Malik Magdon-Ismail

Efficient identification of overlapping communities

In this paper, we present an efficient algorithm for finding overlapping communities in social networks. Our algorithm does not rely on the contents of the messages and uses the communication graph only. The knowledge of the structure of the communities is important for the analysis of social behavior and evolution of the society as a whole, as well as its individual members. This knowledge can be helpful in discovering groups of actors that hide their communications, possibly for malicious reasons. Although the idea of using communication graphs for identifying clusters of actors is not new, most of the traditional approaches, with the exception of the work by Baumes et al, produce disjoint clusters of actors, de facto postulating that an actor is allowed to belong to at most one cluster. Our algorithm is significantly more efficient than the previous algorithm by Baumes et al; it also produces clusters of a comparable or better quality.

Near-Optimal Column-Based Matrix Reconstruction

We consider low-rank reconstruction of a matrix using a subset of its columns and present asymptotically optimal algorithms for both spectral norm and Frobenius norm reconstruction. The main tools ...

Measuring behavioral trust in social networks

Trust is an important yet complex and little understood aspect of the dyadic relationship between two entities. Trust plays an important role in the formation of coalitions in social networks and in determining how high value of information flows through the network. We present algorithmically quantifiable measures of trust based on communication behavior. We propose that trust results in likely communication behaviors which are statistically different from random communications; detecting these trust-like behaviors allows us to develop a quantitative measure of who trusts whom in the network. We develop algorithms to efficiently compute such behavioral trust and validate these measures on the Twitter network.

Discovering Hidden Groups in Communication Networks

We describe models and efficient algorithms for detecting groups (communities) functioning in communication networks which attempt to hide their functionality – hidden groups. Our results reveal the properties of the background network activity that make detection of the hidden group easy, as well as those that make it difficult.

Contention-free MAC protocols for wireless sensor networks

A MAC protocol specifies how nodes in a sensor network access a shared communication channel. Desired properties of such MAC protocol are: it should be distributed and contention-free (avoid collisions); it should self-stabilize to changes in the network (such as arrival of new nodes), and these changes should be contained, i.e., affect only the nodes in the vicinity of the change; it should not assume that nodes have a global time reference, i.e., nodes may not be time-synchronized. We give the first MAC protocols that satisfy all of these requirements, i.e., we give distributed, contention-free, self-stabilizing MAC protocols which do not assume a global time reference. Our protocols self-stabilize from an arbitrary initial state, and if the network changes the changes are contained and the protocol adjusts to the local topology of the network. The communication complexity, number and size of messages, for the protocol to stabilize is small (logarithmic in network size).

No free lunch for early stopping

We show that with a uniform prior on models having the same training error, early stopping at some fixed training error above the training error minimum results in an increase in the expected generalization error.

Distance Matrix Reconstruction from Incomplete Distance Information for Sensor Network Localization

This paper focuses on the principled study of distance reconstruction for distance-based node localization. We address an important issue in node localization by showing that a highly incomplete set of inter-node distance measurements obtained in ad-hoc node deployments carries sufficient information for the accurate reconstruction of the missing distances, even in the presence of noise and sensor node failures. We provide an efficient and provably accurate algorithm for this reconstruction, and we show that the resulting error is bounded, decreasing at a rate that is inversely proportional to radicn, the square root of the number of nodes in the region of deployment. Although this result is applicable to many localization schemes, in this paper we illustrate its use in conjunction with the popular multidimensional scaling algorithm. Our analysis reveals valuable insights and key factors to consider during the sensor network setup phase, to improve the quality of the position estimates

Near Optimal Column-Based Matrix Reconstruction

We consider low-rank reconstruction of a matrix using a subset of its columns and we present asymptotically optimal algorithms for both spectral norm and Frobenius norm reconstruction. The main tools we introduce to obtain our results are: (i) the use of fast approximate SVD-like decompositions for column-based matrix reconstruction, and (ii) two deterministic algorithms for selecting rows from matrices with orthonormal columns, building upon the sparse representation theorem for decompositions of the identity that appeared in [1].

Communities and Balance in Signed Networks: A Spectral Approach

Discussion based websites like Epinions.com and Slashdot.com allow users to identify both friends and foes. Such networks are called Signed Social Networks and mining communities of like-minded users from these networks has potential value. We extend existing community detection algorithms that work only on unsigned networks to be applicable to signed networks. In particular, we develop a spectral approach augmented with iterative optimization. We use our algorithms to study both communities and structural balance. Our results indicate that modularity based communities are distinct from structurally balanced communities.

Finding Overlapping Communities in Social Networks

Increasingly, methods to identify community structure in networks have been proposed which allow groups to overlap. These methods have taken a variety of forms, resulting in a lack of consensus as to what characteristics overlapping communities should have. Furthermore, overlapping community detection algorithms have been justified using intuitive arguments, rather than quantitative observations. This lack of consensus and empirical justification has limited the adoption of methods which identify overlapping communities. In this text, we distil from previous literature a minimal set of axioms which overlapping communities should satisfy. Additionally, we modify a previously published algorithm, Iterative Scan, to ensure that these properties are met. By analyzing the community structure of a large blog network, we present both structural and attribute based verification that overlapping communities naturally and frequently occur.