7,263 research outputs found
Online Tensor Methods for Learning Latent Variable Models
We introduce an online tensor decomposition based approach for two latent
variable modeling problems namely, (1) community detection, in which we learn
the latent communities that the social actors in social networks belong to, and
(2) topic modeling, in which we infer hidden topics of text articles. We
consider decomposition of moment tensors using stochastic gradient descent. We
conduct optimization of multilinear operations in SGD and avoid directly
forming the tensors, to save computational and storage costs. We present
optimized algorithm in two platforms. Our GPU-based implementation exploits the
parallelism of SIMD architectures to allow for maximum speed-up by a careful
optimization of storage and data transfer, whereas our CPU-based implementation
uses efficient sparse matrix computations and is suitable for large sparse
datasets. For the community detection problem, we demonstrate accuracy and
computational efficiency on Facebook, Yelp and DBLP datasets, and for the topic
modeling problem, we also demonstrate good performance on the New York Times
dataset. We compare our results to the state-of-the-art algorithms such as the
variational method, and report a gain of accuracy and a gain of several orders
of magnitude in the execution time.Comment: JMLR 201
Community Detection in Networks with Node Attributes
Community detection algorithms are fundamental tools that allow us to uncover
organizational principles in networks. When detecting communities, there are
two possible sources of information one can use: the network structure, and the
features and attributes of nodes. Even though communities form around nodes
that have common edges and common attributes, typically, algorithms have only
focused on one of these two data modalities: community detection algorithms
traditionally focus only on the network structure, while clustering algorithms
mostly consider only node attributes. In this paper, we develop Communities
from Edge Structure and Node Attributes (CESNA), an accurate and scalable
algorithm for detecting overlapping communities in networks with node
attributes. CESNA statistically models the interaction between the network
structure and the node attributes, which leads to more accurate community
detection as well as improved robustness in the presence of noise in the
network structure. CESNA has a linear runtime in the network size and is able
to process networks an order of magnitude larger than comparable approaches.
Last, CESNA also helps with the interpretation of detected communities by
finding relevant node attributes for each community.Comment: Published in the proceedings of IEEE ICDM '1
Detecting Cohesive and 2-mode Communities in Directed and Undirected Networks
Networks are a general language for representing relational information among
objects. An effective way to model, reason about, and summarize networks, is to
discover sets of nodes with common connectivity patterns. Such sets are
commonly referred to as network communities. Research on network community
detection has predominantly focused on identifying communities of densely
connected nodes in undirected networks.
In this paper we develop a novel overlapping community detection method that
scales to networks of millions of nodes and edges and advances research along
two dimensions: the connectivity structure of communities, and the use of edge
directedness for community detection. First, we extend traditional definitions
of network communities by building on the observation that nodes can be densely
interlinked in two different ways: In cohesive communities nodes link to each
other, while in 2-mode communities nodes link in a bipartite fashion, where
links predominate between the two partitions rather than inside them. Our
method successfully detects both 2-mode as well as cohesive communities, that
may also overlap or be hierarchically nested. Second, while most existing
community detection methods treat directed edges as though they were
undirected, our method accounts for edge directions and is able to identify
novel and meaningful community structures in both directed and undirected
networks, using data from social, biological, and ecological domains.Comment: Published in the proceedings of WSDM '1
Modeling heterogeneity in random graphs through latent space models: a selective review
We present a selective review on probabilistic modeling of heterogeneity in
random graphs. We focus on latent space models and more particularly on
stochastic block models and their extensions that have undergone major
developments in the last five years
A Tensor Approach to Learning Mixed Membership Community Models
Community detection is the task of detecting hidden communities from observed
interactions. Guaranteed community detection has so far been mostly limited to
models with non-overlapping communities such as the stochastic block model. In
this paper, we remove this restriction, and provide guaranteed community
detection for a family of probabilistic network models with overlapping
communities, termed as the mixed membership Dirichlet model, first introduced
by Airoldi et al. This model allows for nodes to have fractional memberships in
multiple communities and assumes that the community memberships are drawn from
a Dirichlet distribution. Moreover, it contains the stochastic block model as a
special case. We propose a unified approach to learning these models via a
tensor spectral decomposition method. Our estimator is based on low-order
moment tensor of the observed network, consisting of 3-star counts. Our
learning method is fast and is based on simple linear algebraic operations,
e.g. singular value decomposition and tensor power iterations. We provide
guaranteed recovery of community memberships and model parameters and present a
careful finite sample analysis of our learning method. As an important special
case, our results match the best known scaling requirements for the
(homogeneous) stochastic block model
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