# A Clustering Approach to Learn Sparsely-Used Overcomplete Dictionaries

arXiv: https://arxiv.org/abs/1309.1952 · HTML: https://mlsanity.com/paper/1309.1952/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2013.

## Built on by (most cited first, 7 of 7)

- [Stable and Interpretable Unrolled Dictionary Learning](https://mlsanity.com/paper/2106.00058/) (2021)
- [Optimal Regularization for a Data Source](https://mlsanity.com/paper/2212.13597/) (2022)
- [Dictionary Learning for the Almost-Linear Sparsity Regime](https://mlsanity.com/paper/2210.10855/) (2022)
- [The Star Geometry of Critic-Based Regularizer Learning](https://mlsanity.com/paper/2408.16852/) (2024)
- [Convergence of alternating minimisation algorithms for dictionary learning](https://mlsanity.com/paper/2304.01768/) (2023)
- [Imaging with super-resolution in changing random media](https://mlsanity.com/paper/2511.14147/) (2025)
- [Wave-informed dictionary learning for high-resolution imaging in complex media](https://mlsanity.com/paper/2310.12990/) (2023)

## Abstract (arXiv)

We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary using an efficient algorithm. Our algorithm is a clustering-style procedure, where each cluster is used to estimate a dictionary element. The resulting solution can often be further cleaned up to obtain a high accuracy estimate, and we provide one simple scenario where ℓ1-regularized regression can be used for such a second stage.