V. Cherkassky and F. Mulier. Learning from data: Concepts, theory, and methods. John Wiley and Sons, Inc., 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of these methods. Keywords Support vector machines, kernelbased methods, nonlinear estimation, ridge regression, regularization, neural networks I. INTRODUCTION In the last decade, neural networks have proven to be a powerful methodology in a wide range of fields and applications [1] [3], 11] 21] 25] 26] Although initially neural nets were often presented as a kind of miracle approach, reliable training methods exist nowadays mainly thanks to interdisciplinary studies and insights from several fields including statistics, circuit , systems and control theory, signal ....

Cherkassky V., Mulier F., Learning from data: concepts, theory and methods, John Wiley and Sons, 1998.

....e#ectiveness of the proposed approach in generating sharp nonlinear classifiers based mostly or totally on prior knowledge. Keywords: prior knowledge, support vector machines, linear programming 1 Introduction Support vector machines (SVMs) have played a major role in classification problems [15, 2, 10]. However unlike other classification tools such as knowledge based neural networks [13, 14, 4] little work [11, 3] has gone into incorporating prior knowledge into support vector machines. In this work we extend the previous work [3] of incorporating multiple polyhedral sets as prior knowledge ....

....other than symmetry, that is K(x # , y) # = K(y # , x) and in particular we shall not assume or make use of Mercer s positive definiteness condition [15, 12] The base of the natural logarithm will be denoted by #. A frequently used kernel in nonlinear classification is the Gaussian kernel [15, 2, 10] whose ijth element, i = 1 . m, j = 1 . k, is given by: K(A, B) ij = # #A i # B j # where A , B and is a positive constant. 2 Prior Knowledge in a Nonlinear Kernel Classifier We begin with a brief description of support vector machines (SVMs) SVMs are used ....

V. Cherkassky and F. Mulier. Learning from Data - Concepts, Theory and Methods. John Wiley & Sons, New York, 1998.

....(EM) 12] The generic maximization step in EM involves estimating the distance of each data point to a representative, and using this estimate as an approximation to the probability of being a member of that cluster. Other well known variations of EM are the Generalized Lloyd Algorithm (or GLA) [11], and fuzzy c clustering [11] With the possible exception of k C L1 Medians [9, 17] all are representative based clustering methods that use the Euclidean metric. The statistical properties upon which these EM variants are based seem to grant special status to the use of sums of squares of the ....

....step in EM involves estimating the distance of each data point to a representative, and using this estimate as an approximation to the probability of being a member of that cluster. Other well known variations of EM are the Generalized Lloyd Algorithm (or GLA) 11] and fuzzy c clustering [11]. With the possible exception of k C L1 Medians [9, 17] all are representative based clustering methods that use the Euclidean metric. The statistical properties upon which these EM variants are based seem to grant special status to the use of sums of squares of the Euclidean metric, and to ....

V. Cherkassky and F. Muller. Learning from Data | Concept, Theory and Methods. John Wiley & Sons, NY, USA, 1998.

.... estimating the prediction risk of the model [21] Even if this double resampling procedure provides an unbiased estimate of the the generalization error, it may be highly variable due to the variance of nite samples and the speci c choice of the prediction sample, especially with small data sets [12]. Having small number of samples (a typical case with gene expression NEURObjects is available on line at: http: www.disi.unige.it person ValentiniG NEURObjects. SVMlight software is available at http: ais.gmd.de thorsten svm light. 11 data) it would be safer to use cross validation ....

V. N. Cherkassky and F. Mulier. Learning from data: Concepts, Theory and Methods. Wiley & Sons, New York, 1998.

....the best) to the trajectory generation problem, the standard back propagation algorithm was used to train the NRNN and no specific efforts were made to optimize the training process. For the same reasons, no particular attention was paid to whether the NRNN had an appropriate VC dimension [46] or not, as long as the ultimate problem of trajectory generation was solved reasonably well. The threshold function for the neurons in the NRNN was also defined by Eq. 3 with the value of ri selected as 2. 18 B. Evaluation of Trajectory Generation Performance To evaluate the performance of the ....

V. Cherkassky and F. Mulier, Learning from Data: Concepts, Theory, and Methods, John Wiley and sons, Inc., 1998.

....e#ectiveness of the proposed approach in generating sharp nonlinear classifiers based mostly or totally on prior knowledge. Keywords: prior knowledge, support vector machines, linear programming 1 Introduction Support vector machines (SVMs) have played a major role in classification problems [15, 2, 10]. However unlike other classification tools such as knowledge based neural networks [13, 14, 4] little work [11, 3] has gone into incorporating prior knowledge into support vector machines. In this work we extend the previous work [3] of incorporating multiple polyhedral sets as prior knowledge ....

....other than symmetry, that is K(x # , y) # = K(y # , x) and in particular we shall not assume or make use of Mercer s positive definiteness condition [15, 12] The base of the natural logarithm will be denoted by #. A frequently used kernel in nonlinear classification is the Gaussian kernel [15, 2, 10] whose ijth element, i = 1 . m, j = 1 . k, is given by: K(A, B) ij = # #A i # B j # where A , B and is a positive constant. 2 Prior Knowledge in a Nonlinear Kernel Classifier We begin with a brief description of support vector machines (SVMs) SVMs are used ....

V. Cherkassky and F. Mulier. Learning from Data - Concepts, Theory and Methods. John Wiley & Sons, New York, 1998.

....Clustering is an important family of algorithms widely employed in several scienti c disciplines and used for a lot of successful applications. Among them there are radial basis function networks [1] pattern recognition [2] computer vision [3] and classi cation tasks [4] Several papers [5,6] demonstrate that, in many cases, clustering is equivalent to Vector Quantization (VQ) a technique often employed in telecommunications and signal compression [7,8] For this reason, in the remainder of the paper, we will use also the term Unsupervised Learning (UL) to indicate one or both of the ....

V. S. Cherkassky and F. M. Mulier, Learning from Data: Concepts, Theory and Methods. John Wiley and Sons, 1998.

....with highest value of map similarity measure is chosen. This process is repeated and it ends when no neighbor has a higher value of map similarity measure, i.e. a local maxima has been found. Clearly, this search algorithm can be improved using a variety of ideas including gradient descent [Cherkassky and Mulier, 1998, Flury, 1997] and simulated annealing [Shekhar and Amin, 1992, Vapnik, 1997] etc. A simple function family is the family of generalized linear models, e.g. logistic regression [LeSage, 1997b] with or without autocorrelation terms. Other interesting families include non linear functions. In the ....

Cherkassky, V. and Mulier, F. (1998). Learning From Data Concepts, Theory, and Methods. John Wiley & SONS Inc.

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V. Cherkassky and F. Mulier. Learning from data: Concepts, theory, and methods. John Wiley and Sons, Inc., 1998.

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V. Cherkassky and F. Mulier. Learning from Data: Concepts, Theory, and Methods. Wiley, New York, 1998.

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Cherkassky V. and Mulier F., 1998. Learning from Data -- Concepts, Theory, and Methods. John Wiley & Sons, USA, 1998. 441 pages.

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V. Cherkassky and F. Mulier, Learning From Data: Concepts, Theory, and Methods. New York: Wiley, 1998.

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V. Cherkassky and F. Mulier, Learning From Data: Concepts, Theory, and Methods. New York: Wiley, 1998.

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Vladimir Cherkassky and Filip Mulier. Learning from data: Concepts, Theory and Methods. John Wiley & Sons, 1998.

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Vladimir Cherkassky and Filip Mulier. Learning from Data: Concepts, Theory, and Methods. Wiley, New York, 1998.

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V. Cherkassky and F. Mulier. Learning from Data | Concepts, Theory and Methods. John Wiley & Sons, New York, 1998.

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V. Cherkassky and F. Mulier, Learning From Data: Concepts, Theory and Methods. New York: Wiley, 1998.

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Cherkassky V, Mulier F (1998) Learning from data: concepts, theory, and methods. Wiley, NewYork

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V. Cherkassky and F. Mulier, Learning from Data: Concepts, Theory, and Methods. New York: Wiley, 1998.

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V. N. Cherkassky and F. Mulier. Learning from data: Concepts, Theory and Methods. Wiley & Sons, New York, 1998.

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V. Cherkassky and F. Mulier, Learning from Data: Concepts, Theory, and Methods. New York: John Wiley & Sons, 1998.

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Vladimir S. Cherkassky and Filip M. Mulier. Learning from Data : Concepts, Theory, and Methods. John Wiley and Sons, 1998. 28

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V. Cherkassky and F. Mulier. Learning from Data: Concepts, Theory and Methods. Wiley, 1998.

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Cherkassky V., Mulier F., Learning from data: concepts, theory and methods, John Wiley and Sons, 1998.

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Cherkassky, V. and Mulier, F.: Learning from Data - Concepts, Theory and Methods. John Wiley & Sons, New York, 1998.

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