The thresholded feature has recently emerged as an extremely efficient, yet rough empirical approximation, of the time-consuming sparse coding inference process. Such an approximation has not yet been rigorously examined, and standard dictionaries often lead to non-optimal performance when used for computing thresholded features. In this paper, we first present two theoretical recovery guarantees for the thresholded feature to exactly recover the nonzero support of the sparse code. Motivated by them, we then formulate the Dictionary Learning for Thresholded Features (DLTF) model, which learns an optimized dictionary for applying the thresholded feature. In particular, for the $(k, 2)$ norm involved, a novel proximal operator with log-linear time complexity $O(m\log m)$ is derived. We evaluate the performance of DLTF on a vast range of synthetic and real-data tasks, where DLTF demonstrates remarkable efficiency, effectiveness and robustness in all experiments. In addition, we briefly discuss the potential link between DLTF and deep learning building blocks.

本文介绍了阈值特征作为稀疏编码推理过程的一个高效近似方法，并提出了字典学习优化模型DLTF，研究了它的性能表现及其与深度学习建筑块之间的潜在联系。

使用稀疏支持恢复学习简单的阈值特征