An Ensemble Framework for Detecting Community Changes in Dynamic Networks

Dynamic networks, especially those representing social networks, undergo constant evolution of their community structure over time. Nodes can migrate between different communities, communities can split into multiple new communities, communities can merge together, etc. In order to represent dynamic networks with evolving communities it is essential to use a dynamic model rather than a static one. Here we use a dynamic stochastic block model where the underlying block model is different at different times. In order to represent the structural changes expressed by this dynamic model the network will be split into discrete time segments and a clustering algorithm will assign block memberships for each segment. In this paper we show that using an ensemble of clustering assignments accommodates for the variance in scalable clustering algorithms and produces superior results in terms of pairwise-precision and pairwise-recall. We also demonstrate that the dynamic clustering produced by the ensemble can be visualized as a flowchart which encapsulates the community evolution succinctly.Comment: 6 pages, under submission to HPEC Graph Challeng

Beyond Hartigan Consistency: Merge Distortion Metric for Hierarchical Clustering

Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given density can look very different than the correct limit tree. Specifically, Hartigan consistency permits two types of undesirable configurations which we term over-segmentation and improper nesting. Moreover, Hartigan consistency is a limit property and does not directly quantify difference between trees. In this paper we identify two limit properties, separation and minimality, which address both over-segmentation and improper nesting and together imply (but are not implied by) Hartigan consistency. We proceed to introduce a merge distortion metric between hierarchical clusterings and show that convergence in our distance implies both separation and minimality. We also prove that uniform separation and minimality imply convergence in the merge distortion metric. Furthermore, we show that our merge distortion metric is stable under perturbations of the density. Finally, we demonstrate applicability of these concepts by proving convergence results for two clustering algorithms. First, we show convergence (and hence separation and minimality) of the recent robust single linkage algorithm of Chaudhuri and Dasgupta (2010). Second, we provide convergence results on manifolds for topological split tree clustering

Machine learning of hierarchical clustering to segment 2D and 3D images

We aim to improve segmentation through the use of machine learning tools during region agglomeration. We propose an active learning approach for performing hierarchical agglomerative segmentation from superpixels. Our method combines multiple features at all scales of the agglomerative process, works for data with an arbitrary number of dimensions, and scales to very large datasets. We advocate the use of variation of information to measure segmentation accuracy, particularly in 3D electron microscopy (EM) images of neural tissue, and using this metric demonstrate an improvement over competing algorithms in EM and natural images.Comment: 15 pages, 8 figure