Modularity functions maximization with nonnegative relaxation facilitates community detection in networks

We show here that the problem of maximizing a family of quantitative functions, encompassing both the modularity (Q-measure) and modularity density (D-measure), for community detection can be uniformly understood as a combinatoric optimization involving the trace of a matrix called modularity Laplacian. Instead of using traditional spectral relaxation, we apply additional nonnegative constraint into this graph clustering problem and design efficient algorithms to optimize the new objective. With the explicit nonnegative constraint, our solutions are very close to the ideal community indicator matrix and can directly assign nodes into communities. The near-orthogonal columns of the solution can be reformulated as the posterior probability of corresponding node belonging to each community. Therefore, the proposed method can be exploited to identify the fuzzy or overlapping communities and thus facilitates the understanding of the intrinsic structure of networks. Experimental results show that our new algorithm consistently, sometimes significantly, outperforms the traditional spectral relaxation approaches

Feedback Allocation For OFDMA Systems With Slow Frequency-domain Scheduling

We study the problem of allocating limited feedback resources across multiple users in an orthogonal-frequency-division-multiple-access downlink system with slow frequency-domain scheduling. Many flavors of slow frequency-domain scheduling (e.g., persistent scheduling, semi-persistent scheduling), that adapt user-sub-band assignments on a slower time-scale, are being considered in standards such as 3GPP Long-Term Evolution. In this paper, we develop a feedback allocation algorithm that operates in conjunction with any arbitrary slow frequency-domain scheduler with the goal of improving the throughput of the system. Given a user-sub-band assignment chosen by the scheduler, the feedback allocation algorithm involves solving a weighted sum-rate maximization at each (slow) scheduling instant. We first develop an optimal dynamic-programming-based algorithm to solve the feedback allocation problem with pseudo-polynomial complexity in the number of users and in the total feedback bit budget. We then propose two approximation algorithms with complexity further reduced, for scenarios where the problem exhibits additional structure.Comment: Accepted to IEEE Transactions on Signal Processin

COMMUNITY DETECTION IN COMPLEX NETWORKS AND APPLICATION TO DENSE WIRELESS SENSOR NETWORKS LOCALIZATION

Complex network analysis is applied in numerous researches. Features and characteristics of complex networks provide information associated with a network feature called community structure. Naturally, nodes with similar attributes will be more likely to form a community. Community detection is described as the process by which complex network data are analyzed to uncover organizational properties, and structure; and ultimately to enable extraction of useful information. Analysis of Wireless Sensor Networks (WSN) is considered as one of the most important categories of network analysis due to their enormous and emerging applications. Most WSN applications are location-aware, which entails precise localization of the deployed sensor nodes. However, localization of sensor nodes in very dense network is a challenging task. Among various challenges associated with localization of dense WSNs, anchor node selection is shown as a prominent open problem. Optimum anchor selection impacts overall sensor node localization in terms of accuracy and consumed energy. In this thesis, various approaches are developed to address both overlapping and non-overlapping community detection. The proposed approaches target small-size to very large-size networks in near linear time, which is important for very large, densely-connected networks. Performance of the proposed techniques are evaluated over real-world data-sets with up to 106 nodes and syntactic networks via Newman\u27s Modularity and Normalized Mutual Information (NMI). Moreover, the proposed community detection approaches are extended to develop a novel criterion for range-free anchor selection in WSNs. Our approach uses novel objective functions based on nodes\u27 community memberships to reveal a set of anchors among all available permutations of anchors-selection sets. The performance---the mean and variance of the localization error---of the proposed approach is evaluated for a variety of node deployment scenarios and compared with random anchor selection and the full-ranging approach. In order to study the effectiveness of our algorithm, the performance is evaluated over several simulations that randomly generate network configurations. By incorporating our proposed criteria, the accuracy of the position estimate is improved significantly relative to random anchor selection localization methods. Simulation results show that the proposed technique significantly improves both the accuracy and the precision of the location estimation

Budget Feasible Mechanisms for Experimental Design

In the classical experimental design setting, an experimenter E has access to a population of $n$ potential experiment subjects $i\in \{1,...,n\}$, each associated with a vector of features $x_i\in R^d$. Conducting an experiment with subject $i$ reveals an unknown value $y_i\in R$ to E. E typically assumes some hypothetical relationship between $x_i$'s and $y_i$'s, e.g., $y_i \approx \beta x_i$, and estimates $\beta$ from experiments, e.g., through linear regression. As a proxy for various practical constraints, E may select only a subset of subjects on which to conduct the experiment. We initiate the study of budgeted mechanisms for experimental design. In this setting, E has a budget $B$. Each subject $i$ declares an associated cost $c_i >0$ to be part of the experiment, and must be paid at least her cost. In particular, the Experimental Design Problem (EDP) is to find a set $S$ of subjects for the experiment that maximizes V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i}) under the constraint $\sum_{i\in S}c_i\leq B$; our objective function corresponds to the information gain in parameter $\beta$ that is learned through linear regression methods, and is related to the so-called $D$-optimality criterion. Further, the subjects are strategic and may lie about their costs. We present a deterministic, polynomial time, budget feasible mechanism scheme, that is approximately truthful and yields a constant factor approximation to EDP. In particular, for any small $\delta > 0$ and $\epsilon > 0$, we can construct a (12.98, $\epsilon$)-approximate mechanism that is $\delta$-truthful and runs in polynomial time in both $n$ and $\log\log\frac{B}{\epsilon\delta}$. We also establish that no truthful, budget-feasible algorithms is possible within a factor 2 approximation, and show how to generalize our approach to a wide class of learning problems, beyond linear regression