Browsing by Subject "Trees (mathematics)"

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Open Access
Adaptive and efficient nonlinear channel equalization for underwater acoustic communication
(Elsevier B.V., 2017) Kari, D.; Vanli, N. D.; Kozat, S. S.
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.
Open Access
Advanced partitioning and communication strategies for the efficient parallelization of the multilevel fast multipole algorithm
(IEEE, 2010) Ergül O.; Gürel, Levent
Large-scale electromagnetics problems can be solved efficiently with the multilevel fast multipole algorithm (MLFMA) [1], which reduces the complexity of matrix-vector multiplications required by iterative solvers from O(N 2) to O(N logN). Parallelization of MLFMA on distributed-memory architectures enables fast and accurate solutions of radiation and scattering problems discretized with millions of unknowns using limited computational resources. Recently, we developed a hierarchical partitioning strategy [2], which provides an efficient parallelization of MLFMA, allowing for the solution of very large problems involving hundreds of millions of unknowns. In this strategy, both clusters (sub-domains) of the multilevel tree structure and their samples are partitioned among processors, which leads to improved load-balancing. We also show that communications between processors are reduced and the communication time is shortened, compared to previous parallelization strategies in the literature. On the other hand, improved partitioning of the tree structure complicates the arrangement of communications between processors. In this paper, we discuss communications in detail when MLFMA is parallelized using the hierarchical partitioning strategy. We present well-organized arrangements of communications in order to maximize the efficiency offered by the improved partitioning. We demonstrate the effectiveness of the resulting parallel implementation on a very large scattering problem involving a conducting sphere discretized with 375 million unknowns. ©2010 IEEE.
Open Access
Bağlam ağaçları ile ardışık doğrusal olmayan bağlanım
(IEEE, 2014-04) Vanlı, N. Denizcan; Kozat, Süleyman S.
Bu bildiride, ardışık doğrusal olmayan bağlanım problemi incelenmiş ve bağlam ağaçları kullanarak etkili bir öğrenme algoritması sunulmuştur. Bu amaçla, bağlanım alanı parçalara ayrılmış ve oluşan bölgeler bağlam ağacı ile simgelenmiştir. Her bölgede bağımsız bağlanım algoritmaları kullanılarak bağlam ağacı tarafından gösterilebilen tüm doğrusal olmayan modellerin kestirimleri, hesaplama karmaşıklığı bağlam ağacının düğüm sayısıyla doğrusal olan bu algoritma ile uyarlanır olarak birleştirilmiştir. Önerilen algoritmanın performans limitleri, veriler üzerinde istatistiksel varsayımlarda bulunmaksızın incelenmiştir. Ayrıca, teorik sonuçları izah etmek için sayısal bir örnek sunulmuştur.
Open Access
Competitive and online piecewise linear classification
(IEEE, 2013) Özkan, Hüseyin; Donmez, M.A.; Pelvan O.S.; Akman, A.; Kozat, Süleyman S.
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.
Open Access
Connectivity-guided adaptive lifting transform for image like compression of meshes
(IEEE, 2007-05) Köse, Kıvanç; Çetin, A. Enis; Güdükbay, Uğur; Onural, Levent
We propose a new connectivity-guided adaptive wavelet transform based mesh compression framework. The 3D mesh is first transformed to 2D images on a regular grid structure by performing orthogonal projections onto the image plane. Then, this image-like representation is wavelet transformed using a lifting structure employing an adaptive predictor that takes advantage of the connectivity information of mesh vertices. Then the wavelet domain data is encoded using "Set Partitioning In Hierarchical Trees" (SPIHT) method or JPEG2000. The SPIHT approach is progressive because the resolution of the reconstructed mesh can be changed by varying the length of the 1D data stream created by the algorithm. In JPEG2000 based approach, quantization of the coefficients determines the quality of the reconstruction. The results of the SPIHT based algorithm is observed to be superior to JPEG200 based mesh coder and MPEG-3DGC in rate-distortion.
