Tree-based iterated local search for Markov random fields with applications in image analysis

The maximum a posteriori assignment for general structure Markov random fields is computationally intractable. In this paper, we exploit tree-based methods to efficiently address this problem. Our novel method, named Tree-based Iterated Local Search (T-ILS), takes advantage of the tractability of tree-structures embedded within MRFs to derive strong local search in an ILS framework. The method efficiently explores exponentially large neighborhoods using a limited memory without any requirement on the cost functions. We evaluate the T-ILS on a simulated Ising model and two real-world vision problems: stereo matching and image denoising. Experimental results demonstrate that our methods are competitive against state-of-the-art rivals with significant computational gain.

Ordinal random fields for recommender systems

Recommender Systems heavily rely on numerical preferences, whereas the importance of ordinal preferences has only been recognised in recent works of Ordinal Matrix Factorisation (OMF). Although the OMF can effectively exploit ordinal properties, it captures only the higher-order interactions among users and items, without considering the localised interactions properly. This paper employs Markov Random Fields (MRF) to investigate the localised interactions, and proposes a unified model called Ordinal Random Fields (ORF) to take advantages of both the representational power of the MRF and the ease of modelling ordinal preferences by the OMF. Experimental result on public datasets demonstrates that the proposed ORF model can capture both types of interactions, resulting in improved recommendation accuracy.

Preference relation-based markov random fields

A preference relation-based Top-N recommendation approach, PrefMRF, is proposed to capture both the second-order and the higher-order interactions among users and items. Traditionally Top-N recommendation was achieved by predicting the item ratings fi rst, and then inferring the item rankings, based on the assumption of availability of explicit feed-backs such as ratings, and the assumption that optimizing the ratings is equivalent to optimizing the item rankings. Nevertheless, both assumptions are not always true in real world applications. The proposed PrefMRF approach drops these assumptions by explicitly exploiting the preference relations, a more practical user feedback. Comparing to related work, the proposed PrefMRF approach has the unique property of modeling both the second-order and the higher-order interactions among users and items. To the best of our knowledge, this is the first time both types of interactions have been captured in preference relation-based method. Experiment results on public datasets demonstrate that both types of interactions have been properly captured, and signifi cantly improved Top-N recommendation performance has been achieved.

OPF-MRF: Optimum-path forest and Markov random fields for contextual-based image classification

Some machine learning methods do not exploit contextual information in the process of discovering, describing and recognizing patterns. However, spatial/temporal neighboring samples are likely to have same behavior. Here, we propose an approach which unifies a supervised learning algorithm - namely Optimum-Path Forest - together with a Markov Random Field in order to build a prior model holding a spatial smoothness assumption, which takes into account the contextual information for classification purposes. We show its robustness for brain tissue classification over some images of the well-known dataset IBSR. © 2013 Springer-Verlag.

Probabilistic approaches in civil engineering: generation of random fields and structural identification with genetic algorithms

The inherent stochastic character of most of the physical quantities involved in engineering models has led to an always increasing interest for probabilistic analysis. Many approaches to stochastic analysis have been proposed. However, it is widely acknowledged that the only universal method available to solve accurately any kind of stochastic mechanics problem is Monte Carlo Simulation. One of the key parts in the implementation of this technique is the accurate and efficient generation of samples of the random processes and fields involved in the problem at hand. In the present thesis an original method for the simulation of homogeneous, multi-dimensional, multi-variate, non-Gaussian random fields is proposed. The algorithm has proved to be very accurate in matching both the target spectrum and the marginal probability. The computational efficiency and robustness are very good too, even when dealing with strongly non-Gaussian distributions. What is more, the resulting samples posses all the relevant, welldefined and desired properties of “translation fields”, including crossing rates and distributions of extremes. The topic of the second part of the thesis lies in the field of non-destructive parametric structural identification. Its objective is to evaluate the mechanical characteristics of constituent bars in existing truss structures, using static loads and strain measurements. In the cases of missing data and of damages that interest only a small portion of the bar, Genetic Algorithm have proved to be an effective tool to solve the problem.

Hierarchical Markov Random Fields Applied to Model Soft Tissue Deformations on Graphics Hardware

Many methodologies dealing with prediction or simulation of soft tissue deformations on medical image data require preprocessing of the data in order to produce a different shape representation that complies with standard methodologies, such as mass–spring networks, finite element method s (FEM). On the other hand, methodologies working directly on the image space normally do not take into account mechanical behavior of tissues and tend to lack physics foundations driving soft tissue deformations. This chapter presents a method to simulate soft tissue deformations based on coupled concepts from image analysis and mechanics theory. The proposed methodology is based on a robust stochastic approach that takes into account material properties retrieved directly from the image, concepts from continuum mechanics and FEM. The optimization framework is solved within a hierarchical Markov random field (HMRF) which is implemented on the graphics processor unit (GPU See Graphics processing unit ).

