Browsing by Subject "Matrix Algebra"
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Item Open Access Automated construction of fuzzy event sets and its application to active databases(IEEE, 2001) Saygin, Y.; Ulusoy, ÖzgürFuzzy sets and fuzzy logic research aims to bridge the gap between the crisp world of math and the real world. Fuzzy set theory was applied to many different areas, from control to databases. Sometimes the number of events in an event-driven system may become very high and unmanageable. Therefore, it is very useful to organize the events into fuzzy event sets also introducing the benefits of the fuzzy set theory. All the events that have occurred in a system can be stored in event histories which contain precious hidden information. In this paper, we propose a method for automated construction of fuzzy event sets out of event histories via data mining techniques. The useful information hidden in the event history is extracted into a matrix called sequential proximity matrix. This matrix shows the proximities of events and it is used for fuzzy rule execution via similarity based event detection and construction of fuzzy event sets. Our application platform is active databases. We describe how fuzzy event sets can be exploited for similarity based event detection and fuzzy rule execution in active database systems.Item Open Access Comparison of multilevel methods for kronecker-based Markovian representations(Springer, 2004) Buchholz, P.; Dayar T.The paper presents a class of numerical methods to compute the stationary distribution of Markov chains (MCs) with large and structured state spaces. A popular way of dealing with large state spaces in Markovian modeling and analysis is to employ Kronecker-based representations for the generator matrix and to exploit this matrix structure in numerical analysis methods. This paper presents various multilevel (ML) methods for a broad class of MCs with a hierarchcial Kronecker structure of the generator matrix. The particular ML methods are inspired by multigrid and aggregation-disaggregation techniques, and differ among each other by the type of multigrid cycle, the type of smoother, and the order of component aggregation they use. Numerical experiments demonstrate that so far ML methods with successive over-relaxation as smoother provide the most effective solvers for considerably large Markov chains modeled as HMMs with multiple macrostates.Item Open Access Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains(SIAM, 2000) Dayar T.; Stewart, W. J.Experimental results for large, sparse Markov chains, especially the ill-conditioned nearly completely decomposable (NCD) ones, are few. We believe there is need for further research in this area, specifically to aid in the understanding of the effects of the degree of coupling of NCD Markov chains and their nonzero structure on the convergence characteristics and space requirements of iterative solvers. The work of several researchers has raised the following questions that led to research in a related direction: How must one go about partitioning the global coefficient matrix into blocks when the system is NCD and a two-level iterative solver (such as block SOR) is to be employed? Are block partitionings dictated by the NCD form of the stochastic one-step transition probability matrix necessarily superior to others? Is it worth investigating alternative partitionings? Better yet, for a fixed labeling and partitioning of the states, how does the performance of block SOR (or even that of point SOR) compare to the performance of the iterative aggregation-disaggregation (IAD) algorithm? Finally, is there any merit in using two-level iterative solvers when preconditioned Krylov subspace methods are available? We seek answers to these questions on a test suite of 13 Markov chains arising in 7 applications.Item Open Access Maximizing benefit of classifications using feature intervals(Springer, Berlin, Heidelberg, 2003) İkizler, Nazlı; Güvenir, H. AltayThere is a great need for classification methods that can properly handle asymmetric cost and benefit constraints of classifications. In this study, we aim to emphasize the importance of classification benefits by means of a new classification algorithm, Benefit-Maximizing classifier with Feature Intervals (BMFI) that uses feature projection based knowledge representation. Empirical results show that BMFI has promising performance compared to recent cost-sensitive algorithms in terms of the benefit gained.Item Open Access A parallel scaled conjugate-gradient algorithm for the solution phase of gathering radiosity on hypercubes(Springer, 1997) Kurç, T. M.; Aykanat, Cevdet; Özgüç, B.Gathering radiosity is a popular method for investigating lighting effects in a closed environment. In lighting simulations, with fixed locations of objects and light sources, the intensity and color and/or reflectivity vary. After the form-factor values are computed, the linear system of equations is solved repeatedly to visualize these changes. The scaled conjugate-gradient method is a powerful technique for solving large sparse linear systems of equations with symmetric positive definite matrices. We investigate this method for the solution phase. The nonsymmetric form-factor matrix is transformed into a symmetric matrix. We propose an efficient data redistribution scheme to achieve almost perfect load balance. We also present several parallel algorithms for form-factor computation.Item Open Access Transforming stochastic matrices for stochastic comparison with the st-order(E D P Sciences, 2003) Dayar T.; Fourneau, J. M.; Pekergin, N.We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution. © EDP Sciences 2003.