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36
Graph Kernels
, 2007
"... We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexit ..."
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Cited by 101 (9 self)
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We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n 6) to O(n 3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixedpoint methods that take O(dn 3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for ddimensional edge kernels, and O(n 4) in the infinitedimensional case; on sparse graphs these algorithms only take O(n 2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to Rconvolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semidefinite.
Access pattern disclosure on searchable encryption: Ramification, attack and mitigation
 in Network and Distributed System Security Symposium (NDSS
, 2012
"... The advent of cloud computing has ushered in an era of mass data storage in remote servers. Remote data storage offers reduced data management overhead for data owners in a cost effective manner. Sensitive documents, however, need to be stored in encrypted format due to security concerns. But, encr ..."
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Cited by 40 (0 self)
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The advent of cloud computing has ushered in an era of mass data storage in remote servers. Remote data storage offers reduced data management overhead for data owners in a cost effective manner. Sensitive documents, however, need to be stored in encrypted format due to security concerns. But, encrypted storage makes it difficult to search on the stored documents. Therefore, this poses a major barrier towards selective retrieval of encrypted documents from the remote servers. Various protocols have been proposed for keyword search over encrypted data to address this issue. Most of the available protocols leak data access patterns due to efficiency reasons. Although, oblivious RAM based protocols can be used to hide data access patterns, such protocols are computationally intensive and do not scale well for real world datasets. In this paper, we introduce a novel attack that exploits data access pattern leakage to disclose significant amount of sensitive information using a modicum of prior knowledge. Our empirical analysis with a real world dataset shows that the proposed attack is able to disclose sensitive information with a very high accuracy. Additionally, we propose a simple technique to mitigate the risk against the proposed attack at the expense of a slight increment in computational resources and communication cost. Furthermore, our proposed mitigation technique is generic enough to be used in conjunction with any searchable encryption scheme that reveals data access pattern. 1.
A.: Mining graph evolution rules
 In: ECML/PKDD
, 2009
"... Abstract. In this paper we introduce graphevolution rules, a novel type of frequencybased pattern that describe the evolution of large networks over time, at a local level. Given a sequence of snapshots of an evolving graph, we aim at discovering rules describing the local changes occurring in it. ..."
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Cited by 37 (4 self)
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Abstract. In this paper we introduce graphevolution rules, a novel type of frequencybased pattern that describe the evolution of large networks over time, at a local level. Given a sequence of snapshots of an evolving graph, we aim at discovering rules describing the local changes occurring in it. Adopting a definition of support based on minimum image we study the problem of extracting patterns whose frequency is larger than a minimum support threshold. Then, similar to the classical association rules framework, we derive graphevolution rules from frequent patterns that satisfy a given minimum confidence constraint. We discuss merits and limits of alternative definitions of support and confidence, justifying the chosen framework. To evaluate our approach we devise GERM (Graph Evolution Rule Miner), an algorithm to mine all graphevolution rules whose support and confidence are greater than given thresholds. The algorithm is applied to analyze four large realworld networks (i.e., two social networks, and two coauthorship networks from bibliographic data), using different time granularities. Our extensive experimentation confirms the feasibility and utility of the presented approach. It further shows that different kinds of networks exhibit different evolution rules, suggesting the usage of these local patterns to globally discriminate different kind of networks. 1
Mining periodic behavior in dynamic social networks
 in Proceedings of the 8th IEEE International Conference on Data Mining
"... Social interactions that occur regularly typically correspond to significant yet often infrequent and hard to detect interaction patterns. To identify such regular behavior, we propose a new mining problem of finding periodic or near periodic subgraphs in dynamic social networks. We analyze the co ..."
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Cited by 21 (0 self)
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Social interactions that occur regularly typically correspond to significant yet often infrequent and hard to detect interaction patterns. To identify such regular behavior, we propose a new mining problem of finding periodic or near periodic subgraphs in dynamic social networks. We analyze the computational complexity of the problem, showing that, unlike any of the related subgraph mining problems, it is polynomial. We propose a practical, efficient and scalable algorithm to find such subgraphs that takes imperfect periodicity into account. We demonstrate the applicability of our approach on several realworld networks and extract meaningful and interesting periodic interaction patterns. 1.
