15,164 research outputs found
Estimating and Sampling Graphs with Multidimensional Random Walks
Estimating characteristics of large graphs via sampling is a vital part of
the study of complex networks. Current sampling methods such as (independent)
random vertex and random walks are useful but have drawbacks. Random vertex
sampling may require too many resources (time, bandwidth, or money). Random
walks, which normally require fewer resources per sample, can suffer from large
estimation errors in the presence of disconnected or loosely connected graphs.
In this work we propose a new -dimensional random walk that uses
dependent random walkers. We show that the proposed sampling method, which we
call Frontier sampling, exhibits all of the nice sampling properties of a
regular random walk. At the same time, our simulations over large real world
graphs show that, in the presence of disconnected or loosely connected
components, Frontier sampling exhibits lower estimation errors than regular
random walks. We also show that Frontier sampling is more suitable than random
vertex sampling to sample the tail of the degree distribution of the graph
Learning Edge Representations via Low-Rank Asymmetric Projections
We propose a new method for embedding graphs while preserving directed edge
information. Learning such continuous-space vector representations (or
embeddings) of nodes in a graph is an important first step for using network
information (from social networks, user-item graphs, knowledge bases, etc.) in
many machine learning tasks.
Unlike previous work, we (1) explicitly model an edge as a function of node
embeddings, and we (2) propose a novel objective, the "graph likelihood", which
contrasts information from sampled random walks with non-existent edges.
Individually, both of these contributions improve the learned representations,
especially when there are memory constraints on the total size of the
embeddings. When combined, our contributions enable us to significantly improve
the state-of-the-art by learning more concise representations that better
preserve the graph structure.
We evaluate our method on a variety of link-prediction task including social
networks, collaboration networks, and protein interactions, showing that our
proposed method learn representations with error reductions of up to 76% and
55%, on directed and undirected graphs. In addition, we show that the
representations learned by our method are quite space efficient, producing
embeddings which have higher structure-preserving accuracy but are 10 times
smaller
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