C. Feustel and L. Shapiro. The nearest neighbor problem in an abstract metric space. Pattern Recognition Letters, 1:125-128, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... computations ( 70 ) Fukunaga and Narendra (1975) 23] A branch and bound algorithm for computing K nearest neighbors based on a hierarchical indexing structure 1000 2D uniform samples data Euclidean distance 580 average distance computations ( 58 ) Feustel and Shapiro (1982) [20]: The nearest neighbor problem in an abstract metric space 29 randomly generated 5vertices directed graphs Graphisomorphism based discretevalued distance 3 average distance computations ( 10 ) Kamgar and Kanal (1985) 38] An improved branch and bound algorithm for computing ....

C. D. Feustel and L. G. Shapiro. "The nearest neighbor problem in an abstract metric space". Pattern Recognition Letters, 1(2):125--128, December 1982.

....is far enough outside of it. While exploring a cluster he observes that the triangle inequality may be used to eliminate some distance computations. A key point missed is that when the query is well inside of a cluster, the exterior need not be searched. Collections of graphs are considered in [14] as an abstract metric space with a metric assuming discrete values only. This work is related to the constructions of [7] In their concluding remarks the authors clearly anticipate generalization to continuous settings such as R n . The idea that vantage points near the corners of the space ....

Feustel, C. D., and Shapiro, L. G. The nearest neighbor problem in an abstract metric space. Pattern Recognition Letters (December 1982).

....R have the property that projected distances are dominated by those in the original space. The two most important such projections are i) inner product with a unit vector in Euclidean space, and ii) distance from a chosen vantage point. 2 These ideas were recognized early on in work including [8, 20, 21, 16, 29]. Taking the inner product with a canonical basis element in Euclidean space leads to the well known kd tree of Friedman and Bentley [17, 18, 4, 3] They recursively divide a pointset in R d by projecting each element onto a distinguished coordinates. Improvements, distribution adaptation, and ....

Feustel, C. D., and Shapiro, L. G. The nearest neighbor problem in an abstract metric space. Pattern Recognition Letters (December 1982).

.... of efficient model representation and access schemes in the context of graph matching have been proposed, like clustering and binary search trees [18] symbolic and attribute differences [19] sharing of common structures [20] or efficient nearest neighbor search in an abstract metric space [21]. In this paper we propose a new approach to the efficient representation and access of a potential large number of prototype graphs. It is based on the RETEmatching algorithm that was developed for the efficient determination of the conflict set, i.e. the set of applicable rules, in the forward ....

Feustel, C.D./ Shapiro, L.G.: The nearest neighbor problem in an abstract metric space, Pattern Recognition Letters, Vol. 1, pp 125--128, 1982

....codeword, which is a computationally intensive operation. Algorithms to reduce search complexity [9] 5] narrow the field of candidate codewords for which the distortion must be calculated. These techniques have their roots in pattern recognition techniques for finding nearest neighbors [12] [4]. Most fast full search measures in the literature have been limited to metrics such as the Euclidean distance. We described extensions of existing fast full search techniques to entropyconstrained vector quantization (ECVQ) in [7] In this correspondence, we present another fast full search ....

C. D. Feustel and L. G. Shapiro. The nearest neighbor problem in an abstract metric space. Pattern Recognition Letters, 1:125--128, December 1982.

....to each codeword, which is a computationally intensive operation. Algorithms to reduce search complexity [9, 5] narrow the field of candidate codewords for which the distortion must be calculated. These techniques have their roots in pattern recognition techniques for finding nearest neighbors [13, 4]. Most fast full search measures in the literature have been limited to metrics such as the Euclidean distance. We described extensions of existing fast full search techniques to entropy constrained vector quantization (ECVQ) in [7] In this correspondence, we present another fast full search ....

C. D. Feustel and L. G. Shapiro. The nearest neighbor problem in an abstract metric space. Pattern Recognition Letters, 1:125--128, December 1982.

