8,705 research outputs found
Graph Sample and Hold: A Framework for Big-Graph Analytics
Sampling is a standard approach in big-graph analytics; the goal is to
efficiently estimate the graph properties by consulting a sample of the whole
population. A perfect sample is assumed to mirror every property of the whole
population. Unfortunately, such a perfect sample is hard to collect in complex
populations such as graphs (e.g. web graphs, social networks etc), where an
underlying network connects the units of the population. Therefore, a good
sample will be representative in the sense that graph properties of interest
can be estimated with a known degree of accuracy. While previous work focused
particularly on sampling schemes used to estimate certain graph properties
(e.g. triangle count), much less is known for the case when we need to estimate
various graph properties with the same sampling scheme. In this paper, we
propose a generic stream sampling framework for big-graph analytics, called
Graph Sample and Hold (gSH). To begin, the proposed framework samples from
massive graphs sequentially in a single pass, one edge at a time, while
maintaining a small state. We then show how to produce unbiased estimators for
various graph properties from the sample. Given that the graph analysis
algorithms will run on a sample instead of the whole population, the runtime
complexity of these algorithm is kept under control. Moreover, given that the
estimators of graph properties are unbiased, the approximation error is kept
under control. Finally, we show the performance of the proposed framework (gSH)
on various types of graphs, such as social graphs, among others
Graph Variogram: A novel tool to measure spatial stationarity
Irregularly sampling a spatially stationary random field does not yield a
graph stationary signal in general. Based on this observation, we build a
definition of graph stationarity based on intrinsic stationarity, a less
restrictive definition of classical stationarity. We introduce the concept of
graph variogram, a novel tool for measuring spatial intrinsic stationarity at
local and global scales for irregularly sampled signals by selecting subgraphs
of local neighborhoods. Graph variograms are extensions of variograms used for
signals defined on continuous Euclidean space. Our experiments with
intrinsically stationary signals sampled on a graph, demonstrate that graph
variograms yield estimates with small bias of true theoretical models, while
being robust to sampling variation of the space.Comment: Submitted to IEEE Global Conference on Signal and Information
Processing 2018 (IEEE GlobalSIP 2018), Nov 2018, Anaheim, CA, United States.
(https://2018.ieeeglobalsip.org/
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