Enrique Vidal. New formulation and improvements of nearest-neighbour approximating and eliminating search algorithm (aesa). Pattern Recognition Letters, 15:17, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the number of distance computations have been proposed. For data that can be represented in a vector space, branch and bound search algorithms have been proposed [2, 3, 4, 5, 6] For nearest neighbors in a metrical space, several approximating and eliminating search algorithms (AESA) are available [7, 8, 9, 10, 11]. In the present work, a branch and bound algorithm is proposed that searches the nearest vectors in a vector space where the dissimilarity between two vectors is expressed by the euclidean distance. The main contribution consists of a very efficient hierarchical decomposition that uses ....

E. Vidal, "New formulation and improvements of the nearest-neighbour approximation and elimination search alorithm (AESA)," Pattern Recognition Letters, vol. 15, pp. 1--7, January 1994.

.... strings, trees or graphs and the distance functions can be some variants of the edit distance ( 9] 10] Many general metric space k NN fast search algorithms have been developed trough these years for the special case where k = 1 (Fukunaga and Narendra s [3] Kalantary and McDonald s [5] AESA [8], LAESA [7] TLAESA [6] One of these algorithms has been extended for the general case (k AESA [1] This paper proposes an extension of LAESA (Linear Approximation Elimination Search Algorithm) fast 1 NN search algorithm to cope with the k NN problem. 2 The LAESA As an evolution of ....

Vidal, E.: New formulation and improvements of the Nearest-Neighbour Approximating and Eliminating Search Algorithm (AESA). Pattern Recognition Letters (1994) 15 17

....image coherence properties, such as the technique NorW described earlier in Section 4.2. Such an approach has been found to improve the overall cost of the search despite the additional cost of improving the initial match [131] Similarly, the additional cost of using such techniques as the AESA [171, 144, 172, 116] to order the codewords may also result in an overall reduction in the cost of the search. The list of things we can do to improve the search goes on. The framework we proposed allows us to consider solutions for each component under certain assumptions which may be specific to a particular ....

Enrique Vidal. New formulation and improvements of nearest-neighbour approximating and eliminating search algorithm (aesa). Pattern Recognition Letters, 15:1--7, 1994.

....the number of distance computations have been proposed. For data that can be represented in a vector space, branch and bound search algorithms have been proposed [3, 4, 8] For nearest neighbors in a metrical space, several approximating and eliminating search algorithms (AESA) are available [9, 6, 10, 7, 5]. In the present work, a new branch and bound algorithm is proposed that searches the nearest vectors in a vector space where the dissimilarity between two vectors is expressed by the euclidean distance. The main contribution consists of a very efficient hierarchical decomposition that uses ....

E. Vidal. New formulation and improvements of the nearest-neighbour approximation and elimination search alorithm (AESA). Pattern Recognition Letters, 15:1--7, January 1994.

....guarantee optimality. 4.6 Distance Matrix Methods 4.6.1 AESA The distance based index methods that we have considered so far impose a hierarchy on the set of objects that guides the order of distance computations during query evaluation. AESA (Approximating and Eliminating Search Algorithm) [67, 68] 20 takes another approach. During preprocessing, all O#N 2 # interobject distances are computed for the N objects in S and stored in a matrix. At query time, the distance matrix is used to provide lower bounds on distances to objects whose distances have not yet been computed, based on object ....

.... than competing methods and was argued to have constanttime behavior with respect to the size of the data set [67] These benefits are obtained at the expense of quadratic space complexity, quadratic time preprocessing cost, and linear time and storage overhead 20 The difference between [67] and [68] lies in the presentation of the algorithm and in the order in which the objects are chosen whose distance from the query object is computed that is, in the approximating step (see footnote 23 below) 43 during search. Thus, although promising, the method is practical only for relatively ....

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E. Vidal. New formulation and improvements of the nearest-neighbour approximating and eliminating search algorithm (aesa). Pattern Recognition Letters, 15(1):1--7, January 1994.

....On the other hand, when working on a metric space 1 in which the temporal cost of calculating the distance between two prototypes is high (as for instance the edit distance when classifying handwritten characters [8] the exhaustive search becomes impractical. Several algorithms (AESA [7], LAESA [5] and TLAESA [4] among others) have been developed which nd the nearest neighbour in a metric space with a low number of distance calculations. Also, the AESA algorithm has been extended [1] to nd the k nearest neighbours with a low number of distance calculations. In this paper, we ....

Vidal, E.: New formulation and improvements of the Nearest-Neighbour Approximating and Eliminating Search Algorithm (AESA). Pattern Recognition Letters (1994) 15 17

....in which the computation of the distance between two elements requires too much time, and thus this classi cation technique becomes impractical. Recently, some algorithms have been developed to nd the nearest neighbour in linear time while highly reducing the number of distance computations [3, 4, 5], thus allowing for a practical use of this classi cation method in those applications where the computation of the distance is very time consuming. One of these algorithms is LAESA [4] which nds the nearest neighbour to a given sample, while maintaining the average number of distance ....

E. Vidal, New formulation and improvements of the Nearest-Neighbour Approximating and Eliminating Search Algorithm (AESA). Pattern Recognition Letters, (1994) 15, pp. 17.

