25 research outputs found
LASAGNE: Locality And Structure Aware Graph Node Embedding
In this work we propose Lasagne, a methodology to learn locality and
structure aware graph node embeddings in an unsupervised way. In particular, we
show that the performance of existing random-walk based approaches depends
strongly on the structural properties of the graph, e.g., the size of the
graph, whether the graph has a flat or upward-sloping Network Community Profile
(NCP), whether the graph is expander-like, whether the classes of interest are
more k-core-like or more peripheral, etc. For larger graphs with flat NCPs that
are strongly expander-like, existing methods lead to random walks that expand
rapidly, touching many dissimilar nodes, thereby leading to lower-quality
vector representations that are less useful for downstream tasks. Rather than
relying on global random walks or neighbors within fixed hop distances, Lasagne
exploits strongly local Approximate Personalized PageRank stationary
distributions to more precisely engineer local information into node
embeddings. This leads, in particular, to more meaningful and more useful
vector representations of nodes in poorly-structured graphs. We show that
Lasagne leads to significant improvement in downstream multi-label
classification for larger graphs with flat NCPs, that it is comparable for
smaller graphs with upward-sloping NCPs, and that is comparable to existing
methods for link prediction tasks
Efficient Estimation of Heat Kernel PageRank for Local Clustering
Given an undirected graph G and a seed node s, the local clustering problem
aims to identify a high-quality cluster containing s in time roughly
proportional to the size of the cluster, regardless of the size of G. This
problem finds numerous applications on large-scale graphs. Recently, heat
kernel PageRank (HKPR), which is a measure of the proximity of nodes in graphs,
is applied to this problem and found to be more efficient compared with prior
methods. However, existing solutions for computing HKPR either are
prohibitively expensive or provide unsatisfactory error approximation on HKPR
values, rendering them impractical especially on billion-edge graphs.
In this paper, we present TEA and TEA+, two novel local graph clustering
algorithms based on HKPR, to address the aforementioned limitations.
Specifically, these algorithms provide non-trivial theoretical guarantees in
relative error of HKPR values and the time complexity. The basic idea is to
utilize deterministic graph traversal to produce a rough estimation of exact
HKPR vector, and then exploit Monte-Carlo random walks to refine the results in
an optimized and non-trivial way. In particular, TEA+ offers practical
efficiency and effectiveness due to non-trivial optimizations. Extensive
experiments on real-world datasets demonstrate that TEA+ outperforms the
state-of-the-art algorithm by more than four times on most benchmark datasets
in terms of computational time when achieving the same clustering quality, and
in particular, is an order of magnitude faster on large graphs including the
widely studied Twitter and Friendster datasets.Comment: The technical report for the full research paper accepted in the
SIGMOD 201
Scalable and Effective Conductance-based Graph Clustering
Conductance-based graph clustering has been recognized as a fundamental
operator in numerous graph analysis applications. Despite the significant
success of conductance-based graph clustering, existing algorithms are either
hard to obtain satisfactory clustering qualities, or have high time and space
complexity to achieve provable clustering qualities. To overcome these
limitations, we devise a powerful \textit{peeling}-based graph clustering
framework \textit{PCon}. We show that many existing solutions can be reduced to
our framework. Namely, they first define a score function for each vertex, then
iteratively remove the vertex with the smallest score. Finally, they output the
result with the smallest conductance during the peeling process. Based on our
framework, we propose two novel algorithms \textit{PCon\_core} and
\emph{PCon\_de} with linear time and space complexity, which can efficiently
and effectively identify clusters from massive graphs with more than a few
billion edges. Surprisingly, we prove that \emph{PCon\_de} can identify
clusters with near-constant approximation ratio, resulting in an important
theoretical improvement over the well-known quadratic Cheeger bound. Empirical
results on real-life and synthetic datasets show that our algorithms can
achieve 542 times speedup with a high clustering accuracy, while using
1.47.8 times less memory than the baseline algorithms
GPOP: A cache- and work-efficient framework for Graph Processing Over Partitions
Past decade has seen the development of many shared-memory graph processing
frameworks, intended to reduce the effort of developing high performance
parallel applications. However many of these frameworks, based on
Vertex-centric or Edge-centric paradigms suffer from several issues, such as
poor cache utilization, irregular memory accesses, heavy use of synchronization
primitives and theoretical inefficiency, that deteriorate overall performance
and scalability.
Recently, we proposed a cache and memory efficient partition-centric paradigm
for computing PageRank. In this paper, we generalize this approach to develop a
novel Graph Processing Over Partitions (GPOP) framework that is
cache-efficient, scalable and work-efficient. GPOP induces locality in memory
accesses by increasing granularity of execution to vertex subsets called
'partitions', thereby dramatically improving the cache performance of a variety
of graph algorithms. It achieves high scalability by enabling completely lock
and atomic free computation. GPOP's built-in analytical performance model
enables it to use a hybrid of source and partitioncentric communication modes
in a way that ensures work-efficiency each iteration, while simultaneously
boosting high bandwidth sequential memory accesses.
We extensively evaluate the performance of GPOP for a variety of graph
algorithms, using several large datasets. We observe that GPOP incurs up to 9x,
6.8x and 5.5x less L2 cache misses compared to Ligra, GraphMat and Galois,
respectively. In terms of execution time, GPOP is upto 19x, 9.3x and 3.6x
faster than Ligra, GraphMat and Galois respectively.Comment: 23 pages, 7 figures, 4 table