The sparse dictionary coding framework represents signals as a linear combination of a few predefined dictionary atoms. It has been employed for images, time series, graph signals and recently for 2-way (or 2D) spatio-temporal data employing jointly temporal and spatial dictionaries. Large and over-complete dictionaries enable high-quality models, but also pose scalability challenges which are exacerbated in multi-dictionary settings. Hence, an important problem that we address in this paper is: How to scale multi-dictionary coding for large dictionaries and datasets? We propose a multi-dictionary atom selection technique for low-rank sparse coding named LRMDS. To enable scalability to large dictionaries and datasets, it progressively selects groups of row-column atom pairs based on their alignment with the data and performs convex relaxation coding via the corresponding sub-dictionaries. We demonstrate both theoretically and experimentally that when the data has a low-rank encoding with a sparse subset of the atoms, LRMDS is able to select them with strong guarantees under mild assumptions. Furthermore, we demonstrate the scalability and quality of LRMDS in both synthetic and real-world datasets and for a range of coding dictionaries. It achieves 3X to 10X speed-up compared to baselines, while obtaining up to two orders of magnitude improvement in representation quality on some of the real world datasets given a fixed target number of atoms.

利用LDRMS方法解决了大字典和数据集下的多字典编码可扩展性问题，并在理论和实验中展示了其在多种编码字典下的可扩展性和表示质量的显著提升。

大规模低秩多字典选择