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In this article we identify social communities among gang members in the Hollenbeck policing district in Los Angeles, based on sparse observations of a combination of social interactions and geographic locations of the individuals. This information, coming from LAPD Field Interview cards, is used to construct a similarity graph for the individuals. We use spectral clustering to identify clusters in the graph, corresponding to communities in Hollenbeck, and compare these with the LAPDs knowledge of the individuals gang membership. We discuss different ways of encoding the geosocial information using a graph structure and the influence on the resulting clusterings. Finally we analyze the robustness of this technique with respect to noisy and incomplete data, thereby providing suggestions about the relative importance of quantity versus quality of collected data.
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Grouping objects into clusters based on similarities or weights between them is one of the most important problems in science and engineering. In this work, by extending message passing algorithms and spectral algorithms proposed for unweighted community detection problem, we develop a non-parametric method based on statistical physics, by mapping the problem to Potts model at the critical temperature of spin glass transition and applying belief propagation to solve the marginals corresponding to the Boltzmann distribution. Our algorithm is robust to over-fitting and gives a principled way to determine whether there are significant clusters in the data and how many clusters there are. We apply our method to different clustering tasks and use extensive numerical experiments to illustrate the advantage of our method over existing algorithms. In the community detection problem in weighted and directed networks, we show that our algorithm significantly outperforms existing algorithms. In the clustering problem when the data was generated by mixture models in the sparse regime we show that our method works to the theoretical limit of detectability and gives accuracy very close to that of the optimal Bayesian inference. In the semi-supervised clustering problem, our method only needs several labels to work perfectly in classic datasets. Finally, we further develop Thouless-Anderson-Palmer equations which reduce heavily the computation complexity in dense-networks but gives almost the same performance as belief propagation.
We apply spectral clustering and multislice modularity optimization to a Los Angeles Police Department field interview card data set. To detect communities (i.e., cohesive groups of vertices), we use both geographic and social information about stops involving street gang members in the LAPD district of Hollenbeck. We then compare the algorithmically detected communities with known gang identifications and argue that discrepancies are due to sparsity of social connections in the data as well as complex underlying sociological factors that blur distinctions between communities.
Spectral clustering methods are widely used for detecting clusters in networks for community detection, while a small change on the graph Laplacian matrix could bring a dramatic improvement. In this paper, we propose a dual regularized graph Laplacian matrix and then employ it to three classical spectral clustering approaches under the degree-corrected stochastic block model. If the number of communities is known as $K$, we consider more than $K$ leading eigenvectors and weight them by their corresponding eigenvalues in the spectral clustering procedure to improve the performance. Three improved spectral clustering methods are dual regularized spectral clustering (DRSC) method, dual regularized spectral clustering on Ratios-of-eigenvectors (DRSCORE) method, and dual regularized symmetrized Laplacian inverse matrix (DRSLIM) method. Theoretical analysis of DRSC and DRSLIM show that under mild conditions DRSC and DRSLIM yield stable consistent community detection, moreover, DRSCORE returns perfect clustering under the ideal case. We compare the performances of DRSC, DRSCORE and DRSLIM with several spectral methods by substantial simulated networks and eight real-world networks.
Macroscopic behavior of scientific and societal systems results from the aggregation of microscopic behaviors of their constituent elements, but connecting the macroscopic with the microscopic in human behavior has traditionally been difficult. Manifestations of homophily, the notion that individuals tend to interact with others who resemble them, have been observed in many small and intermediate size settings. However, whether this behavior translates to truly macroscopic levels, and what its consequences may be, remains unknown. Here, we use call detail records (CDRs) to examine the population dynamics and manifestations of social and spatial homophily at a macroscopic level among the residents of 23 states of India at the Kumbh Mela, a 3-month-long Hindu festival. We estimate that the festival was attended by 61 million people, making it the largest gathering in the history of humanity. While we find strong overall evidence for both types of homophily for residents of different states, participants from low-representation states show considerably stronger propensity for both social and spatial homophily than those from high-representation states. These manifestations of homophily are amplified on crowded days, such as the peak day of the festival, which we estimate was attended by 25 million people. Our findings confirm that homophily, which here likely arises from social influence, permeates all scales of human behavior.
High demands for industrial networks lead to increasingly large sensor networks. However, the complexity of networks and demands for accurate data require better stability and communication quality. Conventional clustering methods for ad-hoc networks are based on topology and connectivity, leading to unstable clustering results and low communication quality. In this paper, we focus on two situations: time-evolving networks, and multi-channel ad-hoc networks. We model ad-hoc networks as graphs and introduce community detection methods to both situations. Particularly, in time-evolving networks, our method utilizes the results of community detection to ensure stability. By using similarity or human-in-the-loop measures, we construct a new weighted graph for final clustering. In multi-channel networks, we perform allocations from the results of multiplex community detection. Experiments on real-world datasets show that our method outperforms baselines in both stability and quality.
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