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281
Discovering Structure in Multiple Learning Tasks: The TC Algorithm
 In International Conference on Machine Learning
, 1996
"... Recently, there has been an increased interest in "lifelong " machine learning methods, that transfer knowledge across multiple learning tasks. Such methods have repeatedly been found to outperform conventional, singletask learning algorithms when the learning tasks are appropriately rela ..."
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Cited by 90 (3 self)
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Recently, there has been an increased interest in "lifelong " machine learning methods, that transfer knowledge across multiple learning tasks. Such methods have repeatedly been found to outperform conventional, singletask learning algorithms when the learning tasks are appropriately related. To increase robustness of such approaches, methods are desirable that can reason about the relatedness of individuallearning tasks, in order to avoid the danger arising from tasks that are unrelated and thus potentially misleading. This paper describes the taskclustering (TC) algorithm. TC clusters learning tasks into classes of mutually related tasks. When facing a new learning task, TC first determines the most related task cluster, then exploits information selectively from this task cluster only. An empirical study carried out in a mobile robot domain shows that TC outperforms its nonselective counterpart in situations where only a small number of tasks is relevant. 1 INTRODUCTION One of t...
Spatial resolution Enhancement of LowResolution . . .
, 1998
"... Recent years have seen growing interest in the problem of superresolution restoration of video sequences. Whereas in the traditional single image restoration problem only a single input image is available for processing, the task of reconstructing superresolution images from multiple undersampled ..."
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Cited by 69 (0 self)
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Recent years have seen growing interest in the problem of superresolution restoration of video sequences. Whereas in the traditional single image restoration problem only a single input image is available for processing, the task of reconstructing superresolution images from multiple undersampled and degraded images can take advantage of the additional spatiotemporal data available in the image sequence. In particular, camera and scene motion lead to frames in the source video sequence containing similar, but not identical information. The additional information available in these frames make possible reconstruction of visually superior frames at higher resolution than that of the original data. In this paper we review the current state of the art and identify promising directions for future research.
Interpolation by Regularized Spline with Tension: II. Application to Terrain Modeling and Surface Geometry Analysis
, 1993
"... A general approach to the computation of basic topographic parameters independent of the spatial distribution of given elevation data is developed. The approach is based on an interpolation function with regular first and second order derivatives and on application of basic principles of differentia ..."
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Cited by 69 (9 self)
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A general approach to the computation of basic topographic parameters independent of the spatial distribution of given elevation data is developed. The approach is based on an interpolation function with regular first and second order derivatives and on application of basic principles of differential geometry. General equations for computation of profile, plan, and tangential curvatures are derived. A new algorithm for construction of slope curves is developed using a combined grid and vector approach. Resulting slope curves better fulfil the condition of orthogonality to contours than standard grid algorithms. Presented methods are applied to topographic analysis of a watershed in central Illinois.
Multistep scattered data interpolation using compactly supported radial basis functions
 J. Comp. Appl. Math
, 1996
"... Abstract. A hierarchical scheme is presented for smoothly interpolating scattered data with radial basis functions of compact support. A nested sequence of subsets of the data is computed efficiently using successive Delaunay triangulations. The scale of the basis function at each level is determine ..."
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Cited by 69 (12 self)
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Abstract. A hierarchical scheme is presented for smoothly interpolating scattered data with radial basis functions of compact support. A nested sequence of subsets of the data is computed efficiently using successive Delaunay triangulations. The scale of the basis function at each level is determined from the current density of the points using information from the triangulation. The method is rotationally invariant and has good reproduction properties. Moreover the solution can be calculated and evaluated in acceptable computing time. During the last two decades radial basis functions have become a well established tool for multivariate interpolation of both scattered and gridded data; see [2,7,8,22,25] for some surveys. The major part
Creating Surfaces from Scattered Data Using Radial Basis Functions
 in Mathematical Methods for Curves and Surfaces
, 1995
"... . This paper gives an introduction to certain techniques for the construction of geometric objects from scattered data. Special emphasis is put on interpolation methods using compactly supported radial basis functions. x1. Introduction We assume a sample of multivariate scattered data to be given a ..."
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Cited by 60 (11 self)
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. This paper gives an introduction to certain techniques for the construction of geometric objects from scattered data. Special emphasis is put on interpolation methods using compactly supported radial basis functions. x1. Introduction We assume a sample of multivariate scattered data to be given as a set X = fx 1 ; : : : ; xN g of N pairwise distinct points x 1 ; : : : ; xN in IR d , called centers, together with N points y 1 ; : : : ; yN in IR D . An interpolating curve, surface, or solid to these data will be the range of a smooth function s : IR d oe\Omega ! IR D with s(x k ) = y k ; 1 k N: (1) Likewise, an approximating curve, surface, or solid will make the differences s(x j ) \Gamma y j small, for instance in the discrete L 2 sense, i.e. N X k=1 ks(x k ) \Gamma y k k 2 2 should be small. Curves, surfaces, and solids will only differ by their appropriate value of d = 1; 2, or 3. We use the term (geometric) objects to stand for curves, surfaces, or solids. Not...
