J.K. Friedman, J.L. Bentley, R.A. Finkel, "An algorithm for finding best matches in logarithmic expected time," ACM Trans. on Math. Software, 3(1977), pp. 209--226. Home/Search Document Not in Database Summary Related Articles Check |
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Analysis of Approximate Nearest Neighbor Searching with.. - Maneewongvatana, Mount (1999) (1 citation) (Correct)
....memory. Since data sets can be large, we limit ourselves to consideration of data structures whose total space grows linearly with d and n. Among the most popular methods are those based on hierarchical decompositions of space. The seminal work in this area was by Friedman, Bentley, and Finkel [FBF77] who showed that O(n) space and O(log n) query time are achievable for fixed dimensional spaces in the expected case for data distributions of bounded density through the use of kd trees. There have been numerous variations on this theme. However, all known methods su#er from the fact that as ....
....spatial decompositions, and the kd tree in particular. In large part this is because of the simplicity and widespread popularity of this data structure. A kd tree is binary tree based on a hierarchical subdivision of space by splitting hyperplanes that are orthogonal to the coordinate axes [FBF77] It is described further in the next section. A key issue in the design of the kd tree is the choice of the splitting hyperplane. Friedman, Bentley, and Finkel proposed a splitting method based on selecting the plane orthogonal to the median coordinate along which the points have the greatest ....
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J. H. Friedman, J. L. Bentley, and R. A. Finkel, An algorithm for finding best matches in logarithmic expected time, ACM Trans. Math. Software 3 (1977), no. 3, 209--226.
Direct Reconstruction of a Displaced Subdivision - Surface From Unorganized (Correct)
.... the bounding box, we simply find the nearest point x j , calculate an attracting force vector f v i , and apply it back to the vertex v i with a projection speed parameter [0, 1] Finding a nearest point is a well known problem, and we used the kd tree searching algorithm in our implementation [3, 6]. f v i = x j b = v i f v i ) For a subdivided bounding box, it is possible that two or more vertices of the box are attracted by the same input point. In such a case, if we apply full attraction force ( 1.0) to those vertices, some of them can meet at the same position by this ....
....points. A tangent plane T x (v) n v d associated with a point x is defined by the least squares fitting plane to the neighborhood N b(x) of x, which consists of all points x i such that x x #. The nearest points are found in logarithmic time by a spatial searching algorithm [3, 6]. The user defined # should be large enough so that the neighborhood represents the local surface shape correctly. Usually 3 10 points are used to calculate a tangent plane in our implementation. After that, we project every point to the mesh. Then we assign corresponding points to each vertex v ....
J. H. Friedman, J. L. Bentley, and R. A. Finkel. An Algorithm for Finding Best Matches in Logarithmic Expected Time. ACM Trans. on Mathematical Software, 3(3):209--226, 1977. 15
Accounting for Boundary Effects in Nearest Neighbor Searching - Arya, Mount, Narayan (1996) (23 citations) (Correct)
.... Cleary analyzed the case of general uniformly distributed point sets [8] A practical and more flexible approach for nearest neighbor searching in high dimensions is based on the k d tree, as introduced by Bentley [5] and applied to the nearest neighbor problem by Friedman, Bentley and Finkel [9]. The analyses of these algorithms presented in the literature [8, 9] show that their running times contain a constant factor, which grows on the order of 2 , assuming the L# metric. The analysis in [8] assumes that the points are uniformly distributed while the analysis in [9] assumes that ....
.... sets [8] A practical and more flexible approach for nearest neighbor searching in high dimensions is based on the k d tree, as introduced by Bentley [5] and applied to the nearest neighbor problem by Friedman, Bentley and Finkel [9] The analyses of these algorithms presented in the literature [8, 9] show that their running times contain a constant factor, which grows on the order of 2 , assuming the L# metric. The analysis in [8] assumes that the points are uniformly distributed while the analysis in [9] assumes that the points are randomly chosen from some smooth underlying distribution. ....
