5,401 research outputs found
DeepWalk: Online Learning of Social Representations
We present DeepWalk, a novel approach for learning latent representations of
vertices in a network. These latent representations encode social relations in
a continuous vector space, which is easily exploited by statistical models.
DeepWalk generalizes recent advancements in language modeling and unsupervised
feature learning (or deep learning) from sequences of words to graphs. DeepWalk
uses local information obtained from truncated random walks to learn latent
representations by treating walks as the equivalent of sentences. We
demonstrate DeepWalk's latent representations on several multi-label network
classification tasks for social networks such as BlogCatalog, Flickr, and
YouTube. Our results show that DeepWalk outperforms challenging baselines which
are allowed a global view of the network, especially in the presence of missing
information. DeepWalk's representations can provide scores up to 10%
higher than competing methods when labeled data is sparse. In some experiments,
DeepWalk's representations are able to outperform all baseline methods while
using 60% less training data. DeepWalk is also scalable. It is an online
learning algorithm which builds useful incremental results, and is trivially
parallelizable. These qualities make it suitable for a broad class of real
world applications such as network classification, and anomaly detection.Comment: 10 pages, 5 figures, 4 table
Community detection and stochastic block models: recent developments
The stochastic block model (SBM) is a random graph model with planted
clusters. It is widely employed as a canonical model to study clustering and
community detection, and provides generally a fertile ground to study the
statistical and computational tradeoffs that arise in network and data
sciences.
This note surveys the recent developments that establish the fundamental
limits for community detection in the SBM, both with respect to
information-theoretic and computational thresholds, and for various recovery
requirements such as exact, partial and weak recovery (a.k.a., detection). The
main results discussed are the phase transitions for exact recovery at the
Chernoff-Hellinger threshold, the phase transition for weak recovery at the
Kesten-Stigum threshold, the optimal distortion-SNR tradeoff for partial
recovery, the learning of the SBM parameters and the gap between
information-theoretic and computational thresholds.
The note also covers some of the algorithms developed in the quest of
achieving the limits, in particular two-round algorithms via graph-splitting,
semi-definite programming, linearized belief propagation, classical and
nonbacktracking spectral methods. A few open problems are also discussed
Quasirandom Load Balancing
We propose a simple distributed algorithm for balancing indivisible tokens on
graphs. The algorithm is completely deterministic, though it tries to imitate
(and enhance) a random algorithm by keeping the accumulated rounding errors as
small as possible.
Our new algorithm surprisingly closely approximates the idealized process
(where the tokens are divisible) on important network topologies. On
d-dimensional torus graphs with n nodes it deviates from the idealized process
only by an additive constant. In contrast to that, the randomized rounding
approach of Friedrich and Sauerwald (2009) can deviate up to Omega(polylog(n))
and the deterministic algorithm of Rabani, Sinclair and Wanka (1998) has a
deviation of Omega(n^{1/d}). This makes our quasirandom algorithm the first
known algorithm for this setting which is optimal both in time and achieved
smoothness. We further show that also on the hypercube our algorithm has a
smaller deviation from the idealized process than the previous algorithms.Comment: 25 page
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