Using formal concept analysis to detect and monitor organised crime

This paper describes some possible uses of Formal Concept Analysis in the detection and monitoring of Organised Crime. After describing FCA and its mathematical basis, the paper suggests, with some simple examples, ways in which FCA and some of its related disciplines can be applied to this problem domain. In particular, the paper proposes FCA-based approaches for finding multiple instances of an activity associated with Organised Crime, finding dependencies between Organised Crime attributes, and finding new indicators of Organised Crime from the analysis of existing data. The paper concludes by suggesting that these approaches will culminate in the creation and implementation of an Organised Crime ‘threat score card’, as part of an overall environmental scanning system that is being developed by the new European ePOOLICE projec

Solving ill-posed bilevel programs

This paper deals with ill-posed bilevel programs, i.e., problems admitting multiple lower-level solutions for some upper-level parameters. Many publications have been devoted to the standard optimistic case of this problem, where the difficulty is essentially moved from the objective function to the feasible set. This new problem is simpler but there is no guaranty to obtain local optimal solutions for the original optimistic problem by this process. Considering the intrinsic non-convexity of bilevel programs, computing local optimal solutions is the best one can hope to get in most cases. To achieve this goal, we start by establishing an equivalence between the original optimistic problem an a certain set-valued optimization problem. Next, we develop optimality conditions for the latter problem and show that they generalize all the results currently known in the literature on optimistic bilevel optimization. Our approach is then extended to multiobjective bilevel optimization, and completely new results are derived for problems with vector-valued upper- and lower-level objective functions. Numerical implementations of the results of this paper are provided on some examples, in order to demonstrate how the original optimistic problem can be solved in practice, by means of a special set-valued optimization problem

On a Convex Set with Nondifferentiable Metric Projection

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with smooth boundary which possesses the same property

A Partial-Closure Canonicity Test to Increase the Efficiency of CbO-Type Algorithms

Computing formal concepts is a fundamental part of Formal Concept Analysis and the design of increasingly efficient algorithms to carry out this task is a continuing strand of FCA research. Most approaches suffer from the repeated computation of the same formal concepts and, initially, algorithms concentrated on efficient searches through already computed results to detect these repeats, until the so-called canonicity test was introduced. The canonicity test meant that it was sufficient to examine the attributes of a computed concept to determine its newness: searching through previously computed concepts was no longer necessary. The employment of this test in Close-by-One type algorithms has proved to be highly effective. The typical CbO approach is to compute a concept and then test its canonicity. This paper describes a more efficient approach, whereby a concept need only be partially computed in order to carry out the test. Only if it passes the test does the computation of the concept need to be completed. This paper presents this ‘partial-closure’ canonicity test in the In-Close algorithm and compares it to a traditional CbO algorithm to demonstrate the increase in efficiency

Some Programming Optimizations for Computing Formal Concepts

This paper describes in detail some optimization approaches taken to improve the efficiency of computing formal concepts. In particular, it describes the use and manipulation of bit-arrays to represent FCA structures and carry out the typical operations undertaken in computing formal concepts, thus providing data structures that are both memoryefficient and time saving. The paper also examines the issues and compromises involved in computing and storing formal concepts, describing a number of data structures that illustrate the classical trade-off between memory footprint and code efficiency. Given that there has been limited publication of these programmatical aspects, these optimizations will be useful to programmers in this area and also to any programmers interested in optimizing software that implements Boolean data structures. The optimizations are shown to significantly increase performance by comparing an unoptimized implementation with the optimized one

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models.

We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an alternative cost based on a Huber-regularised TV seminorm. Differentiability properties of the solution operator are verified and a first-order optimality system is derived. Based on the adjoint information, a combined quasi-Newton/semismooth Newton algorithm is proposed for the numerical solution of the bilevel problems. Numerical experiments are carried out to show the suitability of our approach and the improved performance of the new cost functional. Thanks to the bilevel optimisation framework, also a detailed comparison between TGV 2 and ICTV is carried out, showing the advantages and shortcomings of both regularisers, depending on the structure of the processed images and their noise level.King Abdullah University of Science and Technology (KAUST) (Grant ID: KUKI1-007-43), Engineering and Physical Sciences Research Council (Grant IDs: Nr. EP/J009539/1 “Sparse & Higher-order Image Restoration” and Nr. EP/M00483X/1 “Efficient computational tools for inverse imaging problems”), Escuela Politécnica Nacional de Quito (Grant ID: PIS 12-14, MATHAmSud project SOCDE “Sparse Optimal Control of Differential Equations”), Leverhulme Trust (project on “Breaking the non-convexity barrier”), SENESCYT (Ecuadorian Ministry of Higher Education, Science, Technology and Innovation) (Prometeo Fellowship)This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s10851-016-0662-

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader’s decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal.We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity