S. Knerr, L. Personnaz, and G. Dreyfus. Single-layer learning revisited: a stepwise procedure for building and training a neural network. In J. Fogelman, editor, Neurocomputing: Algorithms, Architectures and Applications. Springer-Verlag, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is integrated software for support vector classification, regression and distribution estimation. LIBSVM is capable of performing cross validation, multi categorization and using different penalty parameters in the SVM formulation for unbalanced data. LIBSVM uses the one against one approach [12] for multi class classification. In the one against one approach, k(k 1) 2 classifiers are constructed where k is the number of classes. Each classifier trains data from two different classes. Chang and Lin [3] utilize a voting strategy where each example is voted against a class or not in each ....

Knerr, S., Personnaz, L., and Dreyfus, G. "Single layer learning revisited: a stepwise procedure for building and training a neural network." Neurocomputing: Algorithms, Architectures and Applications. J. Fogelman (Ed.), SpringerVerlag, 1990.

....of x argmax i=1; k ( w ) 2) Practically we solve the dual problem of (1) whose number of variables is the same as the number of data in (1) Hence k l variable quadratic programming problems are solved. Another major method is called the one against one method. It was introduced in [15], and the rst use of this strategy on SVM was in [9] 16] This method constructs k(k 1) 2 classi ers where each one is trained on data from two classes. For training data from the ith and the jth classes, we solve the following binary classi cation problem: b ; 2 ....

S. Knerr, L. Personnaz, and G. Dreyfus. Single-layer learning revisited: a stepwise procedure for building and training a neural network. In J. Fogelman, editor, Neurocomputing: Algorithms, Architectures and Applications. Springer-Verlag, 1990.

....Q ij (Joachims, 1998) Hence the computational cost of later iterations can be reduced. In LIBSVM, we implement a simple least recent use strategy for the cache. We dynamically cache only recently used columns of QAA of (4. 1) 5 Multi class classi cation We use the one against one approach (Knerr et al. 1990) in which k(k 1) 2 classi ers are constructed and each one trains data from two di erent classes. The rst use of this strategy on SVM was in (Friedman, 1996; Kre el, 1999) For training data from the ith 15 and the jth classes, we solve the following binary classi cation problem: min w ij ....

Knerr, S., Personnaz, L., & Dreyfus, G. (1990). Single-layer learning revisited: a stepwise procedure for building and training a neural network. In J. Fogelman (Ed.), Neurocomputing: Algorithms, architectures and applications. Springer-Verlag.

....( x i ; y i ) by the binary labeled instance ( x i ; b i ) where b i = 1 if y i = l, otherwise b i = 1. Classi cation of a test pattern is done according to the maximum output of these ten classi ers. There are some other ways to combine many two class classi ers into a multiclass classi er [31, 10, 20]. To produce output given a test instance x, besides using the nal hypothesis, we also tried the voting method to convert the standard perceptron algorithm to a batch learning. The voting method is adopted in [9] and is an application of the general leave one out method of [15] It records ....

Knerr, S., L. Personnaz, and G. Dreyfus: 1990, `Single-layer learning revisited: A stepwise procedure for building and training a neural network'. In: FogelmanSoulie and Herault (eds.): Neurocomputing: Algorithms, Architectures and Applications. NATO ASI. Springer.

....quantisation for which these results were replaced by 80:4 Sigma 4:8 , 77:3 Sigma 5:0 , 91:4 Sigma 3:4 and 95:4 Sigma 2:3 respectively. 18 2. 7 Summary Apart from the algorithms mentioned here a number of other constructive techniques have been proposed for solving classification tasks [89, 117, 74, 12, 6, 90]. To date there has been no extensive comparison of the performance of these algorithms and few of them have been applied to real life datasets. In addition to generating feed forward architectures some authors have considered generating higher order weights [112, 100] which can solve non linearly ....

S. Knerr, L. Personnaz, and G. Dreyfus. Single-layer learning revisited: a stepwise procedure for building and training a neural network. In J. Fogelman, editor, Neurocomputing: Algorithms, Architectures and Applications. Springer-Verlag, 1990.

....value. Unfortunately, there is no bound on the generalization error for the 1 v r SVM, and the training time of the standard method scales linearly with N . Another method for constructing N class classifiers from SVMs is derived from previous research into combining two class classifiers. Knerr [5] suggested constructing all possible two class classifiers from a training set of N classes, each classifier being trained on only two out of N classes. There would thus be K = N(N 1) 2 classifiers. When applied to SVMs, we refer to this as 1 v 1 SVMs (short for one versus one) Knerr suggested ....

....from a training set of N classes, each classifier being trained on only two out of N classes. There would thus be K = N(N 1) 2 classifiers. When applied to SVMs, we refer to this as 1 v 1 SVMs (short for one versus one) Knerr suggested combining these two class classifiers with an AND gate [5]. Friedman [4] suggested a Max Wins algorithm: each 1 v 1 classifier casts one vote for its preferred class, and the final result is the class with the most votes. Friedman shows circumstances in which this algorithm is Bayes optimal. Kreel [6] applies the Max Wins algorithm to Support Vector ....

S. Knerr, L. Personnaz, and G. Dreyfus. Single-layer learning revisited: A stepwise procedure for building and training a neural network. In Fogelman-Soulie and Herault, editors, Neurocomputing: Algorithms, Architectures and Applications, NATO ASI. Springer, 1990.