....in which the computation of the distance between two elements requires too much time, and thus this classi cation technique becomes unpractical. Recently, some algorithms have been developed to nd the nearest neighbour in linear time while highly reducing the number of distance computations [3, 4, 5], thus allowing the practical utilization of this classi cation method in those applications where the computation of the distance is highly time consuming. One of these algorithms is the LAESA [4] which nds the nearest neighbour to a given sample, while maintaining the average number of ....

E. Vidal, New formulation and improvements of the Nearest-Neighbour Approximating and Eliminating Search Algorithm (AESA). Pattern Recognition Letters, (1994) 15, pp. 17.

....d are 3 to 8. There are several improvements reported on the AESA, e.g. a version using only linear storage by Ramasubramanian and Paliwal [8] This approach is based on a new spherical distance coordinate formulation, the so called (Incremental) Fixed Anchor Point AESA ( I)FAPAESA) Moreover in [13] and [14] new formulations and slight extensions of [12] are given, e.g. the Reduced Overhead AESA (ROAESA) In all these papers the application to the hypercube with the Hamming distance metric is reported, but the examples given there are only for dimension 10 or less. This means that we have at ....

E. Vidal, New formulation and improvements of the Nearest-Neighbour Approximating and Eliminating Search Algorithm (AESA), Pattern Recognition Letters 15, 1994, pp 1-7

....working on methods to attain the minimum and plan to extract from these information on how to construct function f a . Also, we have observed that the use of the improved edit costs reduces the computational cost (in terms of the number of computed distances) of a fast nearest neighbour classifier [8] [9] Acknowledgements: The authors wish to thank the Comisi on Interministerial de Ciencia y Tecnolog ia of the Government of Spain for financial support through projects TIC93 0633 C02 and TIC95 0984 C0201, and Rafael Carrasco and Jos e Oncina for interesting suggestions. ....

Enrique Vidal: "New formulation and improvements of the Nearest-Neighbour Approximating and Eliminating Search Algorithm (AESA)" Pattern Recognition Letters 15 (1994) 1--7.

....of d are 3 to 8. There are several improvements reported on AESA, e.g. a version using only linear storage by Ramasubramanian and Paliwal [4] This approach is based on a new spherical distance coordinate formulation, the so called (Incremental) Fixed Anchor Point AESA ( I)FAPAESA) Moreover in [6] and [7] new formulations and slight extensions of [5] are given, e.g. the Reduced Overhead AESA (ROAESA) In all these papers the application to the hypercube with the Hamming distance metric is reported, but the examples given there are only for dimension 10 or less. This means that a full table ....

E. Vidal, New formulation and improvements of the Nearest-Neighbour Approximating and Eliminating Search Algorithm (AESA), Pattern Recognition Letters 15, 1994, pp 1-7

....Algorithm (AESA) is probably the fastest one in terms of distance computations required during NN search. Although it was originally developed using geometric arguments [4] an improved version which formally adheres the algorithmic strategy of (bestfirst) Branch Bound has been recently proposed [5]. According to the latter version, the AESA searches for the distance from a test sample to its NN prototype through a very tight Triangle Inequality based lower bound function, both for selecting prototypes which are gradually closer to the test sample (Approximation) and forpruning out those ....

....can be eliminated during these iterations. Consequently, almost the whole set of prototypes is repeatedly processed (at least k times) and the overall overhead (computational cost not alloted to distance computing) becomes significant. In this paper we present the direct extension of the AESA [5] for k NN search, and an improved extension which introduces a Triangle Inequalitybased upper bound function for keeping the overhead low. Results of a number of experiments involving synthetic data are reported, showing that both extensions, and especially the last one, lead to computational ....

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E. Vidal. New formulation and improvements of the nearestneighbours in approximating and eliminating search algorithm (AESA). Pattern Recognition Letters, 15(1), 1994.

.... time, and a linear overhead (computing time not allotted to distance calculations) Although the AESA was originally developed from pure geometric arguments, an improved version which formally adheres the algorithmic strategy of (bestfirst) Branch and Bound has been recently proposed [5]. This improved version has been used as a baseline algorithm for new techniques reducing its computational cost. In particular, the Linear AESA (LAESA) gets over the quadratic preprocessing complexity and cuts it down to linear bounds while keeping the average number of distance computations to ....

....space (E; d) a set of prototypes P ae E and a test sample y 2 E, the NN search problem consists of finding the prototype p 2 P that minimizes its distance to the test sample. The Approximating and Eliminating Search Algorithm (AESA) efficiently solves this problem as discussed below (see [4, 5, 6] for a formal description) The AESA works by iteratively considering candidate prototypes for computing their distance to y and thus updating a current nearest neighbour, p . A set of alive prototypes contains those prototypes that can not be decided as to whether they are closer to y than ....

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E. Vidal. New formulation and improvements of the Nearest-Neighbour Approximating and Eliminating Search Algorithm (AESA). Pattern Recognition Letters, 15:1--7, 1994.

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Enrique Vidal. New formulation and improvements of nearest-neighbour approximating and eliminating search algorithm (aesa). Pattern Recognition Letters, 15:17, 1994.

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E. Vidal, New formulation and improvements of the nearest neighbor approximating and eliminating search algorithm, Pattern Recognition Lett. 15 (1994) 1}8.

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