Open Access
Data imputation through the identification of local anomalies
(Institute of Electrical and Electronics Engineers Inc., 2015) Ozkan, H.; Pelvan, O. S.; Kozat, S. S.
We introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources, e.g., an occluder in the case of a visual recording. Within this framework, we propose: 1) a novel algorithm to efficiently separate, i.e., detect and localize, possible corruptions from a given suspicious data instance and 2) a maximum a posteriori estimator to impute the corrupted data. As a generalization to Euclidean distance, we also propose a novel distance measure, which is based on the ranked deviations among the data attributes and empirically shown to be superior in separating the corruptions. Our algorithm first splits the suspicious instance into parts through a binary partitioning tree in the space of data attributes and iteratively tests those parts to detect local anomalies using the nominal statistics extracted from an uncorrupted (clean) reference data set. Once each part is labeled as anomalous versus normal, the corresponding binary patterns over this tree that characterize corruptions are identified and the affected attributes are imputed. Under a certain conditional independency structure assumed for the binary patterns, we analytically show that the false alarm rate of the introduced algorithm in detecting the corruptions is independent of the data and can be directly set without any parameter tuning. The proposed framework is tested over several well-known machine learning data sets with synthetically generated corruptions and experimentally shown to produce remarkable improvements in terms of classification purposes with strong corruption separation capabilities. Our experiments also indicate that the proposed algorithms outperform the typical approaches and are robust to varying training phase conditions. © 2015 IEEE.
Open Access
A distributed and dynamic data gathering protocol for sensor networks
(IEEE, 2007-05) Tan, Hüseyin Özgür; Körpeoğlu, İbrahim; Stojmenović, I.
In this paper we propose a distributed, self organizing, robust and energy efficient data gathering algorithm for sensor networks operating in environments where all the sensor nodes are not in direct communication range of each other and data aggregation is used while routing. Proposed algorithm is based on local minimum spanning tree (LMST) structure, which nodes can construct from the position of their 1-hop neighbors. Reporting tree is constructed from the sink by allowing only edges of LMST to join the tree, plus possibly some direct links to the sink. Each node selects as parent the LMST neighbor so that the total energy cost of route to the sink is minimal. We also describe route maintenance protocols to respond to predicted sensor failures and addition of new sensors. Our simulation results show that our algorithm prolongs the network lifetime significantly compared to some alternative schemes. © 2007 IEEE.
Open Access
Dynamic point-region quadtrees for particle simulations
(Elsevier Inc., 2013) Oğuz, O.; Durupınar, F.; Güdükbay, Uğur
We propose an algorithm for dynamically updating point-region (PR) quadtrees. Our algorithm is optimized for simultaneous update of data points comprising a quadtree. The intended application area focuses on simulating continuum phenomena, such as crowds, fluids, and smoke. We minimize the number of tree updates by making use of small changes in the positions of data points. We compare the efficiency of the proposed algorithm with two other approaches for updating a quadtree. One of these techniques creates the tree from scratch at each time-step. The second technique subsequently deletes a data point from the tree and reinserts it in its updated position. We achieve significant performance gains with our method in both cases. © 2012 Elsevier Inc. All rights reserved.
Open Access
An energy efficient scatternet formation algorithm for Bluetooth-based sensor networks
(IEEE, 2005-02) Saginbekov, Sain; Körpeoğlu, İbrahim
In this paper, we propose an energy-efficient scatternet formation algorithm for Bluetooth based sensor networks. The algorithm is based on first computing a shortest path tree from the base station to all sensor nodes and then solving the degree constraint problem so that the degree of each node in the network is not greater than seven, which is a Bluetooth constaint. In this way, less amount of energy is spent in each round of communication in the sensor network. The algorithm also tries to balance the load evenly on the high-energy consuming nodes which are the nodes that are close to the base station. In this way, the lifetime of the first dying node is also prolonged. We obtained promising results in the simulations. © 2005 IEEE.
