Browsing by Subject "Binary trees"
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Item Open Access A comprehensive approach to universal piecewise nonlinear regression based on trees(IEEE, 2014) Vanli, N. D.; Kozat, S. S.In this paper, we investigate 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 use a tree notion in order to partition the space of regressors in a nested structure. The introduced algorithms adapt not only their regression functions but also the complete tree structure while achieving the performance of the 'best' linear mixture of a doubly exponential number of partitions, with a computational complexity only polynomial in the number of nodes of the tree. While constructing these algorithms, we also avoid using any artificial 'weighting' of models (with highly data dependent parameters) and, instead, directly minimize the final regression error, which is the ultimate performance goal. The introduced methods are generic such that they can readily incorporate different tree construction methods such as random trees in their framework and can use different regressor or partitioning functions as demonstrated in the paper.Item 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.Item 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.Item Open Access A VLSI receive beamformer for digital ultrasound imaging(IEEE, 1992-03) Karaman, Mustafa; Kolağasıoğlu, Ertuğrul; Atalar, AbdullahA VLSI architecture for real-time digital receive beamforming in phased array ultrasound imaging is proposed. The architecture is an inverse binary tree like structure with N stages where N is the number of array elements. The sampled signals from the phased array channels are coherently added in a pairwise manner within the stages of the architecture in a pipelined data flow scheme. The storage requirement for the synchronization of the asynchronously received samples corresponding to a focal point is significantly reduced. The architecture is modular and has a regular communication scheme which make the VLSI implementation rather easy and straightforward.