10,399 research outputs found
Generative Adversarial Networks (GANs): Challenges, Solutions, and Future Directions
Generative Adversarial Networks (GANs) is a novel class of deep generative
models which has recently gained significant attention. GANs learns complex and
high-dimensional distributions implicitly over images, audio, and data.
However, there exists major challenges in training of GANs, i.e., mode
collapse, non-convergence and instability, due to inappropriate design of
network architecture, use of objective function and selection of optimization
algorithm. Recently, to address these challenges, several solutions for better
design and optimization of GANs have been investigated based on techniques of
re-engineered network architectures, new objective functions and alternative
optimization algorithms. To the best of our knowledge, there is no existing
survey that has particularly focused on broad and systematic developments of
these solutions. In this study, we perform a comprehensive survey of the
advancements in GANs design and optimization solutions proposed to handle GANs
challenges. We first identify key research issues within each design and
optimization technique and then propose a new taxonomy to structure solutions
by key research issues. In accordance with the taxonomy, we provide a detailed
discussion on different GANs variants proposed within each solution and their
relationships. Finally, based on the insights gained, we present the promising
research directions in this rapidly growing field.Comment: 42 pages, Figure 13, Table
Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond
There is a hidden intrigue in the title. CT is one of the most abstract
mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a
recent trend in software development, industrially supported by standards,
tools, and the status of a new "silver bullet". Surprisingly, categorical
patterns turn out to be directly applicable to mathematical modeling of
structures appearing in everyday MDE practice. Model merging, transformation,
synchronization, and other important model management scenarios can be seen as
executions of categorical specifications.
Moreover, the paper aims to elucidate a claim that relationships between CT
and MDE are more complex and richer than is normally assumed for "applied
mathematics". CT provides a toolbox of design patterns and structural
principles of real practical value for MDE. We will present examples of how an
elementary categorical arrangement of a model management scenario reveals
deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430
Axiomatic Construction of Hierarchical Clustering in Asymmetric Networks
This paper considers networks where relationships between nodes are
represented by directed dissimilarities. The goal is to study methods for the
determination of hierarchical clusters, i.e., a family of nested partitions
indexed by a connectivity parameter, induced by the given dissimilarity
structures. Our construction of hierarchical clustering methods is based on
defining admissible methods to be those methods that abide by the axioms of
value - nodes in a network with two nodes are clustered together at the maximum
of the two dissimilarities between them - and transformation - when
dissimilarities are reduced, the network may become more clustered but not
less. Several admissible methods are constructed and two particular methods,
termed reciprocal and nonreciprocal clustering, are shown to provide upper and
lower bounds in the space of admissible methods. Alternative clustering
methodologies and axioms are further considered. Allowing the outcome of
hierarchical clustering to be asymmetric, so that it matches the asymmetry of
the original data, leads to the inception of quasi-clustering methods. The
existence of a unique quasi-clustering method is shown. Allowing clustering in
a two-node network to proceed at the minimum of the two dissimilarities
generates an alternative axiomatic construction. There is a unique clustering
method in this case too. The paper also develops algorithms for the computation
of hierarchical clusters using matrix powers on a min-max dioid algebra and
studies the stability of the methods proposed. We proved that most of the
methods introduced in this paper are such that similar networks yield similar
hierarchical clustering results. Algorithms are exemplified through their
application to networks describing internal migration within states of the
United States (U.S.) and the interrelation between sectors of the U.S. economy.Comment: This is a largely extended version of the previous conference
submission under the same title. The current version contains the material in
the previous version (published in ICASSP 2013) as well as material presented
at the Asilomar Conference on Signal, Systems, and Computers 2013, GlobalSIP
2013, and ICML 2014. Also, unpublished material is included in the current
versio
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