Open Access
An image watermarking algorithm via Zero Assigned Filter Banks
(IEEE, 2005-12) Yücel, Zeyep; Özgüler, A. Bülent
In this paper a new method for digital image watermarking based on Zero Assigned Filter Banks and Embedded Zero Tree Wavelet (EZW) algorithm is presented. An image is partitioned into 128 × 128 subblocks and each block is processed in a three stage decomposition structure by a filter bank which is assigned a zero around the stop band. The coefficients to be marked are chosen according to the EZW algorithm. This method not only provides a robust watermarking scheme but may also be used as an effective compression strategy. The algorithm is tested under white Gaussian noise and against JPEG compression and it is observed to be robust even when exposed to high levels of corruption. © 2005 IEEE.
Open Access
Linear MMSE-optimal turbo equalization using context trees
(IEEE, 2013) Kim, K.; Kalantarova, N.; Kozat, S. S.; Singer, A. C.
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.
Open Access
Nonrectangular wavelets for multiresolution mesh analysis and compression
(IEEE, 2006) Köse, Kıvanç; Çetin, A. Enis; Güdükbay, Uğur; Onural, Levent
We propose a new Set Partitioning In Hierarchical Trees (SPIHT) based mesh compression framework. The 3D mesh is first transformed to 2D images on a regular grid structure. Then, this image-like representation is wavelet transformed and SPIHT is applied on the wavelet domain data. The method is progressive because the resolution of the reconstructed mesh can be changed by varying the length of the one-dimensional data stream created by SPIHT algorithm. Nearly perfect reconstruction is possible if all of the data stream is received. © 2006 IEEE.
Open Access
A novel broadband multilevel fast multipole algorithm with incomplete-leaf tree structures for multiscale electromagnetic problems
(Institute of Electrical and Electronics Engineers Inc., 2016) Takrimi, M.; Ergül, Ö.; Ertürk, V. B.
An efficient and versatile broadband multilevel fast multipole algorithm (MLFMA), which is capable of handling large multiscale electromagnetic problems with a wide dynamic range of mesh sizes, is presented. By invoking a novel concept of incomplete-leaf tree structures, where only the overcrowded boxes are divided into smaller ones for a given population threshold, versatility of using variable-sized boxes is achieved. Consequently, for geometries containing highly overmeshed local regions, the proposed method is always more efficient than the conventional MLFMA for the same accuracy, while it is always more accurate if the efficiency is comparable. Furthermore, in such a population-based clustering scenario, the error is controllable regardless of the number of levels. Several canonical examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison with the conventional MLFMA. ï¿½ 2016 IEEE.
Open Access
Novelty detection using soft partitioning and hierarchical models
(IEEE, 2017) Ergen, Tolga; Gökçesu, Kaan; Şimşek, Mustafa; Kozat, Süleyman Serdar
In this paper, we study novelty detection problem and introduce an online algorithm. The algorithm sequentially receives an observation, generates a decision and then updates its parameters. In the first step, to model the underlying distribution, algorithm constructs a score function. In the second step, this score function is used to make the final decision for the observed data. After thresholding procedure is applied, the final decision is made. We obtain the score using versatile and adaptive nested decision tree. We employ nested soft decision trees to partition the observation space in an hierarchical manner. Based on the sequential performance, we optimize all the components of the tree structure in an adaptive manner. Although this in time adaptation provides powerful modeling abilities, it might suffer from overfitting. To circumvent overfitting problem, we employ the intermediate nodes of tree in order to generate subtrees and we then combine them in an adaptive manner. The experiments illustrate that the introduced algorithm significantly outperforms the state of the art methods.
Open Access
Piecewise nonlinear regression via decision adaptive trees
(IEEE, 2014-09) Vanlı, N. Denizcan; Sayın, Muhammed O.; Ergüt, S.; Kozat, Süleyman S.
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.
