This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing the separable dictionary learning model. Two different approaches for learning mixture of separable dictionaries are explored and sufficient conditions for local identifiability of the underlying dictionary are derived in each case. Moreover, computational algorithms are developed to solve the problem of learning mixture of separable dictionaries in both batch and online settings. Numerical experiments are used to show the usefulness of the proposed model and the efficacy of the developed algorithms.

中文翻译：

---

张量数据的可分离字典的学习混合：分析和算法

这项工作解决了使用结构化字典学习来学习张量数据的稀疏表示的问题。它提出通过推广可分离字典学习模型来学习可分离字典的混合体，以更好地捕获张量数据的结构。探索了两种不同的学习可分离词典混合的方法，并在每种情况下导出了底层词典的局部可识别性的充分条件。此外，还开发了计算算法来解决在批处理和在线设置中学习可分离词典的混合问题。数值实验用于显示所提出模型的有用性和所开发算法的有效性。