Visualizing data with formal concept analysis

Download
2003
Diner, Çağrı
In this thesis, we wanted to stress the tendency to the geometry of data. This should be applicable in almost every branch of science, where data are of great importance, and also in every kind of industry, economy, medicine etc. Since machine's hard-disk capacities which is used for storing datas and the amount of data you can reach through internet is increasing day by day, there should be a need to turn this information into knowledge. This is one of the reasons for studying formal concept analysis. We wanted to point out how this application is related with algebra and logic. The beginning of the first chapter emphasis the relation between closure systems, galois connections, lattice theory as a mathematical structure and concept analysis. Then it describes the basic step in the formalization: An elementary form of the representation of data is defined mathematically. Second chapter explains the logic of formal concept analysis. It also shows how implications, which can be regard as special formulas on a set,between attributes can be shown by fewer implications, so called generating set for implications. These mathematical tools are then used in the last chapter, in order to describe complex 'concept' lattices by means of decomposition methods in examples.

Suggestions

A marginalized multilevel model for bivariate longitudinal binary data
İnan, Gül; İlk Dağ, Özlem; Department of Statistics (2014)
This thesis study considers analysis of bivariate longitudinal binary data. We propose a model based on marginalized multilevel model framework. The proposed model consists of two levels such that the first level associates the marginal mean of responses with covariates through a logistic regression model and the second level includes subject/time specific random intercepts within a probit regression model. The covariance matrix of multiple correlated time-specific random intercepts for each subject is assu...
Modeling and implementation of local volatility surfaces in Bayesian framework
Animoku, Abdulwahab; Uğur, Ömür; Yolcu-Okur, Yeliz (2018-06-01)
In this study, we focus on the reconstruction of volatility surfaces via a Bayesian framework. Apart from classical methods, such as, parametric and non-parametric models, we study the Bayesian analysis of the (stochastically) parametrized volatility structure in Dupire local volatility model. We systematically develop and implement novel mathematical tools for handling the classical methods of constructing local volatility surfaces. The most critical limitation of the classical methods is obtaining negativ...
Nonautonomous Bifurcations in Nonlinear Impulsive Systems
Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01)
In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
Inverse Sturm-Liouville Systems over the whole Real Line
Altundağ, Hüseyin; Taşeli, Hasan; Department of Mathematics (2010)
In this thesis we present a numerical algorithm to solve the singular Inverse Sturm-Liouville problems with symmetric potential functions. The singularity, which comes from the unbounded domain of the problem, is treated by considering the limiting case of the associated problem on the symmetric finite interval. In contrast to regular problems which are considered on a finite interval the singular inverse problem has an ill-conditioned structure despite of the limiting treatment. We use the regularization t...
Equivariant reduction of matrix gauge theories and emergent chaotic dynamics
Toğa, Göksu Can; Kürkcüoğlu, Seçkin; Department of Physics (2018)
In this thesis we focus on a massive deformation of a Yang-Mills matrix gauge theory. We first layout the essential features of this model including fuzzy 4- sphere extremum of the mass deformed potential as well as its relation with string theoretic matrix models such as the BFSS model. Starting with such a model with U(4N) gauge symmetry, we determine the SU(4) equivariant fluctuations modes. We trace over the fuzzy 4-spheres at the matrix levels N = 1 6(n + 1)(n + 2)(n + 3), (n : 1; 2 : : : 5) and obtain...
Citation Formats
Ç. Diner, “Visualizing data with formal concept analysis,” M.S. - Master of Science, Middle East Technical University, 2003.