K. Fukunaga and R.R. Hayes, "Effects of sample size in classifier design, " IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 8, pp. 873--885, Aug. 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Z 1 Gamma1 Z R n Phi (jvjr) jv [p 1 (r) Gamma p 2 (r) drdv; as N 1 (17) with integrals in Phi (jvjR) asymptotically approximated as stated in Lemma 3. 1 with s = jv: Proof: The proof follows from combining the derivation of the expression for the average probability of error in [25] and the asymptotic results stated above. Note that the asymptotic expression for the average probability of error derived in [25] cannot be applied to our problem since the Taylor series expansion used in [25] to approximate the conditional characteristic function of the log likelihood ratio ....

....approximated as stated in Lemma 3.1 with s = jv: Proof: The proof follows from combining the derivation of the expression for the average probability of error in [25] and the asymptotic results stated above. Note that the asymptotic expression for the average probability of error derived in [25] cannot be applied to our problem since the Taylor series expansion used in [25] to approximate the conditional characteristic function of the log likelihood ratio requires the function to be locally continuous around the true parameters. The conditional characteristic function of the modified ....

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K. Fukunaga, R. R. Hayes, "Effect of Sample Size in Classifier Design," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 8, Aug. 1989, pp. 873-885.

....for practical data mining. Even in combination with other approaches to scale up data mining, a fast algorithm is still necessary. Thus, in isolation, fast algorithms are of limited use but when used in conjunction with sampling or other scaling techniques they are indeed very useful and powerful [13, 10]. 4.2 Parallel data mining Although parallel computing has the potential to speed up data mining, it s role in data mining is still an open question [8, 23] The well known application of parallel data mining is in the construction of decision trees. After partitioning the dataset into disjoint ....

K. Fukunaga and R. Hayes. Effects of sample size in classifier design. IEEE Trans. on pattern Analysis and Machine Intelligence., 1985.

....(normal) distribution parameters. This requires a huge sample size for even a modest value of d. Contrary to this, Rousseeuw and Leroy [106] suggest a robust method for parameter estimation in which the sample size grows linearly with d. Research by Wacker and El Sheikh [135] Fukunaga and Hayes [33] and Aberhard et al. 4] also support the 67 idea of using a sample size which is linearly related to the dimension of the pattern space (N = k d for some constant k 1) Both analytical and experimental evidence indicate that the choice for k depends on the decision rule used by the classifier. ....

K. Fukunaga and R. Hayes. Effects of sample size in classifier design. IEEE Transactions On Pattern Analysis and Machine Intelligence, 11(8):873--885, August 1989.

....(normal) distribution parameters. This requires a huge sample size for even a modest value of d. Contrary to this, Rousseeuw and Leroy [106] suggest a robust method for parameter estimation in which the sample size grows linearly with d. Research by Wacker and El Sheikh [135] Fukunaga and Hayes [33] and Aberhard et al. 4] also support the idea of using a sample size which is linearly related to the dimension of the pattern space (N = k d for some constant k 1) Both analytical and experimental evidence indicate that the choice for k depends on the decision rule used by the classifier. ....

K. Fukunaga and R. Hayes. Effects of sample size in classifier design. IEEE Transactions On Pattern Analysis and Machine Intelligence, 11(8):873--885, August 1989.

....developed a program to recognize printed characters in legal text, and Valiveti and Oommen [91] present algorithms for classifying strings into known distributions. In addition, Lund and Lee [66] apply Wald s Sequential Probability Ratio Test (SPRT) to authenticate speakers, and Fukunaga and Hayes [27] study the effect of sample size on parameter estimates used in linear and quadratic classifiers. 8.3 Open Problems Our study of language recognition raises several important questions involving: theoretical models of language, robustness of statistical tests when applied to real language, ....

Fukunaga, Keinosuke; and Raymond R. Hayes, "Effects of sample size in classifier design," IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:8 (August 1989), 873--885.

....dividing the samples into training and test sets is an important problem and must be done in a way that the distributions of the two sets are close to each other. The ratio of the sizes of the training set to the test set is then determined from the bias and the variance of the estimated error [57]. For classification with mixed mode data, the mutual information between a class and an attribute can be combined to determine the membership of an unknown object under the assumption that the given attributes are independent. Clustering Query: We call unsupervised partitioning of tuples of a ....

K. Fukunaga and R. Hayes, "Effects of sample size in classifier design," IEEE Trans. on Pattern analysis and Machine Intelligence, vol. 11, no. 8, pp. 873--885, 1985.

....= a t 1 ; a t 2 : a t d ) PP t = h t ; Sigma t ; M t = n m t 1 ; m t 2 : m t n t o i P t = n p t 1 ; p t 2 : p t q t o Figure 2. 5: A formalization of database model indexing using protoparts pairs of protoparts and on the acceptable classifier error rate [Fukunaga and Hayes 1989a, Fukunaga and Hayes 1989b] If this condition is not met, it is better to ignore correlations altogether since their estimates are likely to be highly unreliable. When the number of model parts indexed by a protopart is relatively small, the estimate of the variance becomes unreliable, too. This ....

K. Fukunaga and R. R. Hayes. Effects of sample size in classifier design. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(8):873-- 885, August 1989.

....dividing the samples into training and test sets is an important problem and must be solved in a way that the distributions of the two sets are close to each other. The ratio of the sizes of the training set to the test set is then determined from the bias and the variance of the estimated error [57]. For classification with mixed mode data [23] the mutual information, between a class and an attribute, can be combined to determine the membership of an unknown object under the assumption that the given attributes are independent. Clustering Query: We call unsupervised partitioning of tuples ....

K. Fukunaga and R. Hayes, "Effects of sample size in classifier design," IEEE Trans. on Pattern analysis and Machine Intelligence, vol. 11, no. 8, pp. 873--885, 1985.

....number of training objects N k are increased correspondingly, the increase in the dimensionaliry will lead to poorly posed settings, i.e. the number of training samples N k in each class is comparable to the dimensionality. In poorly posed settings, parameter estimates have very large variances [4]. Even worse, in ill posed settings, when the number N k of training samples is less than the dimensionality, not all parameters can be estimated. Nonparametric methods on the other hand rely on densely populated feature spaces for reliable classification. In high dimensional settings, this can ....

....the population parameters are usually unknown and are replaced by the sample estimates Sigma k and k . QDA has one major drawback. In order to obtain reliable estimates Sigma k of the class covariance matrices, very large numbers of training samples are required for large dimensionalities [4]. Further, Sigma k cannot be inverted in ill posed cases. For the simulations reported here, singular value perturbation [9] was applied to the covariance matrices to enable inversion in such situations. Linear Discriminant Analysis (LDA) In the same way as QDA, LDA also assumes that the ....

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K. Fukunaga, R. R. Hayes, "Effects of Sample Size in Classifier Design", IEEE Trans. Pattern Anal. Machine Intell. 11, 873 (1989).

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K. Fukunaga and R.R. Hayes, "Effects of sample size in classifier design, " IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 8, pp. 873--885, Aug. 1989.

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