D. L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Transactions on Systems, Man and Cybernetics, 2:408--420, 1972. 4  Home/Search   Document Not in Database   Summary   Related Articles   Check

....boundaries with other surfaces besides hyperplanes. Priebe et al. 85] 84] model the decision surfaces with balls. 3 Editing to Improve Performance Methods that have as their goal the improvement of recognition acuracy rather than data reduction are called editing rules. In 1972 Wilson [132] conceived the idea of editing and proposed the following algorithm. PREPROCESSING A. For each i: 1. Find the k nearest neighbors to X i among fX; Y g (not counting X i ) 6 2. Classify X i to the class associated with the largest number of points among the k nearest neighbors (breaking ties ....

....DECISION RULE Classify a new unknown pattern Z using the 1 NN rule with the edited subset of fX; Y g. This simple editing scheme is so powerful that the error rate of the 1 NN rule that uses the edited subset converges to the Bayes error. We remark here that a gap in the proof of Wilson [132] was pointed out by Devijver and Kittler [34] but alternate proofs were provided by Wagner [128] and Penrod and Wagner [82] Wilson s deleted nearest neighbor rule deletes all the data misclassi ed by the kNN majority rule. A modi ed editing scheme was proposed in 2000 by Hattori and Takahashi ....

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D. L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Transactions on Systems, Man and Cybernetics, 2:408-420, 1972.

....a limiting factor in many cases. This problem can be approached from two points of view: trying to reduce the number of prototypes without degrading the classification power, or using a fast nearest neighbors search algorithm. The first approach has been widely studied in the literature. Editing [12], 3] condensing [6] and their multiple variations are well known representatives. These methods have shown good results equaling or sometimes improving the Work partially supported by the Spanish CICYT under grant TIC2000 1703 CO3 01 classification rates of the k NN rule. Their power resides ....

D.L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Trans. on Systems, Man and Cybernetics, 2:408--420, 1972.

....While the asymptotic optimality of this rule is well know [1] when the number of prototypes is not large enough performance can degrade dramatically. Unfortunately, this is quite often the case in real applications. One idea to circumvent this problem is the use of Editing Techniques [11, 10, 8, 2, 6, 3] which attempt to clean interclass overlap regions, thereby leading to smoother NNbased decision boundaries between classes and hopefully increasing classification accuracy. In [7] a new editing technique called Weighting Prototype Editing (WPE) was introduced . Rather than aiming at ....

....box distance function for the editing techniques tested; that is, a square matrix of distances between every pair of training prototypes has been computed using the TD procedures. For comparison purposes, these distances are supplied both to the well known Wilson editing technique [11] and to the WPE technique here proposed. In the test phase, TDs between test and training images are used for direct NN classification, as well as for classification with the sets edited by Wilson s and the WPE techniques. Wilson s editing technique needs a parameter which is the number of NNs ....

D.L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Trnas. Syst., Man, Cyber, SMC-2:408--421, May/June 1972.

....to the first group. Editing methods are much related to the nearest neighbours (NN) techniques [2] Some of them are briefly cited in the following lines. In [3] is proposed to include in the set of prototypes those examples whose classification is wrong using the nearest neighbour technique; [9] proposed to eliminate the examples with incorrect k NN classification; the works of [6] and [7] follows the same idea. Other variants are based on Voronoi diagrams [4] Gabriel neighbours (two examples are said to be Gabriel neighbours if their diametrical sphere does not contain any other ....

....P I P Figure 6. One possible solution. Before formally exposing the algorithm, we will briefly explain its application. Consider the situation depicted in figure 7: the projection of the examples on the abscissas axis produce four ordered sequences I, P, I, P corresponding to the examples [9, 3, 5, 1, 11], 8] 7] 4, 6, 2, 12, 10] Identically, with the projection on the ordinates axis we can obtain the sequences P, I, P, I formed by the examples [12, 10, 8, 6, 4] 11] 2] 9, 7, 5, 3, 1] Each sequence represents a rectangular region as possible solution of a classifier and the initial ....

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Wilson, D. Asymptotic Properties of Nearest Neighbor Rules using Edited Data. IEEE Transactions on Systems, Man and Cybernetics 2. (1972).

....While the asymptotic optimality of this rule is well know [1] when the number of prototypes is not large enough performance can degrade dramatically. Unfortunately, this is quite often the case in real applications. One idea to circumvent this problem is the use of Editing Techniques [11, 10, 8, 2, 6, 3] which attempt to clean interclass overlap regions, thereby leading to smoother NNbased decision boundaries between classes and hopefully increasing classification accuracy. In [7] a new editing technique called Weighting Prototype Editing (WPE) was introduced . Rather than aiming at ....

....box distance function for the editing techniques tested; that is, a square matrix of 7291 7291 distances between every pair of training prototypes has been computed using the TD procedures. For comparison purposes, these distances are supplied both to the well known Wilson editing technique [11] and to the WPE technique here proposed. In the test phase, TDs between test and training images are used for direct NN classification, as well as for classification with the sets edited by Wilson s and the WPE techniques. Wilson s editing technique needs a parameter k which is the number of NNs ....

D.L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Trnas. Syst., Man, Cyber, SMC-2:408--421, May/June 1972.

....these divergent translations are not filtered out, severe distortions can result, which almost surely would cause a false fault detection. The first approach we tested in order to solve this problem was based on the editing concept used in classifier design in the field of pattern recognition [12], 6] The idea is to delete every control point having a translation direction with a deviation larger than a given threshold from the direction that would be assigned to that particular point in the final registration step if it was not a control point. The process is repeated until no point is ....

