TAILIEUCHUNG - Managing and Mining Graph Data part 46

Managing and Mining Graph Data part 46 is a comprehensive survey book in graph data analytics. It contains extensive surveys on important graph topics such as graph languages, indexing, clustering, data generation, pattern mining, classification, keyword search, pattern matching, and privacy. It also studies a number of domain-specific scenarios such as stream mining, web graphs, social networks, chemical and biological data. The chapters are written by leading researchers, and provide a broad perspective of the area. This is the first comprehensive survey book in the emerging topic of graph data processing. . | A Survey of Privacy-Preservation of Graphs and Social Networks 437 existence of edge i j in the original or a ii. More details will be provided in Section . Reconstruction Recall that the edge randomization process can be written in the matrix form A A E where A A is the adjacency matrix of original random-izedi graph and E is the perturbation maSrix. In the sciting of randomizing numerical . s data set U with m records of n s is periurhed to U hy an additive noise data set V with liic came dimensions as U. In oSher words U U V. ns of U can he approximateSy reconstructed from its perturbed data U using reconstruction approaches . 3 2 when some aspeiori knota lcdgc . distribution statistics etc. about She noise V is available. S occiiiealiy. Agoawal and Aggawal 2 provided an EM aigotitism for reconstructing the distribution of oriainai data from perturbed oSservations. However it is unclear whethes rimilar rtistr iiiutior secenstruction methods can be derived for net-woik . 1 lriii is hccaupc vie hard to itclinc distribution for network data aid 2. rliih randomization i rcclaaiiiaeiii for network data is based on the positions of raodomly chosen adgtts eaihcs than ihe independent random additive values for alii nntoier ios numerical data. In 41 ri Wu eS aL invertigated the use oi iotv rank approximation methods to reconstruct riroiciural features inmi the graph randomized via Rand Add Del. Let Xi Xi he A s A s i-tii Ict-csS eigenvaiuc its magntSude whose eigenvector is xi Xi . Then the rank I apptoximalions of A acd A ate respectively given try i i Ai AiXixf and Ai X X c X f. i 1 i 1 By 4i Hmlngi a proper I Wu el ai. .41 thowed that Al tian preserve the majoo ielormalioa of original graph and hi let out noises added in the rest dimemionr. Thlr is because realiworid data ic usually highly correlated in a low dimcnsSonal space whiie ihe randomly .

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