| Ludmila I. Kuncheva and C.J. Whitaker. Measures of Diversity in Classifier Ensembles. Machine Learning, 51:181--207, 2003. |
....for solving a specific learning problem. We can measure the dependence among the outputs of a learning machine using di#erent statistical tools such as Cramer s V or the contingency coe#cient C [5] that are both # based, the covariance and the correlation coe#cient statistics, the Q statistic [6], or also non parametric correlation coe#cients as the Spearman rank order correlation coe#cient or the Kendall s tau [7] In this paper we use some mutual information based measures for the evaluation of dependence among outputs errors in a learning machine proposed in [10] The main idea behind ....
L. Kuncheva and C. Whitaker. Measures of diversity in classifier ensembles. 2001. (to appear).
.... such that lower in the list the combination of classifiers becomes more successful due to the fact that classifiers are increasingly different and still informative [5,32] How different the resulting classifiers are and especially how this should be measured is an open, but heavily studied topic [20]. It should be realized that training sets for various classifiers may have different sizes and that these sets in particular may differ from a possible training set for the combining classifier as well as from an evaluation set. The objects in these sets need to have representations that can be ....
....region of the object x to be classified. Next, the classification is done by the base classifier assigned to that region. Selection of base classifiers appears to work surprisingly well, even if just a small set of objects is used to define the regions. The large comparison experiment reported in [20] shows the best results for a combiner based on a selection procedure originally proposed in [33] 4.5 The general combining classifier The outputs of the base classifiers can be used as the input features of a general classifier used for combining, e.g. the Parzen classifier, a neural network ....
L.I. Kuncheva, C.J. Whitaker, Measures of diversity in classifier ensembles (submitted).
....ma be a good rule [8] Other combining rules, like minimum, median or majorit voting behave in a similar wa . Having significantl di#erent base classifiers in a collection is important since this gives raise to essentiall di#erent solutions. The concept of diversit is, thereb , crucial [9]. There are various wa s to describe the diversit , usuall producing a single number attributed to the whole collection of base classifiers. Later in this paper, we will use it di#erentl . F. Roli and J. Kittler (Eds. MCS 2002, LNCS 2364, pp. 137 148, 2002. c Springer Verlag Berlin ....
....and not with arbitrary functions of the original features. To achieve that, we propose to studythe collection of classifier pairwise di#erences, an n n dissimilaritymatrix D,before combining them into an output combiner. The dissimilarityvalue maybe based on one of the diversitymeasures [9], like the disagreement [7] Such a matrix D can be then embedded into a space , k n, in a (non )linear way. This means that classifiers are represented as a set of n points in such that their Euclidean distances are identical to the original dissimilarities, given by D.Itis also possible ....
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L.I. Kuncheva and C.J. Whitaker. Measures of diversity in classifier ensembles. submitted, 2002.
....role in performance improvement [15] A plot of the scores in a twodimensional space from the training data for the String F ilter combination is shown in Figure 6.4. The correlation coe#cient, #, between the matching scores can be used as a measure of diversity between a pair of matchers [110]. A positive value 191 Table 6.2: Combining two fingerprint matchers. CS is the class separation statistic. CS and # are computed from the training data. Ranks by EER (Equal Error Rate) are computed from the independent test data. Combination CS (rank) rank by EER # String F ilter 1.95 (1) 1 ....
L. I. Kuncheva, C. J. Whitaker, "Measures of Diversity in Classifier Ensembles", submitted to Machine Learning, 2000.
....we calculate some pairwise measure of diversity and average it across all pairs to get a value for the whole ensemble. An immediate equivalent of the total diversity H(P i , P j ) assuming that # i and # j are two populations produced by classifiers D i and D j is the measure of disagreement Dis [7, 13, 22]. We consider the oracle type of outputs from classifiers D i and D j , i.e. for every object in the data set, the classifier is either correct (output 1) or wrong (output 0) Then the populations of interest consist of 0 s and 1 s. We do not assume that the new distribution is simply a mixture ....
....and what is a good measure of diversity. We will leave this question unanswered here, just acknowledging the diversity of diversity , and will abstain from strongly advocating one measure or definition over another. In our previous studies we sightly favored the Q statistic (for oracle outputs) [13] because of its: a) potential sensitivity to small disagreements; b) value 0 indicating statistical independence; and (c) the relatively small e#ect of the individual accuracies on the possible range of values of Q. In the rest of this study we draw upon the existing literature and in particular ....
[Article contains additional citation context not shown here]
L.I. Kuncheva and C.J. Whitaker. Measures of diversity in classifier ensembles. Machine Learning, 51:181--207, 2003.
...., where and . c) If , set , and renormalize so that . Otherwise, restart the algorithm with weights , 2. Combine base classifiers , by the weighted majority vote with weights to a final decision rule . 3 Diversity Measures Different diversity measures are introduced in the literature [18]. In our study, we consider the Q statistic and the disagreement measure. The Q statistic is the pairwise symmetrical measure of diversity proposed by Yule [19] For two classifiers C i and C j , Q statistic is defined as , where a is the probability that both classifiers C i and C j make the ....
Kuncheva, L.I., Whitaker, C.J.: Measures of Diversity in Classifier Ensembles (submitted)
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Ludmila I. Kuncheva and C.J. Whitaker. Measures of Diversity in Classifier Ensembles. Machine Learning, 51:181--207, 2003.
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Ludmila I. Kuncheva and C.J. Whitaker. Measures of Diversity in Classifier Ensembles. Machine Learning, 51:181--207, 2003.
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Ludmila I. Kuncheva and C.J. Whitaker. Measures of Diversity in Classifier Ensembles. Machine Learning, 51:181--207, 2003.
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L. Kuncheva and C. Whitaker. Measures of diversity in classifier ensembles. Machine Learning, (51):181--207, 2003.
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Kuncheva LI, Whitaker CJ. Measures of diversity in classifier ensembles. Machine Learning. (submited)
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Kuncheva L.I., Whitaker C.J.: Measures of Diversity in Classifier Ensembles. Submitted to Machine Learning.
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L.I. Kuncheva and C.J. Whitaker. Measures of diversity in classifier ensembles. Machine Learning, 51:181--207, 2003.
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Kuncheva L.I., Whitaker C.J.: Measures of Diversity in Classifier Ensembles. Submitted to Machine Learning
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L. Kuncheva, C.Whitaker, Measures of diversity in classifier ensembles, Machine Learning (51) (2003) 181--207.
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L.I. Kuncheva and C.Whitaker. Measures of diversity in classifier ensembles. Machine Learning, (51):181--207, 2003.
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L.I. Kuncheva and C.Whitaker. Measures of diversity in classifier ensembles. Machine Learning, (51):181--207, 2003.
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