论文标题
通过$ \ ell^{4} $分散的完整词典学习 - 规范最大化
Decentralized Complete Dictionary Learning via $\ell^{4}$-Norm Maximization
论文作者
论文摘要
随着信息技术的快速发展，集中式数据处理受到许多局限性，例如计算开销，通信延迟和数据隐私泄漏。网络终端节点上的分散数据处理成为大数据时代的重要技术。字典学习是一种强大的表示学习方法，可从高维数据中利用低维结构。通过利用低维结构，可以有效地减少数据的存储和处理开销。在本文中，我们提出了一种新颖的分散词典学习算法，该算法基于$ \ ell^{4} $ - 标准最大化。与现有的分散词典学习算法相比，全面的数值实验表明，在许多情况下，新型算法在每读计算复杂性，通信成本和收敛率方面具有显着优势。此外，严格的理论分析表明，所提出的算法所学的字典可以将集中式词典学习算法学到的词典以线性速率在某些条件下具有很高概率的线性速率收敛。
With the rapid development of information technologies, centralized data processing is subject to many limitations, such as computational overheads, communication delays, and data privacy leakage. Decentralized data processing over networked terminal nodes becomes an important technology in the era of big data. Dictionary learning is a powerful representation learning method to exploit the low-dimensional structure from the high-dimensional data. By exploiting the low-dimensional structure, the storage and the processing overhead of data can be effectively reduced. In this paper, we propose a novel decentralized complete dictionary learning algorithm, which is based on $\ell^{4}$-norm maximization. Compared with existing decentralized dictionary learning algorithms, comprehensive numerical experiments show that the novel algorithm has significant advantages in terms of per-iteration computational complexity, communication cost, and convergence rate in many scenarios. Moreover, a rigorous theoretical analysis shows that the dictionaries learned by the proposed algorithm can converge to the one learned by a centralized dictionary learning algorithm at a linear rate with high probability under certain conditions.
