skip to main content


Title: Efficient Distributed Community Detection in the Stochastic Block Model
Designing effective algorithms for community detection is an important and challenging problem in large-scale graphs, studied extensively in the literature. Various solutions have been proposed, but many of them are centralized with expensive procedures (requiring full knowledge of the input graph) and have a large running time. In this paper, we present a distributed algorithm for community detection in the stochastic block model (also called planted partition model), a widely-studied and canonical random graph model for community detection and clustering. Our algorithm called CDRW(Community Detection by Random Walks) is based on random walks, and is localized and lightweight, and easy to implement. A novel feature of the algorithm is that it uses the concept of local mixing time to identify the community around a given node. We present a rigorous theoretical analysis that shows that the algorithm can accurately identify the communities in the stochastic block model and characterize the model parameters where the algorithm works. We also present experimental results that validate our theoretical analysis. We also analyze the performance of our distributed algorithm under the CONGEST distributed model as well as the k-machine model, a model for large-scale distributed computations, and show that it can be efficiently implemented.  more » « less
Award ID(s):
1633720
NSF-PAR ID:
10111287
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS)
Page Range / eLocation ID:
409-419
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Community detection in graphs, also known as graph partitioning, is a well-studied NP-hard problem. Various heuristic approaches have been adopted to tackle this problem in polynomial time. One such approach, as outlined in the IEEE HPEC Graph Challenge, is Bayesian statistics-based stochastic block partitioning. This method delivers high-quality partitions in sub-quadratic runtime, but it fails to scale to very large graphs. In this paper, we present sampling as an avenue for speeding up the algorithm on large graphs. We first show that existing sampling techniques can preserve a graph’s community structure. We then show that sampling for stochastic block partitioning can be used to produce a speedup of between 2.18× and 7.26× for graph sizes between 5, 000 and 50, 000 vertices without a significant loss in the accuracy of community detection. 
    more » « less
  2. The brain serotonergic axons (fibers) are quintessential “stochastic” axons in the sense that their individual trajectories are best described as sample paths of a spatial stochastic process. These fibers are present in high densities in virtually all regions of vertebrate brains; more generally, they appear to be an obligatory component of all nervous systems on this planet (from the dominating arthropods to such small phyla as the kinorhynchs). In mammals, serotonergic fibers are nearly unique in their ability to robustly regenerate in the adult brain, and they have been strongly associated with neural plasticity. We have recently developed several experimental approaches to trace individual serotonergic fibers in the mouse brain (Mays et al., 2022). To further advance the theoretical analyses of their stochastic properties (e.g., the increment covariance structure), we developed a convolutional neural network (CNN) that performs high-throughput analysis of experimental data collected with sub-micrometer resolution. In contrast to a recently developed mesoscale platform that can separate large-caliber fiber segments from the background on the whole-brain scale (Friedmann et al., 2020), our microscale model prioritizes the accuracy and continuity of individual fiber trajectories, an essential element in downstream stochastic analyses. In particular, it seamlessly integrates information about the physical properties of serotonergic fibers and high-resolution experimental data to achieve reliable, fully-automated tracing of trajectories in brain regions with different fiber densities. This 3D-spatial information supports our current theoretical frameworks based on step-wise random walks (Janusonis & Detering, 2019) and continuous-time processes (Janusonis et al., 2020). In a complementary approach, we also investigated whether the structure of the serotonergic fibers may provide useful information for machine learning architectures. Specifically, we studied whether dropout, a standard regularization technique in artificial neural networks, can be matched or improved by virtual serotonergic fibers moving through CNN layers (endowed with the Euclidean metric) and triggering spatially correlated dropout events. This research was funded by NSF CRCNS (#1822517 and #2112862), NIMH (#MH117488), and the California NanoSystems Institute. 
