凸更新字典学习（ROMD）
Dictionary Learning with Convex Update (ROMD)
摘要：
字典学习的目的是找到一个字典，在这个字典下训练数据可以被稀疏地表示，它通常通过迭代地应用两个阶段来实现：稀疏编码和字典更新。字典更新的典型方法是利用稀疏编码阶段得到的稀疏模式来细化字典原子及其相应的稀疏系数，因此它是一个非凸双线性逆问题。在本文中，我们提出了一个秩一矩阵分解（ROMD）算法，通过解决这两个变量到一组秩一矩阵重铸这个挑战成一个凸问题。与文献中的方法不同，ROMD使用凸规划一次更新整个字典。因此，优点包括字典更新的收敛保证和整个字典学习的更快收敛。ROMD的性能与其他基准字典学习算法进行了比较。结果表明，ROMD在恢复精度上有明显的提高，特别是在稀疏度较高和观测数据较少的情况下。
英文摘要：
Dictionary learning aims to find a dictionary under which the training data can be sparsely represented, and it is usually achieved by iteratively applying two stages: sparse coding and dictionary update. Typical methods for dictionary update focuses on refining both dictionary atoms and their corresponding sparse coefficients by using the sparsity patterns obtained from sparse coding stage, and hence it is a non-convex bilinear inverse problem. In this paper, we propose a Rank-One Matrix Decomposition (ROMD) algorithm to recast this challenge into a convex problem by resolving these two variables into a set of rank-one matrices. Different from methods in the literature, ROMD updates the whole dictionary at a time using convex programming. The advantages hence include both convergence guarantees for dictionary update and faster convergence of the whole dictionary learning. The performance of ROMD is compared with other benchmark dictionary learning algorithms. The results show the improvement of ROMD in recovery accuracy, especially in the cases of high sparsity level and fewer observation data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
