# Joint Embedding Learning and Low-Rank Approximation: A Framework for Incomplete Multi-view Learning

## TL;DR

This paper introduces the JELLA framework for incomplete multi-view learning, unifying and extending existing methods by approximating data with low-rank matrices and learning a shared embedding, improving efficiency and enabling new algorithm development.

## Contribution

The JELLA framework unifies existing IML methods, adapts complete multi-view methods to incomplete data, and introduces the IML-BDR method with a new optimization algorithm.

## Key findings

- JELLA unifies multiple IML methods.
- IML-BDR improves clustering accuracy.
- Experimental results validate effectiveness.

## Abstract

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.