945 research outputs found
Graph matching with a dual-step EM algorithm
This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. In this way, the two processes bootstrap one another. This provides a means of rejecting structural outliers. We evaluate the technique on two real-world problems. The first involves the matching of different perspective views of 3.5-inch floppy discs. The second example is furnished by the matching of a digital map against aerial images that are subject to severe barrel distortion due to a line-scan sampling process. We complement these experiments with a sensitivity study based on synthetic data
Deep Markov Random Field for Image Modeling
Markov Random Fields (MRFs), a formulation widely used in generative image
modeling, have long been plagued by the lack of expressive power. This issue is
primarily due to the fact that conventional MRFs formulations tend to use
simplistic factors to capture local patterns. In this paper, we move beyond
such limitations, and propose a novel MRF model that uses fully-connected
neurons to express the complex interactions among pixels. Through theoretical
analysis, we reveal an inherent connection between this model and recurrent
neural networks, and thereon derive an approximated feed-forward network that
couples multiple RNNs along opposite directions. This formulation combines the
expressive power of deep neural networks and the cyclic dependency structure of
MRF in a unified model, bringing the modeling capability to a new level. The
feed-forward approximation also allows it to be efficiently learned from data.
Experimental results on a variety of low-level vision tasks show notable
improvement over state-of-the-arts.Comment: Accepted at ECCV 201
Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks
Finding actions that satisfy the constraints imposed by both external inputs
and internal representations is central to decision making. We demonstrate that
some important classes of constraint satisfaction problems (CSPs) can be solved
by networks composed of homogeneous cooperative-competitive modules that have
connectivity similar to motifs observed in the superficial layers of neocortex.
The winner-take-all modules are sparsely coupled by programming neurons that
embed the constraints onto the otherwise homogeneous modular computational
substrate. We show rules that embed any instance of the CSPs planar four-color
graph coloring, maximum independent set, and Sudoku on this substrate, and
provide mathematical proofs that guarantee these graph coloring problems will
convergence to a solution. The network is composed of non-saturating linear
threshold neurons. Their lack of right saturation allows the overall network to
explore the problem space driven through the unstable dynamics generated by
recurrent excitation. The direction of exploration is steered by the constraint
neurons. While many problems can be solved using only linear inhibitory
constraints, network performance on hard problems benefits significantly when
these negative constraints are implemented by non-linear multiplicative
inhibition. Overall, our results demonstrate the importance of instability
rather than stability in network computation, and also offer insight into the
computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018
Inference via low-dimensional couplings
We investigate the low-dimensional structure of deterministic transformations
between random variables, i.e., transport maps between probability measures. In
the context of statistics and machine learning, these transformations can be
used to couple a tractable "reference" measure (e.g., a standard Gaussian) with
a target measure of interest. Direct simulation from the desired measure can
then be achieved by pushing forward reference samples through the map. Yet
characterizing such a map---e.g., representing and evaluating it---grows
challenging in high dimensions. The central contribution of this paper is to
establish a link between the Markov properties of the target measure and the
existence of low-dimensional couplings, induced by transport maps that are
sparse and/or decomposable. Our analysis not only facilitates the construction
of transformations in high-dimensional settings, but also suggests new
inference methodologies for continuous non-Gaussian graphical models. For
instance, in the context of nonlinear state-space models, we describe new
variational algorithms for filtering, smoothing, and sequential parameter
inference. These algorithms can be understood as the natural
generalization---to the non-Gaussian case---of the square-root
Rauch-Tung-Striebel Gaussian smoother.Comment: 78 pages, 25 figure
Detecting partial synchrony in a complex oscillatory network using pseudo-vortices
Partial synchronization is characteristic phase dynamics of coupled
oscillators on various natural and artificial networks, which can remain
undetected due to the complexity of the systems. With an analogy between
pairwise asynchrony of oscillators and topological defects, i.e., vortices, in
the two-dimensional XY spin model, we propose a robust and data-driven method
to identify the partial synchronization on complex networks. The proposed
method is based on an integer matrix whose element is pseudo-vorticity that
discretely quantifies asynchronous phase dynamics in every two oscillators,
which results in graphical and entropic representations of partial synchrony.
As a first trial, we apply our method to 200 FitzHugh-Nagumo neurons on a
complex small-world network. Partially synchronized chimera states are revealed
by discriminating synchronized states even with phase lags. Such phase lags
also appear in partial synchronization in chimera states. Our topological,
graphical, and entropic method is implemented solely with measurable phase
dynamics data, which will lead to a straightforward application to general
oscillatory networks including neural networks in the brain.Comment: 9 pages, 5 figure
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
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