Browsing by Subject "Approximation Theory"
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Item Open Access Clustered linear regression(Elsevier, 2002) Ari, B.; Güvenir, H. A.Clustered linear regression (CLR) is a new machine learning algorithm that improves the accuracy of classical linear regression by partitioning training space into subspaces. CLR makes some assumptions about the domain and the data set. Firstly, target value is assumed to be a function of feature values. Second assumption is that there are some linear approximations for this function in each subspace. Finally, there are enough training instances to determine subspaces and their linear approximations successfully. Tests indicate that if these approximations hold, CLR outperforms all other well-known machine-learning algorithms. Partitioning may continue until linear approximation fits all the instances in the training set - that generally occurs when the number of instances in the subspace is less than or equal to the number of features plus one. In other case, each new subspace will have a better fitting linear approximation. However, this will cause over fitting and gives less accurate results for the test instances. The stopping situation can be determined as no significant decrease or an increase in relative error. CLR uses a small portion of the training instances to determine the number of subspaces. The necessity of high number of training instances makes this algorithm suitable for data mining applications. © 2002 Elsevier Science B.V. All rights reserved.Item Open Access Perspective projections in the space-frequency plane and fractional Fourier transforms(OSA Publishing, 2000-07-06) Yetik, I. S.; Özaktaş, Haldun M.; Barshan, B.; Onural, L.Perspective projections in the space-frequency plane are analyzed, and it is shown that under certain conditions they can he approximately modeled in terms of the fractional Fourier transform, The region of validity of the approximation is examined. Numerical examples are presented. (C) 2000 Optical Society of AmericaItem 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.