Influence maximization, defined by Kempe et al. (SIGKDD 2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. The scalability of influence maximization is a key factor for enabling prevalent viral marketing in large-scale online social networks. Prior solutions, such as the greedy algorithm of Kempe et al. (SIGKDD 2003) and its improvements are slow and not scalable, while other heuristic algorithms do not provide consistently good performance on influence spreads. In this article, we design a new heuristic algorithm that is easily scalable to millions of nodes and edges in our experiments. Our algorithm has a simple tunable parameter for users to control the balance between the running time and the influence spread of the algorithm. Our results from extensive simulations on several real-world and synthetic networks demonstrate that our algorithm is currently the best scalable solution to the influence maximization problem: (a) our algorithm scales beyond million-sized graphs where the greedy algorithm becomes infeasible, and (b) in all size ranges, our algorithm performs consistently well in influence spread—it is always among the best algorithms, and in most cases it significantly outperforms all other scalable heuristics to as much as 100–260% increase in influence spread. 相似文献
In this paper, a robust video zero-watermarking scheme for copyright protection using a combination of convolutional neural network (CNN) and self-organizing map (SOM) in polar complex exponential transform (PCET) space is presented. The scheme is developed not only to remedy the existing problems of lacking in some performance assessments but also to enhance the robustness. It starts with extracting the content feature of each frame by CNN and then some significant frames are selected using SOM clustering and maximum entropy. Secondly, the PCET is applied to all selected frames to abstract invariant moments, and further, is scrambled by a chaotic logistic map and is reduced in dimensions by singular value decomposition (SVD). Next, a binary sequence is generated by comparing adjacent values of the obtained compact PCET moments in the previous step, and further is permuted to produce a binary matrix. Finally, a bitwise exclusive-OR operation is imposed on the binary matrix and the encrypted watermark by the chaotic map to generate a zero-watermark signal. Experimental results demonstrate that the proposed scheme has adequate equalization and distinguishability of zero-watermarks as well as strong robustness against common signal processing, geometric, compression, and inter-frame attacks. Also, compared with existing video zero-watermarking and traditional video watermarking methods, the proposed scheme exhibits superior robustness.
