162 research outputs found
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 âthreat score cardâ, as part of an overall environmental scanning system that is being developed by the new European ePOOLICE projec
Making Use of Empty Intersections to Improve the Performance of CbO-Type Algorithms
This paper describes how improvements in the performance of Close-by-One type algorithms can be achieved by making use of empty intersections in the computation of formal concepts. During the computation, if the intersection between the current concept extent and the next attribute-extent is empty, this fact can be simply inherited by subsequent children of the current concept. Thus subsequent intersections with the same attribute-extent can be skipped. Because these intersections require the testing of each object in the current extent, significant time savings can be made by avoiding them. The paper also shows how further time savings can be made by forgoing the traditional canonicity test for new extents, if the intersection is empty. Finally, the paper describes how, because of typical optimizations made in the implementation of CbO-type algorithms, even more time can be saved by amalgamating inherited attributes with inherited empty intersections into a single, simple test
Effort Maximization in Asymmetric N-Person Contest Games
This paper provides existence and characterization of the optimal contest success function under the condition that the objective of the contest designer is total effort maximization among n heterogeneous players. Heterogeneity of players makes active participation of a player in equilibrium endogenous with respect to the specific contest success function adopted by the contest designer. Hence, the aim of effort maximization implies the identification of those players who should be excluded from making positive efforts. We give a general proof for the existence of an optimal contest success function and provide an algorithm for the determination of the set of actively participating players. This is turn allows to determine optimal efforts in closed form. An important general feature of the solution is that maximization of total effort requires at least three players to be active
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 âpartial-closureâ 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 âSparse & Higher-order Image Restorationâ and Nr. EP/M00483X/1 âEfficient computational tools for inverse imaging problemsâ), Escuela PolitĂ©cnica Nacional de Quito (Grant ID: PIS 12-14, MATHAmSud project SOCDE âSparse Optimal Control of Differential Equationsâ), Leverhulme Trust (project on âBreaking the non-convexity barrierâ), 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-
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