Social network analysis and mining for business applications
 ACM Trans. Intell. Syst. Technol
"... Social network analysis has gained significant attention in recent years, largely due to the success of online social networking and mediasharing sites, and the consequent availability of a wealth of social network data. In spite of the growing interest, however, there is little understanding of th ..."
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Cited by 14 (1 self)
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Social network analysis has gained significant attention in recent years, largely due to the success of online social networking and mediasharing sites, and the consequent availability of a wealth of social network data. In spite of the growing interest, however, there is little understanding of the potential business applications of mining social networks. While there is a large body of research on different problems and methods for social network mining, there is a gap between the techniques developed by the research community and their deployment in realworld applications. Therefore the potential business impact of these techniques is still largely unexplored. In this article we use a business process classification framework to put the research topics in a business context and provide an overview of what we consider key problems and techniques in social network analysis and mining from the perspective of business applications. In particular, we discuss data acquisition and preparation, trust, expertise, community structure, network dynamics, and information propagation. In each case we present a brief overview of the problem, describe stateofthe art approaches, discuss business application examples, and map each of the topics to a business process classification framework. In addition, we provide insights on prospective business applications, challenges, and future research directions. The main contribution of this article is to provide a stateoftheart overview of current techniques while providing a critical perspective on business applications of social network analysis and mining.
Discovering Correlated SpatioTemporal Changes in Evolving Graphs
 UNDER CONSIDERATION FOR PUBLICATION IN KNOWLEDGE AND INFORMATION SYSTEMS
, 2007
"... Graphs provide powerful abstractions of relational data, and are widely used in fields such as network management, web page analysis and sociology. While many graph representations of data describe dynamic and time evolving relationships, most graph mining work treats graphs as static entities. Our ..."
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Cited by 13 (3 self)
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Graphs provide powerful abstractions of relational data, and are widely used in fields such as network management, web page analysis and sociology. While many graph representations of data describe dynamic and time evolving relationships, most graph mining work treats graphs as static entities. Our focus in this paper is to discover regions of a graph that are evolving in a similar manner. To discover regions of correlated spatiotemporal change in graphs, we propose an algorithm called cSTAG. Whereas most clustering techniques are designed to find clusters that optimise a single distance measure, cSTAG addresses the problem of finding clusters that optimise both temporal and spatial distance measures simultaneously. We show the effectiveness of cSTAG using a quantitative analysis of accuracy on synthetic data sets, as well as demonstrating its utility on two large, reallife data sets, where one is the routing topology of the Internet, and the other is the dynamic graph of files accessed together on the 1998 World Cup official website.
Mining the temporal dimension of the information propagation
 In IDA
, 2009
"... Abstract. In the last decade, Social Network Analysis has been a field in which the effort devoted from several researchers in the Data Mining area has increased very fast. Among the possible related topics, the study of the information propagation in a network attracted the interest of many resear ..."
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Cited by 7 (7 self)
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Abstract. In the last decade, Social Network Analysis has been a field in which the effort devoted from several researchers in the Data Mining area has increased very fast. Among the possible related topics, the study of the information propagation in a network attracted the interest of many researchers, also from the industrial world. However, only a few answers to the questions “How does the information propagates over a network, why and how fast? ” have been discovered so far. On the other hand, these answers are of large interest, since they help in the tasks of finding experts in a network, assessing viral marketing strategies, identifying fast or slow paths of the information inside a collaborative network. In this paper we study the problem of finding frequent patterns in a network with the help of two different techniques: TAS (Temporally Annotated Sequences) mining, aimed at extracting sequential patterns where each transition between two events is annotated with a typical transition time that emerges from input data, and Graph Mining, which is helpful for locally analyzing the nodes of the networks with their properties. Finally we show preliminary results done in the direction of mining the information propagation over a network, performed on two well known email datasets, that show the power of the combination of these two approaches. 1
Mining Frequent Graph Sequence Patterns Induced by Vertices
"... The mining of a complete set of frequent subgraphs from labeled graph data has been studied extensively. Furthermore, much attention has recently been paid to frequent pattern mining from graph sequences (dynamic graphs or evolving graphs). In this paper, we define a novel class of subgraph subseque ..."