D.L. Wilson, "Asymptotic Properties of Nearest Neighbor Rules using Edited Data", IEEE Trans. on Systems, Man and Cybernetics, Vol. 2, pp. 408-420, 1972

....behaviour as both k and n tend to infinity, while k=n is kept small. However, for finite data sets it is difficult to fulfill at once these three requirements for n and k in practice. It is also well known that the performance of the plain NN rule can be boosted by using simple Editing Techniques [10, 9, 8, 2, 6, 3] which attempt cleaning inter class overlap regions, thereby leading to smooth NN based decision boundaries between classes. Under the unbounded data setsize (and computing time) assumption, the Multi Edit algorithm [2] has been shown to yield sets of prototypes for which the plain 1 NN rule ....

....in a fairly wide region. A large reduction (condensing) of the number of prototypes is also achieved in this region 3 Experiments an Results. Experiments were carried out to compare the proposed method with other editing techniques. In particular, no editing (1 NN) Wilson Editing (W(k) [10], Repeated Holdout Editing (or MultiEdit, ME(B,I) 2] Repeated CrossValidation Editing (CV(B,I) 4] and the proposed Weighted Prototype Editing (WP E(k,h) were considered. In these methods, k is the number of neighbors of the k NN rule, B is the number of blocks in the partition, I is the ....

D.L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Trnas. Syst., Man, Cyber, SMC-2:408--421, May/June 1972.

....method proposed by Hart [4] Hart s method) It gradually builds the reference set starting with an empty set and including elements of Z until a consistent set is reached. The second approach aims at low error rate in general (not only on Z) The classical example is the Wilson s method [7]. The 3 nn classi er is run on Z by taking each object in turn aside and trying to classify it using the rest of Z as the reference set. All misclassi ed objects are then deleted from Z thereby leaving the reduced Z as the new reference set. Some authors advocate applying the methods in a ....

....tested on the (unseen to that point) testing part. Then the to parts are swapped and the training testing is repeated. The averaged testing results are considered. Table 2: Data editing and feature selection methods Original set No editing, no feature selection Hart (H) 4] Editing Wilson (W) [7] W followed by H (W H) Feature selection SFS H SFS Editing and W SFS feature selection W H SFS (cascade) SFS H SFS W SFS W H Editing and GA feature selection Incremental HC (IHC) simultaneous) Stochastic HC (SHC) show the data on one plot, Figure 3. The methods are plotted as points, ....

D.L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Transactions on Systems, Man, and Cybernetics, SMC-2:408-421, 1972.

....of instances from memory could also alleviate the practical processing burden of the k NN classifier kernel, since it would have less instances to compare new instances to. This potential double pay off spawned a distinct line of work on editing in the k NN classifier quite early Hart (1968) and Wilson (1972) (for overviews, cf. Dasarathy (1991; van den Bosch (1999) TiMBL offers an implementation of one particular editing algorithm called IB2 (Aha, Kibler, and Albert, 1991) an extension to the basic IB1 algorithm introduced in the same article. IB2 implements an incremental editing strategy. ....

Wilson, D. 1972. Asymptotic properties of nearest neighbor rules using edited data. Institute of Electrical and Electronic Engineers Transactions on Systems, Man and Cybernetics, 2:408--421.

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D. L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Transactions on Systems, Man and Cybernetics, 2:408--420, 1972. 4

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D. L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Transactions on Systems, Man and Cybernetics, 2:408--420, 1972.

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D. L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Transactions on Systems, Man and Cybernetics, 2:408-420, 1972.

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Wilson, D.: Asymptotic properties of nearest neighbor rules using edited data. IEEE Transactions on Systems, Man, and Cybernetics 2 (1972) 408--421

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Wilson, D. Asymptotic Properties of Nearest Neighbor Rules using Edited Data. IEEE Transactions on Systems, Man and Cybernetics 2. (1972).

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Wilson, D.L.: Asymptotic Properties of Nearest Neighbor Rules Using Edited Data. IEEE Transactions on Systems, Man, and Communications 2 (1972) 408--421

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Wilson, D. L. Asymptotic Properties of Nearest Neighbor Rules Using Edited Data. IEEE Transactions on Systems, Man, and Communications 2, 3 (1972), 408--421.

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D. L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Transactions on Systems, Man and Cybernetics, 2(3):408--421, 1972.

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D.L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Trans. on Systems, Man and Cybernetics, 2:408420, 1972.

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D.L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Transactions on Systems, Man, and Cybernetics,SMC- 2(3):408--421, 1972.

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D. L. Wilson. Asymptotic properties of nearest neighbor rules using edited data. IEEE Transactions on Systems, Man and Cybernetics, 2(3):408--421, 1972.

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Wilson, D.L. Asymptotic Properties of Nearest Neighbor Rules Using Edited Data. IEEE Transactions on Systems, Man, and Cybernetics 2 (1972), 3, 408-421.

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Wilson, D. (1972). Asymptotic Properties of Nearest Neighbor Rules using Edited Data. IEEE Transactions on Systems, Man and Cybernetics 2.

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D. L. Wilson. Asymptotic Properties of Nearest Neighbor Rules Using Edited Data. In IEEE Transactions on Systems, Man and Cybernetics, volume 2-3, pages 408--421, 1972.

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Wilson, D. L. Asymptotic Properties of Nearest Neighbor Rules Using Edited Data. IEEE Transactions on Systems, Man, and Communications 2, 3 (1972), 408--421.

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Wilson, D.L. (1972). "Asymptotic Properties of Nearest Neighbor Rules using Edited Data", IEEE Trans. on Systems, Man and Cybernetics, Vol.. 2, pp.408-420.

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