Survey on Formal Concept Analysis Based Supervised Classification Techniques

Classification is a data mining task and which is a two-phase process: learning and classification. The learning phase consists of constructing a classifier or a model from a labeled set of objects. The classification phase consists classifying new objects by using the generated classifier. Different approaches have been proposed for supervised classification problems through Formal Concept Analysis, and which is a mathematical theory to build upon hierarchies of formal concepts. The proposed approaches in literature rely on the use of single classifier and ensemble methods. Single classifier methods vary between them according to different criteria especially the number of formal concepts generated. We distinguish overall complete lattice methods, sub-lattice methods and concept cover methods. Methods based on ensemble classifiers rely on the use of many classifiers. Among these methods, there are methods based on sequential training and methods based on parallel training. However, with the large volume of data generated from various sources, the process of knowledge extraction with traditional methods becomes difficult. That’s why new methods based on distributed classifier have recently appeared. In this paper, we present a survey of many FCA-based approaches for classification by dividing them into methods based on a mono-classifier, methods based on ensemble classifiers and methods based on distributed classifiers. Different methods are presented and compared within this paper.

Unsteady Lift Prediction with a Higher-Order Potential Flow Method

An unsteady formulation of the Kutta–Joukowski theorem has been used with a higher-order potential flow method for the prediction of three-dimensional unsteady lift. This study describes the implementation and verification of the approach in detail sufficient for reproduction by future developers. Verification was conducted using the classical responses to a two-dimensional airfoil entering a sharp-edged gust and a sinusoidal gust with errors of less than 1% for both. The method was then compared with the three-dimensional unsteady lift response of a wing as modeled in two unsteady vortex-lattice methods. Results showed agreement in peak lift coefficient prediction to within 1% and 7%, respectively, and mean agreement within 0.25% for the full response.

Design, implementation and validation of advanced lattice techniques for pricing EAKO — European American Knock-Out option

The paper presents a series of advanced lattice methods aimed at evaluating an EAKO European-American Knock-Out contract. The first part of the paper deals with the numerical methods implemented for pricing: Binomial and Trinomial Stochastic trees, Adaptive Mesh Model, Pentanomial and Heptanomial lattice. In the second part, specific tests are designed to validate the code written in Matlab language. The study concludes by applying the most performing model to a real market case.

Derandomised lattice rules for high dimensional integration

We seek shifted lattice rules that are good for high dimensional integration over the unit cube in the setting of an unanchored weighted Sobolev space of functions with square-integrable mixed first derivatives. Many existing studies rely on random shifting of the lattice, whereas here we work with lattice rules with a deterministic shift. Specifically, we consider 'half-shifted' rules in which each component of the shift is an odd multiple of \(1/(2N)\) where \(N\) is the number of points in the lattice. By applying the principle that there is always at least one choice as good as the average, we show that for a given generating vector there exists a half-shifted rule whose squared worst-case error differs from the shift-averaged squared worst-case error by a term of only order \({1/N^2}\). We carry out numerical experiments where the generating vector is chosen component-by-component (CBC), as for randomly shifted lattices, and where the shift is chosen by a new `CBC for shift' algorithm. The numerical results are encouraging. References J. Dick, F. Y. Kuo, and I. H. Sloan. High-dimensional integration: The quasi-Monte Carlo way. Acta Numer., 22:133–288, 2013. doi:10.1017/S0962492913000044. J. Dick, D. Nuyens, and F. Pillichshammer. Lattice rules for nonperiodic smooth integrands. Numer. Math., 126(2):259–291, 2014. doi:10.1007/s00211-013-0566-0. T. Goda, K. Suzuki, and T. Yoshiki. Lattice rules in non-periodic subspaces of sobolev spaces. Numer. Math., 141(2):399–427, 2019. doi:10.1007/s00211-018-1003-1. F. Y. Kuo. Lattice rule generating vectors. URL http://web.maths.unsw.edu.au/ fkuo/lattice/index.html. D. Nuyens and R. Cools. Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces. Math. Comput., 75:903–920, 2006. doi:10.1090/S0025-5718-06-01785-6. I. H. Sloan and S. Joe. Lattice methods for multiple integration. Oxford Science Publications. Clarendon Press and Oxford University Press, 1994. URL https://global.oup.com/academic/product/lattice-methods-for-multiple-integration-9780198534723. I. H. Sloan and H. Wozniakowski. When are quasi-Monte Carlo algorithms efficient for high dimensional integrals? J. Complex., 14(1):1–33, 1998. doi:10.1006/jcom.1997.0463. I. H. Sloan, F. Y. Kuo, and S. Joe. On the step-by-step construction of quasi-Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces. Math. Comput., 71:1609–1641, 2002. doi:10.1090/S0025-5718-02-01420-5.

Weakly coupled conformal gauge theories on the lattice

Results are reported for the β-function of weakly coupled conformal gauge theories on the lattice, SU(3) with Nf = 14 fundamental and Nf = 3 sextet fermions. The models are chosen to be close to the upper end of the conformal window where perturbation theory is reliable hence a fixed point is expected. The study serves as a test of how well lattice methods perform in the weakly coupled conformal cases. We also comment on the 5-loop β-function of two models close to the lower end of the conformal window, SU(3) with Nf = 12 fundamental and Nf = 2 sextet fermions.

Looking behind the Standard Model with lattice gauge theory

Models for what may lie behind the Standard Model often require nonperturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to address fundamental dynamical questions. I survey recent work in this area.