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J. H. Friedman, J. L. Bentley, and R.A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209-- 226, September 1977.
Algorithms for Fast Vector Quantization - Arya, Mount (1993) (24 citations) (Correct)
....to it can be found rapidly [6, 11, 17, 20, 22] Some deterioration in performance occurs because the imposition of structure results in a non optimal codebook. The second approach is to preprocess the unstructured codebook so that the complexity of nearest neighbor searching is reduced [8, 9, 14, 21, 28]. Although methods based on preprocessing an unstructured codebook appear to work well in low dimensions, their complexity increases so rapidly with dimension that their running time is little better than brute force linear search in moderately large dimensions [23] In this paper we show that if ....
....this approach has been studied by us and some others from a theoretical perspective [1, 2, 10, 7] In this work, however, we are more concerned with practical aspects of the search algorithms. We present three algorithms for nearest neighbor searching: 1) the standard k d tree search algorithm [14, 23], which has been enhanced to use incremental distance calculation, 2) a further improvement, which we call priority k d tree search, which visits the cells of the search tree in increasing order of distance from the query point, and (3) a neighborhood graph search algorithm [1] in which a ....
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J. H. Friedman, J. L. Bentley, and R.A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209-- 226, September 1977.
The Trimmed Iterative Closest Point Algorithm - Chetverikov, Svirko, Stepanov, .. (2002) (2 citations) (Correct)
....combinations are difficult to analyse; in particular, convergence properties remain unclear. Computational efficiency is another important issue, since some applications require fast real time operation for medium size datasets, such as range images [10] Various data structures, like k D tree [7] or spatial bins [16] are used to facilitate search of the closest point. To speed up the convergence, normal vectors are considered, which is mainly helpful in the beginning of the iteration process [10] In this paper, we concentrate on the issue of robustness. A new robustified extension of ....
J. Friedman, J. Bentley, and R. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Trans. on Mathematical Software, 3:209--226, 1977.
Low Latency Photon Mapping Using Block Hashing - Ma, McCool (2002) (4 citations) (Correct)
....rejected during the kNN query when the group is deemed farther away from the query point then the current set of kNN candidates. 2.2. Previous Work 7 Amongst algorithms in the recursive spatial subdivision category, the kd tree [8] method is the approach commonly used to solve the kNN problem [21,66]. An advantage of the kd tree is that if the tree is balanced it can be stored as a heap in a single array, avoiding the use of pointers and memory for a separate index structure. While it has been shown that kd trees have optimal expected time complexity [9] in the worst case finding the k ....
J. H. Freidman, J. L. Bentley, and R. A. Finkel. An Algorithm for Finding Best Matches in Logarithmic Expected Time. ACM TOMS, 3(3):209--226, 1977. 2.2
Information Retrieval Using Statistical Classification - Hull (1994) (2 citations) Self-citation (Friedman) (Correct)
....term space. For example, if relevance feedback is conducted using the full text of the relevant documents, the number of terms in the query is likely to grow to be many times the number of LSI vectors, leading to a corresponding increase in search time. While data structures such as the k d Tree [25] exist which can speed the search for nearest neighbors, they are most effective in lower dimensions and only provide a partial ordering of the document collection. However, other techniques, such as query expansion, suffer just as heavily from the problems described above, and LSI performs ....
J. Friedman, J. Bentley, and R. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, 1977.
Two Algorithms for Nearest-Neighbor Search in High Dimensions - Kleinberg (1997) (91 citations) (Correct)
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J.K. Friedman, J.L. Bentley, R.A. Finkel, "An algorithm for finding best matches in logarithmic expected time," ACM Trans. on Math. Software, 3(1977), pp. 209--226.
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J.H. Friedman, J.L. Bentley, R.A. Finkel, An algorithm for finding best matches in logarithmic expected time, ACM Transactions on Mathematical Software 3 (3) (1977) 209--226.
