propose the Joint Embedding Learning and Low-Rank
Approximation (JELLA) framework for IML. The JELLA framework 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 complete multi-view methods can be adapted to IML directly
with the guidance of the framework. Thus, the JELLA framework improves the
efficiency of processing incomplete multi-view data, and bridges the gap
between complete multi-view learning and IML. Moreover, the JELLA framework can
provide guidance for developing new algorithms. For illustration, within the
framework, we propose the Incomplete Multi-view Learning with Block Diagonal
Representation (IML-BDR) method. Assuming 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 optimization technique is devised for optimization.
Experimental results on various datasets demonstrate the effectiveness of
IML-BDR.
