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

arXiv: https://arxiv.org/abs/1812.10012 · HTML: https://mlsanity.com/paper/1812.10012/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2018.

## Built on by (most cited first, 4 of 4)

- [Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view](https://mlsanity.com/paper/2102.07943/) (2021)
- [Preventing Model Collapse in Deep Canonical Correlation Analysis by Noise Regularization](https://mlsanity.com/paper/2411.00383/) (2024)
- [Cross-view Joint Learning for Mixed-Missing Multi-view Unsupervised Feature Selection](https://mlsanity.com/paper/2511.12261/) (2025)
- [Joint Learning of Unsupervised Multi-view Feature and Instance Co-selection with Cross-view Imputation](https://mlsanity.com/paper/2512.15574/) (2025)

## Abstract (arXiv)

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.