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J. H. Friedman, J. L. Bentley, and R. A. Finkel, "An Algorithm for Finding Best Matches in Logarithmic Expected Time", ACM Transactions on Mathematical Software, vol. 3, no. 3, 1977, pp. 209--226.
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J.H. Friedman, J.L. Bentley, and R.A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, September 1977.
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J.H. Friedman, J.L. Bentley, and R.A. Finkel, "An Algorithm for Finding Best Matches in Logarithmic Expected Time," ACM Trans. Math. Software, vol. 3, no. 3, pp. 209-226, 1977.
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J. Friedman, J. Bentley, and R. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Trans. Math. Softw, 3:209--226, 1977.
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J. H. Friedman, J. L. Bentley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, September 1977.
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J. H. Friedman, J. L. Bentley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, September 1977.
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Jerome H. Friedman, Jon Bentley, and Raphael Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software,Vol. 3, No. 3, pp. 209-- 226, 1977.
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J. H. Friedman, J. L. Bentley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, 1977.
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J. H. Friedman, J. L. Bentley, and R. A. Finkel, `An algorithm for finding best matches in logarithmic expected time', ACM Transactions on Mathematical Software, 3(3), 209--226, (1977).
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J. H. Friedman, J. L. Bentley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, 1977.
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Jerome H. Friedman, Jon Louis Bentley, and Raphael Ari Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(2):209--226, June 1977.
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J. H. Friedman, J. L. Bentley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, 1977.
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J. H. Friedman, J. L. Bentley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transaction on Mathematical Software, 3(3):209 -- 226, September 1977.
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J. H. Friedman, J. L. Bentley, and R.A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, September 1977.
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Friedman, J. H., Bentley, J. H., and Finkel, R. A, An algorithm for finding best matches in logarithmic expected time, ACM Transactions on Mathematical Software, Vol.3, Num.3, 1977, pp. 209-226.
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J.H. Friedman, J.L. Bentley, and R.A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Trans. on Math Software (TOMS), (3):209--226, 1977.
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J. H. Friedman, J. L. Bentley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, September 1977.
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Jerome H. Friedman, J. Bentely, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3), 1977.
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J. H. Friedman, J. L. Bentley and R. A. Finkel, An algorithm for finding best matches in logarithmic expected time, ACM Transactions on Mathematical Software, 3 (1977), 209--226.
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J.H. Friedman, J.L. Bentley, and R.A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 209, 1977.
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J. H. Friedman, J. L. Bentley and R. A. Finkel, An algorithm for finding best matches in logarithmic expected time, ACM Transactions on Mathematical Software, 3 (1977), 209--226.
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Friedman JH Bentley JL, Finkel RA (1977) An algorithm for finding best matches in logarithmic expected time. ACM Trans Math Softw 3(3):209--226
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J. H. Friedman, J. L. Bentley, and R. A. Finkel, "An Algorithm for Finding Best Matches in Logarithmic Expected Time", ACM Transactions on Mathematical Software, vol. 3, no. 3, 1977, pp. 209--226.
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J. H. Friedman, J. L. Bentley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, September 1977.
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J.H. Friedman, J.L. Bentley, R.A. Finkel, An algorithm for finding best matches in logarithmic expected time, ACM Transactions on Mathematical Software 3 (3) (1977) 209--226.
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J. H. Friedman, J. L. Bentley, and R. A. Finkel, "An algorithm for finding best matches in logarithmic expected time," ACM Transactions on Mathmatical Software, vol. 3, no. 3, pp. 209--226, Sep. 1977.
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J. H. Friedman, J. L. Bentley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, September 1977.
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J. H. Friedman, J. L. Bentley, and R.A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209--226, September 1977.
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J.H.Friedman,J.L.Bentley,andR.A.Finkel, "An Algorithm for Finding Best Matches in Logarithmic Expected Time", ACM Transactions on Mathematical Software, vol. 3, no. 3, 1977, pp. 209--226.
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J.H. Friedman, J.L. Bentley and R.A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):200-226, 1977.
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