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25
Locally weighted learning
 ARTIFICIAL INTELLIGENCE REVIEW
, 1997
"... This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, ass ..."
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Cited by 594 (53 self)
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This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning t parameters, interference between old and new data, implementing locally weighted learning e ciently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.
Parallel Algorithms for Hierarchical Clustering
 Parallel Computing
, 1995
"... Hierarchical clustering is a common method used to determine clusters of similar data points in multidimensional spaces. O(n 2 ) algorithms are known for this problem [3, 4, 10, 18]. This paper reviews important results for sequential algorithms and describes previous work on parallel algorithms f ..."
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Cited by 107 (2 self)
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Hierarchical clustering is a common method used to determine clusters of similar data points in multidimensional spaces. O(n 2 ) algorithms are known for this problem [3, 4, 10, 18]. This paper reviews important results for sequential algorithms and describes previous work on parallel algorithms for hierarchical clustering. Parallel algorithms to perform hierarchical clustering using several distance metrics are then described. Optimal PRAM algorithms using n log n processors are given for the average link, complete link, centroid, median, and minimum variance metrics. Optimal butterfly and tree algorithms using n log n processors are given for the centroid, median, and minimum variance metrics. Optimal asymptotic speedups are achieved for the best practical algorithm to perform clustering using the single link metric on a n log n processor PRAM, butterfly, or tree. Keywords. Hierarchical clustering, pattern analysis, parallel algorithm, butterfly network, PRAM algorithm. 1 In...
ClosestPoint Problems in Computational Geometry
, 1997
"... This is the preliminary version of a chapter that will appear in the Handbook on Computational Geometry, edited by J.R. Sack and J. Urrutia. A comprehensive overview is given of algorithms and data structures for proximity problems on point sets in IR D . In particular, the closest pair problem, th ..."
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Cited by 73 (13 self)
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This is the preliminary version of a chapter that will appear in the Handbook on Computational Geometry, edited by J.R. Sack and J. Urrutia. A comprehensive overview is given of algorithms and data structures for proximity problems on point sets in IR D . In particular, the closest pair problem, the exact and approximate postoffice problem, and the problem of constructing spanners are discussed in detail. Contents 1 Introduction 1 2 The static closest pair problem 4 2.1 Preliminary remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Algorithms that are optimal in the algebraic computation tree model . 5 2.2.1 An algorithm based on the Voronoi diagram . . . . . . . . . . . 5 2.2.2 A divideandconquer algorithm . . . . . . . . . . . . . . . . . . 5 2.2.3 A plane sweep algorithm . . . . . . . . . . . . . . . . . . . . . . 6 2.3 A deterministic algorithm that uses indirect addressing . . . . . . . . . 7 2.3.1 The degraded grid . . . . . . . . . . . . . . . . . . ...
A Comparison of Sequential Delaunay Triangulation Algorithms
, 1996
"... This paper presents an experimental comparison of a number of different algorithms for computing the Deluanay triangulation. The algorithms examined are: Dwyer’s divide and conquer algorithm, Fortune’s sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri, an ..."
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Cited by 68 (0 self)
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This paper presents an experimental comparison of a number of different algorithms for computing the Deluanay triangulation. The algorithms examined are: Dwyer’s divide and conquer algorithm, Fortune’s sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri, and Murota, a new bucketingbased algorithm described in this paper, and Devillers’s version of a Delaunaytree based algorithm that appears in LEDA), an algorithm that incrementally adds a correct Delaunay triangle adjacent to a current triangle in a manner similar to gift wrapping algorithms for convex hulls, and Barber’s convex hull based algorithm. Most of the algorithms examined are designed for good performance on uniformly distributed sites. However, we also test implementations of these algorithms on a number of nonuniform distibutions. The experiments go beyond measuring total running time, which tends to be machinedependent. We also analyze the major highlevel primitives that algorithms use and do an experimental analysis of how often implementations of these algorithms perform each operation.
Probabilistic selflocalization for mobile robots
 IEEE Transactions on Robotics and Automation
, 2000
"... Localization is a critical issue in mobile robotics. If the robot does not know where it is, it, cannot effectively plan movements, locate objects, or reach goals. In this paper, we describe probabilistic selflocalization techniques for mobile robots that are based on the principal of maximumlikel ..."
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Cited by 62 (3 self)
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Localization is a critical issue in mobile robotics. If the robot does not know where it is, it, cannot effectively plan movements, locate objects, or reach goals. In this paper, we describe probabilistic selflocalization techniques for mobile robots that are based on the principal of maximumlikelihood estimation. The basic method is to compare a map generated at the current robot position to a previously generated map of the environment to prohabilistically maximize the agreement between the maps. This method is able to operate in both indoor and outdoor environments using either discrete features or an occupancy grid to represent the world map. The map may be generated using any method to detect features in the robot's surroundings, including vision, sonar, a d laser rangefinder. A global search of the pose space is performed that guarantees that the best position in a discretized pose space is found according to the probabilistic: map agreement measure. In addition, fitting the likelihood function with a parameterized smface allows both subpixel localization and uncertainty estimation to be performed. The application of these techniques in several experiments is described, including experimental localization results for the Sojourner Mars rover. 1
Computational geometry  a survey
 IEEE TRANSACTIONS ON COMPUTERS
, 1984
"... We survey the state of the art of computational geometry, a discipline that deals with the complexity of geometric problems within the framework of the analysis ofalgorithms. This newly emerged area of activities has found numerous applications in various other disciplines, such as computeraided de ..."
