55,727 research outputs found
Node Embedding over Temporal Graphs
In this work, we present a method for node embedding in temporal graphs. We
propose an algorithm that learns the evolution of a temporal graph's nodes and
edges over time and incorporates this dynamics in a temporal node embedding
framework for different graph prediction tasks. We present a joint loss
function that creates a temporal embedding of a node by learning to combine its
historical temporal embeddings, such that it optimizes per given task (e.g.,
link prediction). The algorithm is initialized using static node embeddings,
which are then aligned over the representations of a node at different time
points, and eventually adapted for the given task in a joint optimization. We
evaluate the effectiveness of our approach over a variety of temporal graphs
for the two fundamental tasks of temporal link prediction and multi-label node
classification, comparing to competitive baselines and algorithmic
alternatives. Our algorithm shows performance improvements across many of the
datasets and baselines and is found particularly effective for graphs that are
less cohesive, with a lower clustering coefficient
Representation Learning for Attributed Multiplex Heterogeneous Network
Network embedding (or graph embedding) has been widely used in many
real-world applications. However, existing methods mainly focus on networks
with single-typed nodes/edges and cannot scale well to handle large networks.
Many real-world networks consist of billions of nodes and edges of multiple
types, and each node is associated with different attributes. In this paper, we
formalize the problem of embedding learning for the Attributed Multiplex
Heterogeneous Network and propose a unified framework to address this problem.
The framework supports both transductive and inductive learning. We also give
the theoretical analysis of the proposed framework, showing its connection with
previous works and proving its better expressiveness. We conduct systematical
evaluations for the proposed framework on four different genres of challenging
datasets: Amazon, YouTube, Twitter, and Alibaba. Experimental results
demonstrate that with the learned embeddings from the proposed framework, we
can achieve statistically significant improvements (e.g., 5.99-28.23% lift by
F1 scores; p<<0.01, t-test) over previous state-of-the-art methods for link
prediction. The framework has also been successfully deployed on the
recommendation system of a worldwide leading e-commerce company, Alibaba Group.
Results of the offline A/B tests on product recommendation further confirm the
effectiveness and efficiency of the framework in practice.Comment: Accepted to KDD 2019. Website: https://sites.google.com/view/gatn
Obstructions to embeddability into hyperquadrics and explicit examples
We give series of explicit examples of Levi-nondegenerate real-analytic
hypersurfaces in complex spaces that are not transversally holomorphically
embeddable into hyperquadrics of any dimension. For this, we construct
invariants attached to a given hypersurface that serve as obstructions to
embeddability. We further study the embeddability problem for real-analytic
submanifolds of higher codimension and answer a question by Forstneri\v{c}.Comment: Revised version, appendix and references adde
Clustering and Community Detection in Directed Networks: A Survey
Networks (or graphs) appear as dominant structures in diverse domains,
including sociology, biology, neuroscience and computer science. In most of the
aforementioned cases graphs are directed - in the sense that there is
directionality on the edges, making the semantics of the edges non symmetric.
An interesting feature that real networks present is the clustering or
community structure property, under which the graph topology is organized into
modules commonly called communities or clusters. The essence here is that nodes
of the same community are highly similar while on the contrary, nodes across
communities present low similarity. Revealing the underlying community
structure of directed complex networks has become a crucial and
interdisciplinary topic with a plethora of applications. Therefore, naturally
there is a recent wealth of research production in the area of mining directed
graphs - with clustering being the primary method and tool for community
detection and evaluation. The goal of this paper is to offer an in-depth review
of the methods presented so far for clustering directed networks along with the
relevant necessary methodological background and also related applications. The
survey commences by offering a concise review of the fundamental concepts and
methodological base on which graph clustering algorithms capitalize on. Then we
present the relevant work along two orthogonal classifications. The first one
is mostly concerned with the methodological principles of the clustering
algorithms, while the second one approaches the methods from the viewpoint
regarding the properties of a good cluster in a directed network. Further, we
present methods and metrics for evaluating graph clustering results,
demonstrate interesting application domains and provide promising future
research directions.Comment: 86 pages, 17 figures. Physics Reports Journal (To Appear
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