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Then we can sort ∣ 𝑣 𝑖𝑗 ∣ in the descending order, take the top-𝑘 elements and set all the other elements to zero.. It can be verified by substituting the definition of 𝛼 𝑗 in Eq.(3.5) into Eq.(3.6). So in the non-deflation algorithm, the pre- weight vector 𝑣 is obtained as the direction that maximizes the covariance with residues....
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As the first step, ORIGAMI mines a set of maximal subgraphs, on which the 𝛼-orthogonal, 𝛽-representative graph pattern set is generated. This is based on the observation that the number of maximal frequent subgraphs is much fewer than that of frequent subgraphs, and the maximal subgraphs provide a synopsis of the frequent ones to some extent. Thus it is reasonable...
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Other variants of the streaming model also exist. These annotations can then be utilized by the algorithm in the successive passes. In this section, we describe a set of problems that involve graphs but es- sentially can be reduced to problems whose input is an array presented as a stream of the array elements (or as a sequence of increments...
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of the graph 𝐺 = (𝑉, 𝐸) is an (additive) (𝛼, 𝛽)-spanner of 𝐺 if for every pair of vertices 𝑢, 𝑣 ∈ 𝑉 , 𝑑𝑖𝑠𝑡 𝐺 ′ (𝑢, 𝑣. We describe the algorithm of [21] and its subroutine in the following fash- ion. We describe first the distributed version of the algorithm and then its adap- tation to the...
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In IEEE Symposium on Foundations of Computer Science, pages . 13th ACM-SIAM Symposium on Discrete Algorithms, pages . Counting triangles in data streams. In Proceedings of ACM Symposium on Principles of Database Systems, pages . In ACM-SIAM Symposium on Discrete Algorithms, pages . Finding frequent items in data streams. 418 MANAGING AND MINING GRAPH DATA [11] E. Fast algorithms for...
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studied three types of background knowledge to be used by adversaries to attack naively-anonymized networks. They modeled adver- saries’ external information as the access to a source that provides answers to a restricted knowledge query Q about a single target node in the original graph. Specifically, background knowledge of adversaries is modeled using the following three types of queries.. These...
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existence of edge (𝑖, 𝑗) in the original graph. Recall that the edge randomization process can be written in the matrix form 𝐴. 𝐴 + 𝐸, where 𝐴 ( 𝐴) is the adjacency matrix of the original (random. In the setting of randomizing numerical data, a data set 𝑈 with 𝑚 records of 𝑛 attributes is perturbed to 𝑈 ˜...
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It considered the case where no underlying graph is released, and, in fact, the owner of the network would like to keep the entire structure of the graph hidden from any one. The goal of the adversary is, rather than to de-anonymize particular individuals from that graph, to compromise the link privacy of as many individuals as possible. Specifically, the...
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On the other hand, the in-degree is the most straightforward measure for the popularity of each node in the network. Com- plex networks exhibit large variance in the values of their degrees: very few nodes have the capacity of attracting a large fraction of links while the largest majority of nodes are connected to the network by few in-coming and...
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Moreover 𝑝 ′ 𝑥 is the vector of PageRank scores in the transposed graph.. It is the hub score in the “best answer” graph, in which an out-link from 𝑢 to 𝑣 means that 𝑢 gave a best answer to user 𝑣. Then, ℎ 𝑏 represents the answers of users, and is assigned to the record (UA) of the person...
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For a meaningful notion of distance between nodes in the click graph, Mei et al. Hitting time captures not only nodes that are connected by short paths in the graph but also nodes that are connected by many paths. In addition, Mei et al. The idea is to adjust the weights of the edges of the click graph so that...
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Hopefully, their adoption can influence other members in the network, so the benefit is maximized.. How to mine the patterns in the graph for the above tasks becomes a hot topic thanks to the availability of enormous social network data. Number of vertexes and edges of a network are ∣ 𝑉. Graph Patterns in Large-Scale Networks. For instance, the height...
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Clearly, the quasi-clique becomes a clique when 𝛾 = 1. Note that this density- based group typically does not guarantee the nodal degree or reachbility for each node in the group. In [1], the maximum 𝛾 -dense quasi-cliques are explored. A greedy algo- rithm is adopted to find a maximal quasi-clique. The quasi-clique is initialized with a vertex with the...
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In Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies, volume 2, pages 638–. In PODS ’06: Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Prin- ciples of database systems, pages 253–262, New York, NY, USA, 2006.. Graph mining: Laws, generators, and algorithms. Finding community structure in very large networks. Extraction and classification of dense communities in the...
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needed to find discriminative patterns in the last step. Step 2: Call-graph reduction is necessary to overcome the huge sizes of call graphs. Details on call-graph reduction are presented in Section 4.. Step 3: This step includes frequent subgraph mining and the analysis of the resulting frequent subgraphs. The rationale is that such a ranking is given to a software...
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Be- sides that, recursion has not been investigated much in the context of call-graph reduction and in particular not as a starting point for reductions in addition to iterations. The reason for that is, as we will see in the following, that the re- duction of recursion is less obvious than reducing iterations and might finally result in the same...
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Subsec- tion 5.1), but based on the unordered R 01m unord reduction.. Subsection 5.2) based on the R subtree reduction.. Subsection 5.3) based on the R 01m unord and R subtree reductions.. Subsection 5.3) based on the R subtree reduction.. Subsection 5.3) but with the R total w reduction like in [25] (but with weights and without temporal edges, cf....
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The Tree of Life 3 is an example of such a tree illustrating the phylogeny of life on Earth that is based on the collective evidence from many different fields of biology and bioscience. The organisms over which a phylogenetic tree is induced are referred to as taxa, and they form the leaf nodes in the tree. Sometimes it is...
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Two of the topological structures discovered with their toolkit are depicted in Figure 18.2. In addition to subgraphs that are frequent across many networks, substruc- tures that are repeated frequently within a single and large network can be use- ful for knowledge discovery. Network motifs can be particularly effective in understanding the modularity and the global structure of biological networks....
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This list is by no means a comprehensive list but highlight some of the potential opportunities researchers may avail of.. Scalable algorithms for analyzing time varying networks: A large ma- jority of the work to date in this field has focused on the analysis of static networks. Underpinning this effort, given the size and dynamics of the data involved are...