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Cited by 27 (4 self)
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We survey the state of the art of computational geometry, a discipline that deals with the complexity of geometric problems within the framework of the analysis ofalgorithms. This newly emerged area of activities has found numerous applications in various other disciplines, such as computeraided design, computer graphics, operations research, pattern recognition, robotics, and statistics. Five major problem areasconvex hulls, intersections, searching, proximity, and combinatorial optimizationsare discussed. Seven algorithmic techniques incremental construction, planesweep, locus, divideandconquer, geometric transformation, pruneandsearch, and dynamizationare each illustrated with an example.Acollection of problem transformations to establish lower bounds for geometric problems in the algebraic computation/decision model is also included.
Clustering in Massive Data Sets
 Handbook of massive data sets
, 1999
"... We review the time and storage costs of search and clustering algorithms. We exemplify these, based on casestudies in astronomy, information retrieval, visual user interfaces, chemical databases, and other areas. Sections 2 to 6 relate to nearest neighbor searching, an elemental form of clustering, ..."
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Cited by 17 (0 self)
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We review the time and storage costs of search and clustering algorithms. We exemplify these, based on casestudies in astronomy, information retrieval, visual user interfaces, chemical databases, and other areas. Sections 2 to 6 relate to nearest neighbor searching, an elemental form of clustering, and a basis for clustering algorithms to follow. Sections 7 to 11 review a number of families of clustering algorithm. Sections 12 to 14 relate to visual or image representations of data sets, from which a number of interesting algorithmic developments arise.
Training Set Expansion in Handwritten Character Recognition
 Structural, Syntactic and Statistical Pattern Recognition, pages 548– 556. LNCS 2396
, 2002
"... In this paper, a process of expansion of the training set by synthetic generation of handwritten uppercase letters via deformations of natural images is tested in combination with an approximate k Nearest Neighbor (k NN) classifier. It has been previously shown [11] [10] that approximate nearest nei ..."
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Cited by 12 (1 self)
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In this paper, a process of expansion of the training set by synthetic generation of handwritten uppercase letters via deformations of natural images is tested in combination with an approximate k Nearest Neighbor (k NN) classifier. It has been previously shown [11] [10] that approximate nearest neighbors search in large databases can be successfully used in an OCR task, and that significant performance improvements can be consistently obtained by simply increasing the size of the training set. In this work, extensive experiments adding distorted characters to the training set are performed, and the results are compared to directly adding new natural samples to the set of prototypes.
Efficient parallel algorithms for closest point problems
, 1994
"... This dissertation develops and studies fast algorithms for solving closest point problems. Algorithms for such problems have applications in many areas including statistical classification, crystallography, data compression, and finite element analysis. In addition to a comprehensive empirical study ..."
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Cited by 11 (1 self)
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This dissertation develops and studies fast algorithms for solving closest point problems. Algorithms for such problems have applications in many areas including statistical classification, crystallography, data compression, and finite element analysis. In addition to a comprehensive empirical study of known sequential methods, I introduce new parallel algorithms for these problems that are both efficient and practical. I present a simple and flexible programming model for designing and analyzing parallel algorithms. Also, I describe fast parallel algorithms for nearestneighbor searching and constructing Voronoi diagrams. Finally, I demonstrate that my algorithms actually obtain good performance on a wide variety of machine architectures. The key algorithmic ideas that I examine are exploiting spatial locality, and random sampling. Spatial decomposition provides allows many concurrent threads to work independently of one another in local areas of a shared data structure. Random sampling provides a simple way to adaptively decompose irregular problems, and to balance workload among many threads. Used together, these techniques result in effective algorithms for a wide range of geometric problems. The key
Symmetry in Data Mining and Analysis: A Unifying View based on Hierarchy
"... Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical domain of interest. “Structure ” has long been understood as s ..."
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Cited by 7 (7 self)
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Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical domain of interest. “Structure ” has long been understood as symmetry which can take many forms with respect to any transformation, including point, translational, rotational, and many others. Beginning with the role of number theory in expressing data, we show how we can naturally proceed to hierarchical structures. We show how this both encapsulates traditional paradigms in data analysis, and also opens up new perspectives towards issues that are on the order of the day, including data mining of massive, high dimensional, heterogeneous data sets. Linkages with other fields are also discussed including computational logic and symbolic dynamics.