12,290 research outputs found
Affine buildings for dihedral groups
We construct rank 2 thick nondiscrete affine buildings associated with an
arbitrary finite dihedral group.Comment: 40 pages, 10 figure
Efficient Computation of Multiple Density-Based Clustering Hierarchies
HDBSCAN*, a state-of-the-art density-based hierarchical clustering method,
produces a hierarchical organization of clusters in a dataset w.r.t. a
parameter mpts. While the performance of HDBSCAN* is robust w.r.t. mpts in the
sense that a small change in mpts typically leads to only a small or no change
in the clustering structure, choosing a "good" mpts value can be challenging:
depending on the data distribution, a high or low value for mpts may be more
appropriate, and certain data clusters may reveal themselves at different
values of mpts. To explore results for a range of mpts values, however, one has
to run HDBSCAN* for each value in the range independently, which is
computationally inefficient. In this paper, we propose an efficient approach to
compute all HDBSCAN* hierarchies for a range of mpts values by replacing the
graph used by HDBSCAN* with a much smaller graph that is guaranteed to contain
the required information. An extensive experimental evaluation shows that with
our approach one can obtain over one hundred hierarchies for the computational
cost equivalent to running HDBSCAN* about 2 times.Comment: A short version of this paper appears at IEEE ICDM 2017. Corrected
typos. Revised abstrac
Measuring relative opinion from location-based social media: A case study of the 2016 U.S. presidential election
Social media has become an emerging alternative to opinion polls for public
opinion collection, while it is still posing many challenges as a passive data
source, such as structurelessness, quantifiability, and representativeness.
Social media data with geotags provide new opportunities to unveil the
geographic locations of users expressing their opinions. This paper aims to
answer two questions: 1) whether quantifiable measurement of public opinion can
be obtained from social media and 2) whether it can produce better or
complementary measures compared to opinion polls. This research proposes a
novel approach to measure the relative opinion of Twitter users towards public
issues in order to accommodate more complex opinion structures and take
advantage of the geography pertaining to the public issues. To ensure that this
new measure is technically feasible, a modeling framework is developed
including building a training dataset by adopting a state-of-the-art approach
and devising a new deep learning method called Opinion-Oriented Word Embedding.
With a case study of the tweets selected for the 2016 U.S. presidential
election, we demonstrate the predictive superiority of our relative opinion
approach and we show how it can aid visual analytics and support opinion
predictions. Although the relative opinion measure is proved to be more robust
compared to polling, our study also suggests that the former can advantageously
complement the later in opinion prediction
Geometric deep learning: going beyond Euclidean data
Many scientific fields study data with an underlying structure that is a
non-Euclidean space. Some examples include social networks in computational
social sciences, sensor networks in communications, functional networks in
brain imaging, regulatory networks in genetics, and meshed surfaces in computer
graphics. In many applications, such geometric data are large and complex (in
the case of social networks, on the scale of billions), and are natural targets
for machine learning techniques. In particular, we would like to use deep
neural networks, which have recently proven to be powerful tools for a broad
range of problems from computer vision, natural language processing, and audio
analysis. However, these tools have been most successful on data with an
underlying Euclidean or grid-like structure, and in cases where the invariances
of these structures are built into networks used to model them. Geometric deep
learning is an umbrella term for emerging techniques attempting to generalize
(structured) deep neural models to non-Euclidean domains such as graphs and
manifolds. The purpose of this paper is to overview different examples of
geometric deep learning problems and present available solutions, key
difficulties, applications, and future research directions in this nascent
field
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