B. Kamgar and L. N. Kanal, "An improved branch and bound algorithm for computing k-nearest neighbors", in Pattern Recognition Letters,vol- ume 3, pages 7--12, 1985. 128  Home/Search   Document Not in Database   Summary   Related Articles   Check

....systems (GIS) pattern recog ACM Transactions on Database Systems 24, 2 (June 1999) pp. 265 318 3 nition, document retrieval, and learning theory. Almost all of these algorithms, many of them coming from the field of computational geometry, are for points in a d dimensional vector space [12, 16, 21, 22, 33, 45, 51], but some allow for arbitrary spatial objects [26, 30] although most are still limited to a point as the query object. In many applications, a rough answer suffices, so that algorithms have been developed that return an approximate result [4, 10, 54] thereby saving time in computing it. Many of ....

....most are still limited to a point as the query object. In many applications, a rough answer suffices, so that algorithms have been developed that return an approximate result [4, 10, 54] thereby saving time in computing it. Many of the above algorithms require specialized search structures [4, 10, 16, 22, 33], but some employ commonly used spatial data structures. For example, algorithms exist for the k d tree [12, 21, 41, 51] quadtree related structures [29, 30] the Rtree [45, 54] the LSD tree [26] and others. In addition, many of the algorithms can be applied to other spatial data structures. To ....

B. Kamgar-Parsi and L. N. Kanal. An improved branch and bound algorithm for computing k-nearest neighbors. Pattern Recognition Letters, 3(1), January 1985.

....p #M) D(B p #M p ) # because, D(Min p #M) D(B p #M p ) 0 # then, D(X#B p ) D(X#X i ) # D(X#B) D(X#X i ) # By the definition of nearest search,we conclude that, no X i 2 S p can be the nearest neighbor to X. These rules is actually very similar to those in branch and bound algorithm [28] . The main differentbetween these two rules and those in branchand bound algorithm is in branch and bound algorithm, they use the absolute distance as the measurement. While in our elimination rules, we use fuzzy membership value as the measurement, which is more flexible then using absolute ....

B. Kamgar and L. N. Kanal, "An improved branch and bound algorithm for computing knearest neighbors," Pattern Recognition Letters, vol. 3, pp. 7--12, Jan. 1985. 9

....by using an inverted file structure for retrieval [44, 43, 47] On the other hand, the hierarchical approach transforms a feature space into a sequence of nested clusters and builds a hierarchical binary indexing tree (RPCL b tree) based on the clusters. We then apply a branchand bound technique [38] on the indexing structure for efficient retrieval (see Section 5.5 for details) In short, these two approaches make use of the information of natural clusters for efficient and effective indexing and retrieval. Our experimental results show that: 1. RPCL is faster than k means, competitive ....

.... 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 k nearest neighbors based on a hierarchical indexing structure 1000 2D samples uniform sample data Euclidean distance 165 average distance computations ( 16.5 ) Roussopoulos et al. 1995) 61] Nearest neighbor queries for ....

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B. Kamgar and L. N. Kanal. "An improved branch and bound algorithm for computing k-nearest neighbors". Pattern Recognition Letters, 3(1):7--12, January 1985.

....search algorithms are actually nearest neighbour search algorithms with an option to ignore nodes that are not close enough to the query vector. Hence, we can utilize the algorithms developed for nearest neighbour searches Burkhard and Keller (1973) Fukunaga and Narendra (1975) Brin (1995) Kamgar Parsi and Kanal (1985); Hjaltason and Samet (1995) Roussopoulos et al. 1995) to do the search. Region queries can be answered by searching all the nodes whose envelope intersect the given region. If we only care about the final result, then there will not be much difference between the search algorithms. To obtain a ....

....bound of the distance between the query point and the nodes centroid Two rules based on the triangle inequality. The pruning criteria used in (Burkhard and Keller, 1973; Fukunaga and Narendra, 1975) is further improved by refinements based on the minimum distance of the points to the centroids (Kamgar Parsi and Kanal, 1985). Some other variations of the algorithm can be found in (Brin, 1995) Hjaltason and Samet (1995) BFS Minimum distance There are some criteria to prevent entering duplicates, but there is no criteria to delete entries from the queue once it is inserted except when it finally get processed. White ....

KAMGAR-PARSI, B. and KANAL, L. N. (1985). An improved branch and bound algorithm for computing k-nearest neighbours. Pattern Recognition Letters, 3:7--12.

....proceeds to the lower nodes until it reaches a leaf node. In this leaf node, the elements will be the results of the query if they satisfy the criteria of the nearest neighbor search. To ensure the index accuracy is 100 , we can implement backtracking based on a branch and bound algorithm [1]. In this branch and bound algorithm, each node is tested to determine whether or not possibly containing the nearest neighbor to a query by a set of rules [5] 3 Regression Model for RPCL b tree 3.1 Index Efficiency Measurement In this paper, we define the index efficiency measurement, Y ,as ....