Open Access
The robust spanning tree problem with interval data
(Elsevier, 2001) Yaman, H.; Karaşan, O. E.; Pınar, M. Ç.
Motivated by telecommunications applications we investigate the minimum spanning tree problem where edge costs are interval numbers. Since minimum spanning trees depend on the realization of the edge costs, we de5ne the robust spanning tree problem to hedge against the worst case contingency, and present a mixed integer programming formulation of the problem. We also de5ne some useful optimality concepts, and present characterizations for these entities leading to polynomial time recognition algorithms. These entities are then used to preprocess a given graph with interval data prior to the solution of the robust spanning tree problem. Computational results show that these preprocessing procedures are quite e9ective in reducing the time to compute a robust spanning tree.
Open Access
Searching for repeated video sequences
(ACM, 2007-09) Can, Tolga; Duygulu, Pınar
In this paper, we propose a new method to search different instances of a video sequence inside a long video and/or video collection. The proposed method is robust to view point and illumination changes which may occur since the sequences are captured in different times with different cameras, and to the differences in the order and the number of frames in the sequences which may occur due to editing. The algorithm does not require any query to be given for searching, and finds all repeating video sequences inside a long video in a fully automatic way. First, the frames in a video are ranked according to their similarity on the distribution of salient points and colour values. Then, a tree based approach is used to seek for the repetitions of a video sequence if there is any. Results are provided on a full length feature movie, Run Lola Run and on commercials of TRECVID 2004 news video corpus. Copyright 2007 ACM.
Open Access
Sequential Decoding of Low-Density Parity-Check Codes by Adaptive Reordering of Parity Checks
(1992) Radosavljevic, B.; Arikan, E.; Hajek, B.
Decoding algorithms are investigated in which unpruned codeword trees are generated from an ordered list of parity checks. The order is computed from the received message, and low-density parity-check codes are used to help control the growth of the tree. Simulation results are given for the binary erasure channel. © 1992 IEEE
Open Access
Shortest unique substring query revisited
(Springer, Cham, 2014) Ileri, Atalay Mert; Külekci, M.O.; Xu, B.
We revisit the problem of finding shortest unique substring (SUS) proposed recently by Pei et al. (ICDE'13). We propose an optimal O(n) time and space algorithm that can find an SUS for every location of a string of size n and thus significantly improve their O(n 2) time complexity. Our method also supports finding all the SUSes covering every location, whereas theirs can find only one SUS for every location. Further, our solution is simpler and easier to implement and can also be more space efficient in practice, since we only use the inverse suffix array and the longest common prefix array of the string, while their algorithm uses the suffix tree of the string and other auxiliary data structures. Our theoretical results are validated by an empirical study that shows our method is much faster and more space-saving. © 2014 Springer International Publishing Switzerland.
Open Access
Stereoscopic view-dependent visualization of terrain height fields
(IEEE, 2002) Güdükbay, Uğur; Yilmaz, T.
Visualization of large geometric environments has always been an important problem of computer graphics. In this paper, we present a framework for the stereoscopic view-dependent visualization of large scale terrain models. We use a quadtree based multiresolution representation for the terrain data. This structure is queried to obtain the view-dependent approximations of the terrain model at different levels of detail. In order not to lose depth information, which is crucial for the stereoscopic visualization, we make use of a different simplification criterion, namely, distance-based angular error threshold. We also present an algorithm for the construction of stereo pairs in order to speed up the view-dependent stereoscopic visualization. The approach we use is the simultaneous generation of the triangles for two stereo images using a single draw-list so that the view frustum culling and vertex activation is done only once for each frame. The cracking problem is solved using the dependency information stored for each vertex. We eliminate the popping artifacts that can occur while switching between different resolutions of the data using morphing. We implemented the proposed algorithms on personal computers and graphics workstations. Performance experiments show that the second eye image can be produced approximately 45 percent faster than drawing the two images separately and a smooth stereoscopic visualization can be achieved at interactive frame rates using continuous multiresolution representation of height fields.