Community detection is an important problem in complex network analysis. Among numerous approaches for community detection, label propagation (LP) has attracted a lot of attention. LP selects the optimum community (i.e., label) of a network vertex by optimizing an objective function (e.g., Newman’s modularity) subject to the available labels in the vicinity of the vertex. In this article, a novel analysis of Newman’s modularity gain with respect to label transitions in graphs is presented. Here, we propose a new form of Newman’s modularity gain calculation that quantifies available label transitions for any LP based community detection. The proposed approach is called Modularity Gain Acceleration (MGA) and is simplified and divided into two components, the local and global sum-weights. The Local Sum-Weight (LSW) is the component with lower complexity and is calculated for each candidate label transition. The General Sum-Weight (GSW) is more computationally complex, and is calculated only once per each label. GSW is updated by leveraging a simple process for each node-label transition, instead of for all available labels. The proposed technique is applied to selected state-of-the-art LP-based community detection methods and the resulting network modularity and execution time are compared with traditional methods over small to big real world data sets. By applying MGA to LP-based methods, the run-time is significantly reduced–sometimes finishing before the traditional approach even finishes one iteration–achieving the same modularity performance and number of communities, i.e., community detection result. The MGA approach leads to significant efficiency improvements by reducing time consumption up to 85 percent relative to the original algorithms with the exact same quality in terms of modularity value which is highly valuable in analyses of big data sets.

Soft overlapping clustering is one of the notable problems of community detection. Extensive research has been conducted to develop efficient methods for nonoverlapping and crisp-overlapping community detection in large-scale networks. In this article, fast fuzzy modularity maximization (FFMM) for soft overlapping community detection is proposed. FFMM exploits novel iterative equations to calculate the modularity gain associated with changing the fuzzy membership values of network vertices. The simplicity of the proposed scheme enables efficient modifications, reducing computational complexity to a linear function of the network size, and the number of communities. Moreover, to further reduce the complexity of FFMM for very large networks, multicycle FFMM (McFFMM) is proposed. The proposed McFFMM reduces complexity by breaking networks into multiple subnetworks and applying FFMM to detect their communities. Performance of the proposed techniques is demonstrated with real-world data and the Lancichinetti-Fortunato-Radicchi benchmark networks. Moreover, the performance of the proposed techniques is evaluated versus some state-of-the-art soft overlapping community detection approaches. Results show that the McFFMM produces a remarkable performance in terms of overlapping modularity with fuzzy memberships, computational time, number of detected overlapping nodes, and overlapping normalized mutual information.

This paper introduces an effective ranging technique for sensor nodes implanted within human body leveraging a novel merger of high-resolution time-of-arrival (ToA) and direction-of-arrival (DoA) estimations. Human body is an in-homogeneous media (IHM) consisting of frequency dispersive sub-media (body organs) with unknown thicknesses that entail addressing two open problems: 1) high-resolution ToA estimation of a wideband ranging waveform propagated within IHM consisting of multipath and dispersive channels and 2) calculation of straight line range between implanted sensor node and receiver sensor array on human body. In the proposed technique, pre-allocated orthogonal frequency division multiplexing is utilized to construct a ranging waveform leveraging equally spaced and orthogonality properties of its sub-carriers which enable high-performance ToA estimation in frequency domain. The estimated ToA, however, cannot be utilized to calculate the straight line range due to refraction of propagated waveform at sub-media boundaries. Therefore, a merger of ToA and DoA is proposed that exploits multiple measurements at different carrier frequencies to develop a system of linear equations. The straight line range, then, is estimated by solving this system of equations with respect to thicknesses of available sub-media. The exploited approximations are discussed and verified via theoretical evaluations and simulations for human body to prove the feasibility of the proposed technique.

This paper introduces a novel method to improve the Time of Arrival (ToA) estimation resolution for a fixed available bandwidth in the presence of unknown multipath frequency selective (MPFS) channels. Here, the maximum rising level detector technique is proposed which utilizes oversampling and multiple correlation paths to evaluate with high resolution the path corresponding to the maximum rising level of matched filters output. However, employing such technique demands for transmission of waveform that creates a very high rising level at autocorrelation center. This paper proposes an efficient technique to design proper waveforms (very high rising level at autocorrelation center) via minimization of weighted integrated sidelobe level, exploiting the trust-region algorithm. The performance of the proposed technique is evaluated via simulations of the ToA mean square error, and compared with the state-of-the-art approaches considering the same bandwidth, and Cramer-Rao lower bound as benchmark. Simulations confirm that the ToA resolution is improved as the number of correlation paths increases and verify the feasibility of the proposed technique compared with the available approaches for the MPFS channels.

This paper introduces a novel and effective ranging approach in nonhomogeneous (NH) media consisting of frequency dispersive submedia via time-of-arrival (ToA). Here, the NH environment consists of sublayers with a specific thickness that is estimated throughout the ranging process. First, a novel technique for ToA estimation in the presence of frequency dispersive submedia via orthogonal frequency division multiple access subcarriers is proposed. In the proposed technique, preallocated orthogonal subcarriers are utilized to construct a ranging waveform that enables high-performance ToA estimation in dispersive NH media in the frequency domain. The proposed ToA technique is exploited for multiple ToA measurements at different carrier frequencies, which leads to a system of linear equations that can be solved to compute the thickness of the available submedia and calculate the range. Simulation results for underwater-airborne media and underground channel confirm that the proposed technique offers high-resolution ranging at different signal to noise ratio regimes in the NH media.

This paper introduces the coarse time-of-arrival (ToA) estimation in wireless sensor networks (WSN) via orthogonal frequency division multiple access (OFDMA). In the proposed technique, each sensor node exploits a set of orthogonal subcarrier as its allocated signature to respond of the ToA estimation requests transmitted by target nodes. The target node utilizes the orthogonality across sub-carriers to detect the transmitted signatures and their corresponding delays. This technique is energy efficient as it avoids multiple transmissions and receptions inherent in traditional neighbor discovery protocols and ToA estimation techniques in WSN. Moreover, in this technique, network initiation process does not require channel information or time synchronization across sensor nodes. ToA estimation error is calculated theoretically and via simulations. Moreover, the impact of available bandwidth on the performance of ToA estimation is investigated. Simulation results confirm the feasibility of the proposed method even at low signal to noise ratio (SNR) regimes and in multi- path and frequency selective (MPFS) channels.