A Cooperative and Adaptive Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows

In this paper we propose two cooperation schemes to compose new parallel variants of the Variable Neighborhood Search (VNS). On the one hand, a coarse-grained cooperation scheme is introduced which is well suited for being enhanced with a solution warehouse to store and manage the so far best found solutions and a self-adapting mechanism for the most important search parameters. This makes an a priori parameter tuning obsolete. On the other hand, a fine-grained scheme was designed to reproduce the successful properties of the sequential VNS. In combination with the use of parallel exploration threads all of the best solutions and 11 out of 20 new best solutions for the Multi Depot Vehicle Routing Problem with Time Windows were found.

On degeneracy and invariances of random fields paths with applications in Gaussian process modelling

We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling. The key idea is that a number of structural properties one may wish to impose a priori on functions boil down to degeneracy properties under well-chosen linear operators. We first show in a second order set-up that almost sure degeneracy of random field paths under some class of linear operators defined in terms of signed measures can be controlled through the two first moments. A special focus is then put on the Gaussian case, where these results are revisited and extended to further linear operators thanks to state-of-the-art representations. Several degeneracy properties are tackled, including random fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process modelling. In a first numerical experiment, it is shown that dedicated kernels can be used to infer an axis of symmetry. Our second numerical experiment deals with conditional simulations of a solution to the heat equation, and it is found that adapted kernels notably enable improved predictions of non-linear functionals of the field such as its maximum.

Designer-driven 3D buildings generated using variable neighborhood search

This paper presents a mechanism to generate virtual buildings considering designer constraints and guidelines. This mechanism is implemented as a pipeline of different Variable Neighborhood Search (VNS) optimization processes in which several subproblems are tackled (1) rooms locations, (2) connectivity graph, and (3) element placement. The core VNS algorithm includes some variants to improve its performance, such as, for example constraint handling and biased operator selection. The optimization process uses a toolkit of construction primitives implemented as "smart objects" providing basic elements such as rooms, doors, staircases and other connectors. The paper also shows experimental results of the application of different designer constraints to a wide range of buildings from small houses to a large castle with several underground levels.

Rotation invariant iris feature extraction using Gaussian Markov random fields with non-separable wavelet

Rotation invariance is important for an iris recognition system since changes of head orientation and binocular vergence may cause eye rotation. The conventional methods of iris recognition cannot achieve true rotation invariance. They only achieve approximate rotation invariance by rotating the feature vector before matching or unwrapping the iris ring at different initial angles. In these methods, the complexity of the method is increased, and when the rotation scale is beyond the certain scope, the error rates of these methods may substantially increase. In order to solve this problem, a new rotation invariant approach for iris feature extraction based on the non-separable wavelet is proposed in this paper. Firstly, a bank of non-separable orthogonal wavelet filters is used to capture characteristics of the iris. Secondly, a method of Markov random fields is used to capture rotation invariant iris feature. Finally, two-class kernel Fisher classifiers are adopted for classification. Experimental results on public iris databases show that the proposed approach has a low error rate and achieves true rotation invariance. © 2010.

Solving the Task Assignment Problem with a Variable Neighborhood Search

In this paper a variable neighborhood search (VNS) approach for the task assignment problem (TAP) is considered. An appropriate neighborhood scheme along with a shaking operator and local search procedure are constructed specifically for this problem. The computational results are presented for the instances from the literature, and compared to optimal solutions obtained by the CPLEX solver and heuristic solutions generated by the genetic algorithm. It can be seen that the proposed VNS approach reaches all optimal solutions in a quite short amount of computational time.

Variable Neighborhood Search for the File Transfer Scheduling Problem

ACM Computing Classification System (1998): I.2.8, G.1.6.

A Variable Neighborhood Search Approach for Solving the Maximum Set Splitting Problem

This paper presents a Variable neighbourhood search (VNS) approach for solving the Maximum Set Splitting Problem (MSSP). The algorithm forms a system of neighborhoods based on changing the component for an increasing number of elements. An efficient local search procedure swaps the components of pairs of elements and yields a relatively short running time. Numerical experiments are performed on the instances known in the literature: minimum hitting set and Steiner triple systems. Computational results show that the proposed VNS achieves all optimal or best known solutions in short times. The experiments indicate that the VNS compares favorably with other methods previously used for solving the MSSP. ACM Computing Classification System (1998): I.2.8.

Variable Neighborhood Search for Solving the Capacitated Single Allocation Hub Location Problem

In this paper a Variable Neighborhood Search (VNS) algorithm for solving the Capacitated Single Allocation Hub Location Problem (CSAHLP) is presented. CSAHLP consists of two subproblems; the first is choosing a set of hubs from all nodes in a network, while the other comprises finding the optimal allocation of non-hubs to hubs when a set of hubs is already known. The VNS algorithm was used for the first subproblem, while the CPLEX solver was used for the second. Computational results demonstrate that the proposed algorithm has reached optimal solutions on all 20 test instances for which optimal solutions are known, and this in short computational time.