.... Gamma y i j k . So L 1 is the familiar city block distance and L 2 is the Euclidean distance. 2 Some of the papers we mention below address the problem of finding nearest neighbors. However, their methods can be applied to finding all near neighbors with minimal change. range of the search [FS82] or if preprocessing is not allowed and only arbitrary pre computed distances are given [SW90] For the examples mentioned in Section 1 neither of these hold and, while distance computations are expensive, the O(n) cost of such an algorithm would dominate for a large data set. The other category ....

C.D. Feustel and L. G. Shapiro. The nearest neighbor problem in an abstract metric space. Pattern Recognition Letters, pages 125--128, December 1982.

....is far enough outside of it. While exploring a cluster he observes that the triangle inequality may be used to eliminate some distance computations. A key point missed is that when the query is well inside of a cluster, the exterior need not be searched. Collections of graphs are considered in [14] as an abstract metric space with a metric assuming discrete values only. This work is related to the constructions of [7] In their concluding remarks the authors clearly anticipate generalization to continuous settings such as R n . The idea that vantage points near the corners of the space ....

Feustel, C. D., and Shapiro, L. G. The nearest neighbor problem in an abstract metric space. Pattern Recognition Letters (December 1982).

....selecting the codeword with lowest distortion. Algorithms to reduce search complexity ( 1] 2] concentrate on narrowing the field of candidate codewords for which distortion must be calculated. These techniques have their roots in pattern recognition techniques for finding nearest neighbors [5] [6]. The fast full search measures described and implemented thus far have been limited to metrics such as the Euclidean distance. An algorithm for fast nearest neighbor search presented by Orchard [1] precomputes and stores the distance between each pair of codewords. When searching for the best ....

C. D. Feustel and L. G. Shapiro. The nearest neighbor problem in an abstract metric space. Pattern Recognition Letters, 1:125--128, December 1982.

....In one category, we assume that distance calculations are so expensive that even an O(n) or O(n log n) search algorithm is acceptable as long as it reduces the number of distance calculations. This is the case as long as the database size is fairly small compared to the range of the search [FS82] or if preprocessing is not allowed and only arbitrary precomputed distances are given [SW90] The other category of solutions are hierarchical and typically have an O(logn) query time given a sufficiently small range (typically too small to be practical) They are of the following form: The ....

C.D. Feustel and L. G. Shapiro. The nearest neighbor problem in an abstract metric space. Pattern Recognition Letters, December 1982.

....at the lowest level, Fukunaga further points out that the triangle inequality may be used to eliminate additional distance computations. A key point apparently overlooked, is that when the query is well inside of a cluster, the exterior need not be searched. Collections of graphs are considered in [11] as an abstract metric space with a metric assuming discrete values only. This work is thus highly related to the constructions of [7] In their concluding remarks the authors correctly anticipate generalization to more continuous settings such as R n . The kd tree of Friedman and Bentley [12, ....

....provide a framework for drawing more conclusions. The ZPS distribution restriction is key to achieving them; and our overall outlook in which finite cases are imagined to be drawn from a larger more continuous space, distinguishes in part this work from the discrete distance setting of [7, 11]. 2.6 Set Perspectives. We have seen that a single distinguished element p, induces a pseudo metric d p , which is always dominated by d. More generally, we observe that each size n finite subset P of a metric space, considered as vantage points, induces a natural mapping into Euclidian n space. ....

C. D. Feustel and L. G. Shapiro, "The nearest neighbor problem in an abstract metric space," Pattern Recognition Letters, December 1982.

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C. Feustel and L. Shapiro. The nearest neighbor problem in an abstract metric space. Pattern Recognition Letters, 1:125-128, 1982.

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C. D. Feustel and L. G. Shapiro, "The nearest neighbor problem in an abstract metric space", in Pattern Recognition Letters, volume 1, pages 125--128, 1982.

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C. Feustel and L. Shapiro. The nearest neighbor problem in an abstract metric space. Pattern Recognition Letters, 1:125-128, 1982.

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