  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.