    more » « less
  3. Consider an algorithm performing a computation on a huge random object. Is it necessary to generate the entire object up front, or is it possible to provide query access to the object and sample it incrementally "on-the-fly"? Such an implementation should emulate the object by answering queries in a manner consistent with a random instance sampled from the true distribution. Our first set of results focus on undirected graphs with independent edge probabilities, under certain assumptions. Then, we use this to obtain the first efficient implementations for the Erdos-Renyi model and the Stochastic Block model. As in previous local-access implementations for random graphs, we support Vertex-Pair and Next-Neighbor queries. We also introduce a new Random-Neighbor query. Next, we show how to implement random Catalan objects, specifically focusing on Dyck paths (always positive random walks on the integer line). Here, we support Height queries to find the position of the walk, and First-Return queries to find the time when the walk returns to a specified height. This in turn can be used to implement Next-Neighbor queries on random rooted/binary trees, and Matching-Bracket queries on random well bracketed expressions. Finally, we define a new model that: (1) allows multiple independent simultaneous instantiations of the same implementation to be consistent with each other without communication (2) allows us to generate a richer class of random objects that do not have a succinct description. Specifically, we study uniformly random valid q-colorings of an input graph G with max degree Δ. The distribution over valid colorings is specified via a "huge" underlying graph G, that is far too large to be read in sub-linear time. Instead, we access G through local neighborhood probes. We are able to answer queries to the color of any vertex in sub-linear time for q>9Δ. 
    more » « less
  4. null (Ed.)
    Consider an algorithm performing a computation on a huge random object (for example a random graph or a "long" random walk). Is it necessary to generate the entire object prior to the computation, or is it possible to provide query access to the object and sample it incrementally "on-the-fly" (as requested by the algorithm)? Such an implementation should emulate the random object by answering queries in a manner consistent with an instance of the random object sampled from the true distribution (or close to it). This paradigm is useful when the algorithm is sub-linear and thus, sampling the entire object up front would ruin its efficiency. Our first set of results focus on undirected graphs with independent edge probabilities, i.e. each edge is chosen as an independent Bernoulli random variable. We provide a general implementation for this model under certain assumptions. Then, we use this to obtain the first efficient local implementations for the Erdös-Rényi G(n,p) model for all values of p, and the Stochastic Block model. As in previous local-access implementations for random graphs, we support Vertex-Pair and Next-Neighbor queries. In addition, we introduce a new Random-Neighbor query. Next, we give the first local-access implementation for All-Neighbors queries in the (sparse and directed) Kleinberg’s Small-World model. Our implementations require no pre-processing time, and answer each query using O(poly(log n)) time, random bits, and additional space. Next, we show how to implement random Catalan objects, specifically focusing on Dyck paths (balanced random walks on the integer line that are always non-negative). Here, we support Height queries to find the location of the walk, and First-Return queries to find the time when the walk returns to a specified location. This in turn can be used to implement Next-Neighbor queries on random rooted ordered trees, and Matching-Bracket queries on random well bracketed expressions (the Dyck language). Finally, we introduce two features to define a new model that: (1) allows multiple independent (and even simultaneous) instantiations of the same implementation, to be consistent with each other without the need for communication, (2) allows us to generate a richer class of random objects that do not have a succinct description. Specifically, we study uniformly random valid q-colorings of an input graph G with maximum degree Δ. This is in contrast to prior work in the area, where the relevant random objects are defined as a distribution with O(1) parameters (for example, n and p in the G(n,p) model). The distribution over valid colorings is instead specified via a "huge" input (the underlying graph G), that is far too large to be read by a sub-linear time algorithm. Instead, our implementation accesses G through local neighborhood probes, and is able to answer queries to the color of any given vertex in sub-linear time for q ≥ 9Δ, in a manner that is consistent with a specific random valid coloring of G. Furthermore, the implementation is memory-less, and can maintain consistency with non-communicating copies of itself. 
    more » « less
  5. Community detection in graphs can be solved via spectral methods or posterior inference under certain probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified both approaches and identified both statistical and computational detection thresholds in terms of the signal-to-noise ratio. By recasting community detection as a node-wise classification problem on graphs, we can also study it from a learning perspective. We present a novel family of Graph Neural Networks (GNNs) for solving community detection problems in a supervised learning setting. We show that, in a data-driven manner and without access to the underlying generative models, they can match or even surpass the performance of the belief propagation algorithm on binary and multiclass stochastic block models, which is believed to reach the computational threshold in these cases. In particular, we propose to augment GNNs with the non-backtracking operator defined on the line graph of edge adjacencies. The GNNs are achieved good performance on real-world datasets. In addition, we perform the first analysis of the optimization landscape of using (linear) GNNs to solve community detection problems, demonstrating that under certain simplifications and assumptions, the loss value at any local minimum is close to the loss value at the global minimum/minima. 
    more » « less