....value. Unfortunately, there is no bound on the generalization error for the 1 v r SVM, and the training time of the standard method scales linearly with N . Another method for constructing N class classifiers from SVMs is derived from previous research into combining two class classifiers. Knerr [5] suggested constructing all possible two class classifiers from a training set of N classes, each classifier being trained on only two out of N classes. There would thus be K = N(N 1) 2 classifiers. When applied to SVMs, we refer to this as 1 v 1 SVMs (short for one versus one) Knerr suggested ....

....from a training set of N classes, each classifier being trained on only two out of N classes. There would thus be K = N(N 1) 2 classifiers. When applied to SVMs, we refer to this as 1 v 1 SVMs (short for one versus one) Knerr suggested combining these two class classifiers with an AND gate [5]. Friedman [4] suggested a Max Wins algorithm: each 1 v 1 classifier casts one vote for its preferred class, and the final result is the class with the most votes. Friedman shows circumstances in which this algorithm is Bayes optimal. A significant disadvantage of the 1 v 1 approach is that, ....

S. Knerr, L. Personnaz, and G. Dreyfus. Single-layer learning revisited: A stepwise procedure for building and training a neural network. In Fogelman-Soulie and Herault, editors, Neurocomputing: Algorithms, Architectures and Applications, NATO ASI Series. Springer, 1990.

....a classification network with one hidden layer, it is possible to select, in an obvious way, an architecture that is designed specifically for the problem. This can be done by ensuring that for each pair of classes there is at least one separating hyperplane. 1. 1 Single layer learning Knerr et al. [1] present such a network using subnets of different conceptual interpretation. Their network relies on each unit in a layer starting off with random weights but, unlike a standard multi layer perceptron, each unit responds only to exemplars from 2 classes. Hence after training, for each pair of ....

....in the first stage of the algorithm. Pair wise separation would then be attempted on classes f1,2,4,5g, using 6 units. With the exception of classes 2 and 5, these classes are linearly separable. Below the unit assigned to separate classes 2 and 5, a sub network would be implemented (see [1] for further details) An inspection of this diagram shows that 3 of the units are redundant from the point of view of positioning a separating hyperplane between each pair of classes, and so this network is in the position of having an excess of task based units. 1.2 Linear Discriminant ....

S. Knerr, L. Personnaz, and G. Dreyfus. Single layer learning revisited: A stepwise procedure for building and training a neural network. In F. Fogelman-Souli'e and J H'erault, editors, Neurocomputing: Algorithms, architectures, and applications, volume F 68. NATO ASI Series, SpringerVerlag, 1990.

....practical problems are considered such as evaluating the pruned networks and the effects of varying the pruning schedule. 1 Introduction The task based MLP and associated pruning algorithm were introduced in [3] where further details may be found. It has similarities to the model proposed by [4]. Briefly the approach may be described as follows: for a given multi class classification problem, we determine the weights so that each hidden layer unit has a particular task which consists of separating a pair of classes (or super classes formed by the union of classes) A pruning strategy ....

S. Knerr, L. Personnaz, and G. Dreyfus. Single layer learning revisited: A stepwise procedure for building and training a neural network. In F. Fogelman-Souli'e and J H'erault, editors, Neurocomputing: Algorithms, architectures, and applications, volume F 68. NATO ASI Series, SpringerVerlag, 1990.

....problems can be efficiently solved by divide and conquer strategies which partition the original problem into a set of K(K 1) 2 two class problems. For each pair of classes w i and w j , a (potentially small) neural network with a single output unit is trained on the data of the two classes [Knerr et al. 1990, and references therein] In this section, we show how to obtain probabilistic outputs from each of the twoclass classifiers in the pairwise neural network classifier (Figure 1) x x x x 1 1 2 3 N inputs K(K 1) 2 two class networks . w w 1 2 w w 1 4 w w 1 3 w w 1 ....

S. Knerr, L. Personnaz, G. Dreyfus (1990). Single-Layer Learning Revisited: A Stepwise Procedure for Building and Training a Neural Network. In Neurocomputing: Algorithms, Architectures and Applications, Fogelman-Soulie and Herault (eds.).

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S. Knerr, L. Personnaz, and G. Dreyfus. Single-layer learning revisited: a stepwise procedure for building and training a neural network. In J. Fogelman, editor, Neurocomputing: Algorithms, Architectures and Applications. Springer-Verlag, 1990.

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S. Knerr, L. Personnaz, and G. Dreyfus. Single-layer learning revisited: a stepwise procedure for building and training a neural network. In J. Fogelman, editor, Neurocomputing: Algorithms, Architectures and Applications. Springer-Verlag, 1990.

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S. Knerr, L. Personnaz, and G. Dreyfus, "Single-layer learning revisited: A stepwise procedure for building and training a neural network," in Neurocomputing: Algorithms, Architectures and Applications, F. Fogelman-Soulie and J. Herault, Eds., pp. 41--50. Springer-Verlag, 1990.

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Knerr, S., Personnaz, L., and Dreyfus, G. (1990). Single layer learning revisited: A stepwise procedure for building and training a neural network. In Fogelman-Souli'e, F. and H'erault, J., editors, Neurocomputing: Algorithms, architectures, and applications, volume F 68. NATO ASI Series, Springer-Verlag.

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Knerr, S., Personnaz, L., Dreyfus, G. (1989) "Single layer learning revisited: A stepwise procedure for building and training a neural network," in Neurocomputing: Algorithms, architectures, and applications, F. Fogelman-Souli'e, J. H'erault (eds.), NATO ASI Series, Springer, in print.

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