# Browsing by Subject "Piecewise linear techniques"

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Item Open Access Adaptive and efficient nonlinear channel equalization for underwater acoustic communication(Elsevier B.V., 2017) Kari, D.; Vanli, N. D.; Kozat, S. S.Show more We investigate underwater acoustic (UWA) channel equalization and introduce hierarchical and adaptive nonlinear (piecewise linear) channel equalization algorithms that are highly efficient and provide significantly improved bit error rate (BER) performance. Due to the high complexity of conventional nonlinear equalizers and poor performance of linear ones, to equalize highly difficult underwater acoustic channels, we employ piecewise linear equalizers. However, in order to achieve the performance of the best piecewise linear model, we use a tree structure to hierarchically partition the space of the received signal. Furthermore, the equalization algorithm should be completely adaptive, since due to the highly non-stationary nature of the underwater medium, the optimal mean squared error (MSE) equalizer as well as the best piecewise linear equalizer changes in time. To this end, we introduce an adaptive piecewise linear equalization algorithm that not only adapts the linear equalizer at each region but also learns the complete hierarchical structure with a computational complexity only polynomial in the number of nodes of the tree. Furthermore, our algorithm is constructed to directly minimize the final squared error without introducing any ad-hoc parameters. We demonstrate the performance of our algorithms through highly realistic experiments performed on practical field data as well as accurately simulated underwater acoustic channels. © 2017 Elsevier B.V.Show more Item Open Access Boosted LMS-based piecewise linear adaptive filters(IEEE, 2016) Kari, Dariush; Marivani, Iman; Delibalta, İ.; Kozat, Süleyman SerdarShow more We introduce the boosting notion extensively used in different machine learning applications to adaptive signal processing literature and implement several different adaptive filtering algorithms. In this framework, we have several adaptive constituent filters that run in parallel. For each newly received input vector and observation pair, each filter adapts itself based on the performance of the other adaptive filters in the mixture on this current data pair. These relative updates provide the boosting effect such that the filters in the mixture learn a different attribute of the data providing diversity. The outputs of these constituent filters are then combined using adaptive mixture approaches. We provide the computational complexity bounds for the boosted adaptive filters. The introduced methods demonstrate improvement in the performances of conventional adaptive filtering algorithms due to the boosting effect.Show more Item Open Access Competitive and online piecewise linear classification(IEEE, 2013) Özkan, Hüseyin; Donmez, M.A.; Pelvan O.S.; Akman, A.; Kozat, Süleyman S.Show more In this paper, we study the binary classification problem in machine learning and introduce a novel classification algorithm based on the 'Context Tree Weighting Method'. The introduced algorithm incrementally learns a classification model through sequential updates in the course of a given data stream, i.e., each data point is processed only once and forgotten after the classifier is updated, and asymptotically achieves the performance of the best piecewise linear classifiers defined by the 'context tree'. Since the computational complexity is only linear in the depth of the context tree, our algorithm is highly scalable and appropriate for real time processing. We present experimental results on several benchmark data sets and demonstrate that our method provides significant computational improvement both in the test (5 ∼ 35×) and training phases (40 ∼ 1000×), while achieving high classification accuracy in comparison to the SVM with RBF kernel. © 2013 IEEE.Show more Item Open Access Fast and accurate analysis of large-scale composite structures with the parallel multilevel fast multipole algorithm(Optical Society of America, 2013) Ergül, Özgür; Gürel, LeventShow more Accurate electromagnetic modeling of complicated optical structures poses several challenges. Optical metamaterial and plasmonic structures are composed of multiple coexisting dielectric and/or conducting parts. Such composite structures may possess diverse values of conductivities and dielectric constants, including negative permittivity and permeability. Further challenges are the large sizes of the structures with respect to wavelength and the complexities of the geometries. In order to overcome these challenges and to achieve rigorous and efficient electromagnetic modeling of three-dimensional optical composite structures, we have developed a parallel implementation of the multilevel fast multipole algorithm (MLFMA). Precise formulation of composite structures is achieved with the so-called "electric and magnetic current combined-field integral equation." Surface integral equations are carefully discretized with piecewise linear basis functions, and the ensuing dense matrix equations are solved iteratively with parallel MLFMA. The hierarchical strategy is used for the efficient parallelization of MLFMA on distributed-memory architectures. In this paper, fast and accurate solutions of large-scale canonical and complicated real-life problems, such as optical metamaterials, discretized with tens of millions of unknowns are presented in order to demonstrate the capabilities of the proposed electromagnetic solver.Show more Item Open Access Linear MMSE-optimal turbo equalization using context trees(IEEE, 2013) Kim, K.; Kalantarova, N.; Kozat, S. S.; Singer, A. C.Show more Formulations of the turbo equalization approach to iterative equalization and decoding vary greatly when channel knowledge is either partially or completely unknown. Maximum aposteriori probability (MAP) and minimum mean-square error (MMSE) approaches leverage channel knowledge to make explicit use of soft information (priors over the transmitted data bits) in a manner that is distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization methods either estimate the channel or use a direct adaptation equalizer in which estimates of the transmitted data are formed from an expressly linear function of the received data and soft information, with this latter formulation being most common. We study a class of direct adaptation turbo equalizers that are both adaptive and nonlinear functions of the soft information from the decoder. We introduce piecewise linear models based on context trees that can adaptively approximate the nonlinear dependence of the equalizer on the soft information such that it can choose both the partition regions as well as the locally linear equalizer coefficients in each region independently, with computational complexity that remains of the order of a traditional direct adaptive linear equalizer. This approach is guaranteed to asymptotically achieve the performance of the best piecewise linear equalizer, and we quantify the MSE performance of the resulting algorithm and the convergence of its MSE to that of the linear minimum MSE estimator as the depth of the context tree and the data length increase.Show more Item Open Access A new method for nonlinear circuit simulation in time domain: NOWE(Institute of Electrical and Electronics Engineers, 1996-03) Ocalı, O.; Tan, M. A.; Atalar, AbdullahShow more A new method for the time-domain solution of general nonlinear dynamic circuits is presented. In this method, the solutions of the state variables are computed by using their time derivatives up to some order at the initial time instant. The computation of the higher order derivatives is equivalent to solving the same linear circuit for various sets of dc excitations. Once the time derivatives of the state variables are obtained, an approximation to the solution can be found as a polynomial rational function of time. The time derivatives of the approximation at the initial time instant are matched to those of the exact solution. This method is promising in terms of execution speed, since it can achieve the same accuracy as the trapezoidal approximation with much smaller number of matrix inversions.Show more Item Open Access Piecewise nonlinear regression via decision adaptive trees(IEEE, 2014-09) Vanlı, N. Denizcan; Sayın, Muhammed O.; Ergüt, S.; Kozat, Süleyman S.Show more We investigate the problem of adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an individual sequence manner. We partition the regressor space using hyperplanes in a nested structure according to the notion of a tree. In this manner, we introduce an adaptive nonlinear regression algorithm that not only adapts the regressor of each partition but also learns the complete tree structure with a computational complexity only polynomial in the number of nodes of the tree. Our algorithm is constructed to directly minimize the final regression error without introducing any ad-hoc parameters. Moreover, our method can be readily incorporated with any tree construction method as demonstrated in the paper. © 2014 EURASIP.Show more Item Open Access Quantitative comparison of rooftop and RWG basis functions(IEEE, 1997-07) Gürel, Levent; Şendur, İbrahim Kürşad; Sertel, KubilayShow more The `rooftops' (RT) basis functions (BFs) are well suited for the modeling of geometries that conform to Cartesian coordinates, whereas the Rao, Wilton, and Glisson subdomains (RWG) BFs are capable of modeling flat-faceted approximations of arbitrary geometries. Both basis functions can also be used in modeling unknown functions transformed from the real space to the parametric space of a curved surface. The RT and RWG basis functions have many common features: they are defined on tow neighboring subdomains and the unknown is associated with the common edge between these two subdomains; thus they are edge functions. The two BFs also differ in the way they define the direction of the current.Show more Item Open Access Solution of radiation problems using the fast multipole method(IEEE, 1997-07) Gürel, Levent; Şendur, İbrahim KürşatShow more Electromagnetic radiation problems involving electrically large radiators and reflectors are solved using the fast multipole method (FMM). The FMM enables the solution of large problems with existing computational resources by reducing the computational complexity by a faster equivalent of O(N) complexity in each iteration of an iterative scheme. Three dimensional radiation problems involving complicated geometries are modeled using arbitrary surface triangulations. Piecewise linear basis functions defined on triangular domains due to Rao, Wilton, and Glisson (RWG) basis functions are used to approximate the induced currents. Using delta-gap voltage sources and prescribed current distributions, the operations of various antennas are simulated.Show more Item Open Access Utilization of the recursive shortest spanning tree algorithm for video-object segmentation by 2-D affine motion modeling(IEEE, 2000) Tuncel, E.; Onural, L.Show more A novel video-object segmentation algorithm is proposed, which takes the previously estimated 2-D dense motion vector field as input and uses the generalized recursive shortest spanning tree method to approximate each component of the motion vector field as a piecewise planar function. The algorithm is successful in capturing 3-D planar objects in the scene correctly, with acceptable accuracy at the boundaries. The proposed algorithm is fast and requires no initial guess about the segmentation mask. Moreover, it is a hierarchical scheme which gives finest to coarsest segmentation results. The only external parameter needed by the algorithm is the number of segmented regions that essentially control the level at which the coarseness the algorithm would stop. The proposed algorithm improves the `analysis model' developed in the European COST211 framework.Show more