983 research outputs found
Quadratically-Regularized Optimal Transport on Graphs
Optimal transportation provides a means of lifting distances between points
on a geometric domain to distances between signals over the domain, expressed
as probability distributions. On a graph, transportation problems can be used
to express challenging tasks involving matching supply to demand with minimal
shipment expense; in discrete language, these become minimum-cost network flow
problems. Regularization typically is needed to ensure uniqueness for the
linear ground distance case and to improve optimization convergence;
state-of-the-art techniques employ entropic regularization on the
transportation matrix. In this paper, we explore a quadratic alternative to
entropic regularization for transport over a graph. We theoretically analyze
the behavior of quadratically-regularized graph transport, characterizing how
regularization affects the structure of flows in the regime of small but
nonzero regularization. We further exploit elegant second-order structure in
the dual of this problem to derive an easily-implemented Newton-type
optimization algorithm.Comment: 27 page
Tripartite Graph Clustering for Dynamic Sentiment Analysis on Social Media
The growing popularity of social media (e.g, Twitter) allows users to easily
share information with each other and influence others by expressing their own
sentiments on various subjects. In this work, we propose an unsupervised
\emph{tri-clustering} framework, which analyzes both user-level and tweet-level
sentiments through co-clustering of a tripartite graph. A compelling feature of
the proposed framework is that the quality of sentiment clustering of tweets,
users, and features can be mutually improved by joint clustering. We further
investigate the evolution of user-level sentiments and latent feature vectors
in an online framework and devise an efficient online algorithm to sequentially
update the clustering of tweets, users and features with newly arrived data.
The online framework not only provides better quality of both dynamic
user-level and tweet-level sentiment analysis, but also improves the
computational and storage efficiency. We verified the effectiveness and
efficiency of the proposed approaches on the November 2012 California ballot
Twitter data.Comment: A short version is in Proceeding of the 2014 ACM SIGMOD International
Conference on Management of dat
Compressive PCA for Low-Rank Matrices on Graphs
We introduce a novel framework for an approxi- mate recovery of data matrices
which are low-rank on graphs, from sampled measurements. The rows and columns
of such matrices belong to the span of the first few eigenvectors of the graphs
constructed between their rows and columns. We leverage this property to
recover the non-linear low-rank structures efficiently from sampled data
measurements, with a low cost (linear in n). First, a Resrtricted Isometry
Property (RIP) condition is introduced for efficient uniform sampling of the
rows and columns of such matrices based on the cumulative coherence of graph
eigenvectors. Secondly, a state-of-the-art fast low-rank recovery method is
suggested for the sampled data. Finally, several efficient, parallel and
parameter-free decoders are presented along with their theoretical analysis for
decoding the low-rank and cluster indicators for the full data matrix. Thus, we
overcome the computational limitations of the standard linear low-rank recovery
methods for big datasets. Our method can also be seen as a major step towards
efficient recovery of non- linear low-rank structures. For a matrix of size n X
p, on a single core machine, our method gains a speed up of over Robust
Principal Component Analysis (RPCA), where k << p is the subspace dimension.
Numerically, we can recover a low-rank matrix of size 10304 X 1000, 100 times
faster than Robust PCA
Graph Regularized Nonnegative Latent Factor Analysis Model for Temporal Link Prediction in Cryptocurrency Transaction Networks
With the development of blockchain technology, the cryptocurrency based on
blockchain technology is becoming more and more popular. This gave birth to a
huge cryptocurrency transaction network has received widespread attention. Link
prediction learning structure of network is helpful to understand the mechanism
of network, so it is also widely studied in cryptocurrency network. However,
the dynamics of cryptocurrency transaction networks have been neglected in the
past researches. We use graph regularized method to link past transaction
records with future transactions. Based on this, we propose a single latent
factor-dependent, non-negative, multiplicative and graph
regularized-incorporated update (SLF-NMGRU) algorithm and further propose graph
regularized nonnegative latent factor analysis (GrNLFA) model. Finally,
experiments on a real cryptocurrency transaction network show that the proposed
method improves both the accuracy and the computational efficienc
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