B. Kamgar and L. N. Kanal. An improvedbranch and bound algorithm for computingk-nearest neighbors. Pattern Recognition Letters, 3(1):7--12,January 1985.

....lower bounds is greater than the distance to the kth nearest neighbor found so far, the point can be eliminated from consideration without explicitly calculating the distance to that point. Subsets of points can also be eliminated by ndingalower bound on the distance to an enclosing hypersphere [1,12,17,18,27,42]. In low dimensional spaces both types of nearest neighbor algorithms have been shown to perform drastically better than the brute force approach. In low dimensions most of these algorithms achieve O(log n # ) search time and require only O(n # log n # ) preprocessing time and storage, where n # ....

....the distance from each point, x # # S # , to the query point, q. Rule 2: No point x # in the terminal node i can be the kth nearest neighbor of q if # d(x # ;q) #d(M # ;q) # d(M # ;x # )# Several additional rules have been proposed to eliminate more points than the rules described here [18]. However, Larsen and Kanal have shown these additional rules are rarely invoked, especially for highdimensional problems [23] Other improvements have been suggested by various researchers but the additional overhead imposed by more extensiverulechecking often outweighs the savings [16,26,32] ....

[Article contains additional citation context not shown here]

Behrooz Kamgar-Parsi and Laveen N. Kanal. An improved branch and bound algorithm for computing k-nearest neighbors. Pattern Recognition Letters, 3:7-12, January 1985.

....in O(log n (1=ffl) d ) time (assuming fixed d) Recently, Clarkson [16] has presented an alternative approach in which the constant factors show a lower dependence on the dimension. The chromatic version of the k nearest neighbor problem has been studied in applications contexts (see e.g. [20, 25, 26, 27]) but not from the perspective of worst case asymptotic complexity. One reason is that in the worst case, it is not clear how to determine the most common color among the k nearest neighbors without explicitly computing the k nearest neighbors. However, in many of the applications of chromatic ....

B. Kamgar-Parsi and L. N. Kanal. An improved branch-and-bound algorithm for computing k-nearest neighbors. Pattern Recognition Letters, 3:7--12, 1985.

....pursuit required more than a week of CPU time, while SPC required about one hour. The reason is that our algorithm does not scale with the dimension of the data D, whereas the complexity of projection pursuit increases 5 Near neighbors can be efficiently computed by branch and bound algorithms (Kamgar Parsi and Kanal 1985) whose computational complexity is of order O(N log N) 1 2) 6 We thank Jerome Friedman for allowing public use his program. a) ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVXYZ W W ABCDEFGHJKLMNOPSTVXZ IRY QU ABCDEGJKLMNOPTVZ HFSX ABCDEGJKMNPTVZ W IR Y U Q I R ABDEGJKPTV W ....

Kamgar-Parsi, B., Kanal, L.N. 1985. "An improved branch and bound algorithm for computing k--nearest neighbors, Pattern recognition letters 3, 7--12.

....by the importance of these queries in fields including geographical information systems (GIS) pattern recognition, document retrieval, and learning theory. Almost all of these algorithms, many of them coming from the field of computationalgeometry, are for points in a d dimensional vector space [12, 16, 21, 22, 33, 45, 51], but some allow for arbitrary spatial objects [26, 30] although most are still limited to a point as the query object. In many applications, a rough answer suffices, so that algorithms have been developed that return an approximate result [4, 10, 54] thereby saving time in computing it. Many of ....

....most are still limited to a point as the query object. In many applications, a rough answer suffices, so that algorithms have been developed that return an approximate result [4, 10, 54] thereby saving time in computing it. Many of the above algorithms require specialized search structures [4, 10, 16, 22, 33], but some employ commonly used spatial data structures. For example, algorithms exist for the k d tree [12, 21, 41, 51] quadtree related structures [29, 30] the Rtree [45, 54] the LSD tree [26] and others. In addition, many of the algorithms can be applied to other spatial data structures. To ....

B. Kamgar-Parsi and L. N. Kanal. An improved branch and bound algorithm for computing k-nearest neighbors. Pattern Recognition Letters, 3(1), January 1985.

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B. Kamgar and L. N. Kanal, "An improved branch and bound algorithm for computing k-nearest neighbors", in Pattern Recognition Letters,vol- ume 3, pages 7--12, 1985. 128

No context found.

Kamgar-Parsi, B. and Kanal, L.N., \An improved branch and bound algorithm for computing k-nearest neighbors", Pattern Recognition Letters, 3, 7-12, 1985.

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