32,102 research outputs found
Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks
Graph convolutional network (GCN) has been successfully applied to many
graph-based applications; however, training a large-scale GCN remains
challenging. Current SGD-based algorithms suffer from either a high
computational cost that exponentially grows with number of GCN layers, or a
large space requirement for keeping the entire graph and the embedding of each
node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm
that is suitable for SGD-based training by exploiting the graph clustering
structure. Cluster-GCN works as the following: at each step, it samples a block
of nodes that associate with a dense subgraph identified by a graph clustering
algorithm, and restricts the neighborhood search within this subgraph. This
simple but effective strategy leads to significantly improved memory and
computational efficiency while being able to achieve comparable test accuracy
with previous algorithms. To test the scalability of our algorithm, we create a
new Amazon2M data with 2 million nodes and 61 million edges which is more than
5 times larger than the previous largest publicly available dataset (Reddit).
For training a 3-layer GCN on this data, Cluster-GCN is faster than the
previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much
less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this
data, our algorithm can finish in around 36 minutes while all the existing GCN
training algorithms fail to train due to the out-of-memory issue. Furthermore,
Cluster-GCN allows us to train much deeper GCN without much time and memory
overhead, which leads to improved prediction accuracy---using a 5-layer
Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI
dataset, while the previous best result was 98.71 by [16]. Our codes are
publicly available at
https://github.com/google-research/google-research/tree/master/cluster_gcn.Comment: In Proceedings of the 25th ACM SIGKDD International Conference on
Knowledge Discovery & Data Mining (KDD'19
Fast Deterministic Selection
The Median of Medians (also known as BFPRT) algorithm, although a landmark
theoretical achievement, is seldom used in practice because it and its variants
are slower than simple approaches based on sampling. The main contribution of
this paper is a fast linear-time deterministic selection algorithm
QuickselectAdaptive based on a refined definition of MedianOfMedians. The
algorithm's performance brings deterministic selection---along with its
desirable properties of reproducible runs, predictable run times, and immunity
to pathological inputs---in the range of practicality. We demonstrate results
on independent and identically distributed random inputs and on
normally-distributed inputs. Measurements show that QuickselectAdaptive is
faster than state-of-the-art baselines.Comment: Pre-publication draf
Comparing Community Structure to Characteristics in Online Collegiate Social Networks
We study the structure of social networks of students by examining the graphs
of Facebook "friendships" at five American universities at a single point in
time. We investigate each single-institution network's community structure and
employ graphical and quantitative tools, including standardized pair-counting
methods, to measure the correlations between the network communities and a set
of self-identified user characteristics (residence, class year, major, and high
school). We review the basic properties and statistics of the pair-counting
indices employed and recall, in simplified notation, a useful analytical
formula for the z-score of the Rand coefficient. Our study illustrates how to
examine different instances of social networks constructed in similar
environments, emphasizes the array of social forces that combine to form
"communities," and leads to comparative observations about online social lives
that can be used to infer comparisons about offline social structures. In our
illustration of this methodology, we calculate the relative contributions of
different characteristics to the community structure of individual universities
and subsequently compare these relative contributions at different
universities, measuring for example the importance of common high school
affiliation to large state universities and the varying degrees of influence
common major can have on the social structure at different universities. The
heterogeneity of communities that we observe indicates that these networks
typically have multiple organizing factors rather than a single dominant one.Comment: Version 3 (17 pages, 5 multi-part figures), accepted in SIAM Revie
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