Scattered Data Interpolation Methods for Electronic Imaging Systems: A Survey
, 2002
"... Numerous problems in electronic imaging systems involve the need to interpolate from irregularly spaced data. One example is the calibration of color input/output devices with respect to a common intermediate objective color space, such as XYZ or L*a*b*. In the present report we survey some of the m ..."
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Cited by 55 (0 self)
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Numerous problems in electronic imaging systems involve the need to interpolate from irregularly spaced data. One example is the calibration of color input/output devices with respect to a common intermediate objective color space, such as XYZ or L*a*b*. In the present report we survey some of the most important methods of scattered data interpolation in twodimensional and in threedimensional spaces. We review both singlevalued cases, where the underlying function has the form f:R #R, and multivalued cases, where the underlying function is f:R . The main methods we review include linear triangular (or tetrahedral) interpolation, cubic triangular (CloughTocher) interpolation, triangle based blending interpolation, inverse distance weighted methods, radial basis function methods, and natural neighbor interpolation methods. We also review one method of scattered data fitting, as an illustration to the basic differences between scattered data interpolation and scattered data fitting.
Scattered Data Interpolation in Three or More Variables
 Mathematical Methods in Computer Aided Geometric Design
, 1989
"... This is a survey of techniques for the interpolation of scattered data in three or more independent variables. It covers schemes that can be used for any number of variables as well as schemes specifically designed for three variables. Emphasis is on breadth rather than depth, but there are expl ..."
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Cited by 50 (0 self)
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This is a survey of techniques for the interpolation of scattered data in three or more independent variables. It covers schemes that can be used for any number of variables as well as schemes specifically designed for three variables. Emphasis is on breadth rather than depth, but there are explicit illustrations of different techniques used in the solution of multivariate interpolation problems. List of Contents 1. Introduction 2. Rendering of Trivariate Functions 3. Tensor Product Schemes 4. Point Schemes 4.1 Shepard's Methods 4.2 Radial Interpolants 4.2.1 Hardy Multiquadrics 4.2.2 Duchon Thin Plate Splines 5. Natural Neighbor Interpolation 6. kdimensional Triangulations 7. Tetrahedral Schemes 7.1 Polynomial Schemes 7.2 Rational Schemes 8. Simplicial Schemes 8.1 Polynomial Schemes 8.2 Rational Schemes 8.3 A Transfinite Scheme 9. Multivariate Splines 10. Transfinite Hypercubal Methods 11. Derivative Generation 12. Interpolation on the sphere and other surfa...
Survey of Neural Transfer Functions
 Neural Computing Surveys
, 1999
"... The choice of transfer functions may strongly influence complexity and performance of neural networks. Although sigmoidal transfer functions are the most common there is no apriorireason why models based on such functions should always provide optimal decision borders. A large number of alternative ..."
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Cited by 42 (21 self)
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The choice of transfer functions may strongly influence complexity and performance of neural networks. Although sigmoidal transfer functions are the most common there is no apriorireason why models based on such functions should always provide optimal decision borders. A large number of alternative transfer functions has been described in the literature. A taxonomy of activation and output functions is proposed, and advantages of various nonlocal and local neural transfer functions are discussed. Several lessknown types of transfer functions and new combinations of activation/output functions are described. Universal transfer functions, parametrized to change from localized to delocalized type, are of greatest interest. Other types of neural transfer functions discussed here include functions with activations based on nonEuclidean distance measures, bicentral functions, formed from products or linear combinations of pairs of sigmoids, and extensions of such functions making rotations...
Scattered Data Fitting on the Sphere
 in Mathematical Methods for Curves and Surfaces II
, 1998
"... . We discuss several approaches to the problem of interpolating or approximating data given at scattered points lying on the surface of the sphere. These include methods based on spherical harmonics, tensorproduct spaces on a rectangular map of the sphere, functions defined over spherical triangulat ..."
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Cited by 40 (5 self)
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. We discuss several approaches to the problem of interpolating or approximating data given at scattered points lying on the surface of the sphere. These include methods based on spherical harmonics, tensorproduct spaces on a rectangular map of the sphere, functions defined over spherical triangulations, spherical splines, spherical radial basis functions, and some associated multiresolution methods. In addition, we briefly discuss spherelike surfaces, visualization, and methods for more general surfaces. The paper includes a total of 206 references. x1. Introduction Let S be the unit sphere in IR 3 , and suppose that fv i g n i=1 is a set of scattered points lying on S. In this paper we are interested in the following problem: Problem 1. Given real numbers fr i g n i=1 , find a (smooth) function s defined on S which interpolates the data in the sense that s(v i ) = r i ; i = 1; : : : ; n; (1) or approximates it in the sense that s(v i ) ß r i ; i = 1; : : : ; n: (2) Data f...