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Cited by 6 (0 self)
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The mining of a complete set of frequent subgraphs from labeled graph data has been studied extensively. Furthermore, much attention has recently been paid to frequent pattern mining from graph sequences (dynamic graphs or evolving graphs). In this paper, we define a novel class of subgraph subsequence called an “induced subgraph subsequence ” to enable efficient mining of a complete set of frequent patterns from graph sequences containing large graphs and long sequences. We also propose an efficient method to mine frequent patterns, called “FRISSs (Frequent Relevant, and Induced Subgraph Subsequences)”, from graph sequences. The fundamental performance of the method has been evaluated using artificial datasets, and its practicality has been confirmed through experiments using a realworld dataset. 1
ConstraintBased Mining of Sets of Cliques Sharing Vertex Properties
 In ACNE’10
, 2010
"... Abstract. We consider data mining methods on large graphs where a set of labels is associated to each vertex. A typical example of such graphs is a social network of collaborating researchers where additional information represent the main publication targets (preferred conferences or journals) for ..."
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Cited by 4 (0 self)
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Abstract. We consider data mining methods on large graphs where a set of labels is associated to each vertex. A typical example of such graphs is a social network of collaborating researchers where additional information represent the main publication targets (preferred conferences or journals) for each author. We investigate the extraction of sets of dense subgraphs such that the vertices in all subgraphs of a set share a large enough set of labels. As a first step, we consider here the special case of dense subgraphs that are cliques. We proposed a method to compute all maximal homogeneous clique sets that satisfy userdefined constraints on the number of separated cliques, on the size of the cliques, and on the number of labels shared by all the vertices. The empirical validation illustrates the scalability of our approach and it provides experimental feedback on two real datasets, more precisely an annotated social network derived from the DBLP database and an enriched biological network of proteinprotein interactions. In both cases, we discuss the relevancy of extracted patterns thanks to available domain knowledge.
Mining evolving network processes
"... Abstract—Processes within real world networks evolve according to the underlying graph structure. A bounty of examples exists in diverse network genres: botnet communication growth, moving traffic jams [25], information foraging [37] in document networks (WWW and Wikipedia), and spread of viral meme ..."
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Cited by 3 (1 self)
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Abstract—Processes within real world networks evolve according to the underlying graph structure. A bounty of examples exists in diverse network genres: botnet communication growth, moving traffic jams [25], information foraging [37] in document networks (WWW and Wikipedia), and spread of viral memes or opinions in social networks. The network structure in all the above examples remains relatively fixed, while the shape, size and position of the affected network regions change gradually with time. Traffic jams grow, move, shrink and eventually disappear. Public attention shifts among current hot topics inducing a similar shift of highly accessed Wikipedia articles. Discovery of such smoothly evolving network processes has the potential to expose the intrinsic mechanisms of complex network dynamics, enable new datadriven models and improve network design. We introduce the novel problem of Mining smoothly evolving processes (MINESMOOTH) in networks with dynamic realvalued node/edge weights. We show that ensuring smooth transitions in the solution is NPhard even on restricted network structures such as trees. We propose an efficient filteringbased framework, called LEGATO. It achieves 3−7 times improvement in the obtained process scores (i.e. larger and strongerimpact processes) compared to alternatives on real networks, and above 80 % accuracy in discovering realistic “embedded ” processes in synthetic networks. In transportation networks, LEGATO discovers processes that conform to existing theoretical models for traffic jams, while its obtained processes in Wikipedia reveal the temporal evolution of information seeking of Internet users. I.