Search

This paper examines the stability of the à trous algorithm under arbitrary iteration in the context of a more general study of shift-invariant filter banks. The main results describe sufficient conditions on the associated filters under which an infinitely iterated shift-invariant filter bank is stable. Moreover, it is shown that the stability of an infinitely iterated shift-invariant filter bank guarantees that of any associated finitely iterated shift-invariant filter bank, with uniform bounds. The reverse implication is shown to hold under an additional assumption on the low-pass filter. Finally, it is also shown that the separable product of stable one-dimensional shift-invariant filter banks produces a stable two-dimensional shift-invariant filter bank. [ABSTRACT FROM AUTHOR]

Recently, research on complex networks has become a hot topic. Community detection, as a main task in social network analysis, plays an important role in complex networks. In this paper, we survey and summarize the development and trend of community detection and analyze typical algorithms presented in recent years. We first discuss the algorithms from algorithmic thinking, key technology and the advantages and disadvantages. Second, evaluation metrics and datasets are introduced. Finally, some application scenarios are pointed out for the potential application in the future. It is hoped that this review will serve as the steppingstone for those interested in community detection. [ABSTRACT FROM AUTHOR]