153 research outputs found
Scaling Up Network Analysis and Mining: Statistical Sampling, Estimation, and Pattern Discovery
Network analysis and graph mining play a prominent role in providing insights and studying phenomena across various domains, including social, behavioral, biological, transportation, communication, and financial domains. Across all these domains, networks arise as a natural and rich representation for data. Studying these real-world networks is crucial for solving numerous problems that lead to high-impact applications. For example, identifying the behavior and interests of users in online social networks (e.g., viral marketing), monitoring and detecting virus outbreaks in human contact networks, predicting protein functions in biological networks, and detecting anomalous behavior in computer networks. A key characteristic of these networks is that their complex structure is massive and continuously evolving over time, which makes it challenging and computationally intensive to analyze, query, and model these networks in their entirety. In this dissertation, we propose sampling as well as fast, efficient, and scalable methods for network analysis and mining in both static and streaming graphs
Network Sampling: From Static to Streaming Graphs
Network sampling is integral to the analysis of social, information, and
biological networks. Since many real-world networks are massive in size,
continuously evolving, and/or distributed in nature, the network structure is
often sampled in order to facilitate study. For these reasons, a more thorough
and complete understanding of network sampling is critical to support the field
of network science. In this paper, we outline a framework for the general
problem of network sampling, by highlighting the different objectives,
population and units of interest, and classes of network sampling methods. In
addition, we propose a spectrum of computational models for network sampling
methods, ranging from the traditionally studied model based on the assumption
of a static domain to a more challenging model that is appropriate for
streaming domains. We design a family of sampling methods based on the concept
of graph induction that generalize across the full spectrum of computational
models (from static to streaming) while efficiently preserving many of the
topological properties of the input graphs. Furthermore, we demonstrate how
traditional static sampling algorithms can be modified for graph streams for
each of the three main classes of sampling methods: node, edge, and
topology-based sampling. Our experimental results indicate that our proposed
family of sampling methods more accurately preserves the underlying properties
of the graph for both static and streaming graphs. Finally, we study the impact
of network sampling algorithms on the parameter estimation and performance
evaluation of relational classification algorithms
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
Stream Aggregation Through Order Sampling
This is paper introduces a new single-pass reservoir weighted-sampling stream
aggregation algorithm, Priority-Based Aggregation (PBA). While order sampling
is a powerful and e cient method for weighted sampling from a stream of
uniquely keyed items, there is no current algorithm that realizes the benefits
of order sampling in the context of stream aggregation over non-unique keys. A
naive approach to order sample regardless of key then aggregate the results is
hopelessly inefficient. In distinction, our proposed algorithm uses a single
persistent random variable across the lifetime of each key in the cache, and
maintains unbiased estimates of the key aggregates that can be queried at any
point in the stream. The basic approach can be supplemented with a Sample and
Hold pre-sampling stage with a sampling rate adaptation controlled by PBA. This
approach represents a considerable reduction in computational complexity
compared with the state of the art in adapting Sample and Hold to operate with
a fixed cache size. Concerning statistical properties, we prove that PBA
provides unbiased estimates of the true aggregates. We analyze the
computational complexity of PBA and its variants, and provide a detailed
evaluation of its accuracy on synthetic and trace data. Weighted relative error
is reduced by 40% to 65% at sampling rates of 5% to 17%, relative to Adaptive
Sample and Hold; there is also substantial improvement for rank queriesComment: 10 page
- …