11,626 research outputs found
Deterministic Annealing and Nonlinear Assignment
For combinatorial optimization problems that can be formulated as Ising or
Potts spin systems, the Mean Field (MF) approximation yields a versatile and
simple ANN heuristic, Deterministic Annealing. For assignment problems the
situation is more complex -- the natural analog of the MF approximation lacks
the simplicity present in the Potts and Ising cases. In this article the
difficulties associated with this issue are investigated, and the options for
solving them discussed. Improvements to existing Potts-based MF-inspired
heuristics are suggested, and the possibilities for defining a proper
variational approach are scrutinized.Comment: 15 pages, 3 figure
Discrete-Continuous ADMM for Transductive Inference in Higher-Order MRFs
This paper introduces a novel algorithm for transductive inference in
higher-order MRFs, where the unary energies are parameterized by a variable
classifier. The considered task is posed as a joint optimization problem in the
continuous classifier parameters and the discrete label variables. In contrast
to prior approaches such as convex relaxations, we propose an advantageous
decoupling of the objective function into discrete and continuous subproblems
and a novel, efficient optimization method related to ADMM. This approach
preserves integrality of the discrete label variables and guarantees global
convergence to a critical point. We demonstrate the advantages of our approach
in several experiments including video object segmentation on the DAVIS data
set and interactive image segmentation
Facility layout problem: Bibliometric and benchmarking analysis
Facility layout problem is related to the location of departments in a facility area, with the aim of determining the most effective configuration. Researches based on different approaches have been published in the last six decades and, to prove the effectiveness of the results obtained, several instances have been developed. This paper presents a general overview on the extant literature on facility layout problems in order to identify the main research trends and propose future research questions. Firstly, in order to give the reader an overview of the literature, a bibliometric analysis is presented. Then, a clusterization of the papers referred to the main instances reported in literature was carried out in order to create a database that can be a useful tool in the benchmarking procedure for researchers that would approach this kind of problems
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Random Neural Networks and Optimisation
In this thesis we introduce new models and learning algorithms for the Random
Neural Network (RNN), and we develop RNN-based and other approaches for the
solution of emergency management optimisation problems.
With respect to RNN developments, two novel supervised learning algorithms are
proposed. The first, is a gradient descent algorithm for an RNN extension model
that we have introduced, the RNN with synchronised interactions (RNNSI), which
was inspired from the synchronised firing activity observed in brain neural circuits.
The second algorithm is based on modelling the signal-flow equations in RNN as a
nonnegative least squares (NNLS) problem. NNLS is solved using a limited-memory
quasi-Newton algorithm specifically designed for the RNN case.
Regarding the investigation of emergency management optimisation problems,
we examine combinatorial assignment problems that require fast, distributed and
close to optimal solution, under information uncertainty. We consider three different
problems with the above characteristics associated with the assignment of
emergency units to incidents with injured civilians (AEUI), the assignment of assets
to tasks under execution uncertainty (ATAU), and the deployment of a robotic
network to establish communication with trapped civilians (DRNCTC).
AEUI is solved by training an RNN tool with instances of the optimisation problem
and then using the trained RNN for decision making; training is achieved using
the developed learning algorithms. For the solution of ATAU problem, we introduce
two different approaches. The first is based on mapping parameters of the
optimisation problem to RNN parameters, and the second on solving a sequence of
minimum cost flow problems on appropriately constructed networks with estimated
arc costs. For the exact solution of DRNCTC problem, we develop a mixed-integer
linear programming formulation, which is based on network flows. Finally, we design
and implement distributed heuristic algorithms for the deployment of robots
when the civilian locations are known or uncertain
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