M. Kubat. Decision trees can initialize radialbasis function networks. IEEE Transactions on Neural Networks, 9:813--821, 1998. http://www.cacs.usl.edu/~mkubat/ publications/dtrbf.ps.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... w j Rules of this type can be easily learned using an algorithm for inducing decision trees, such as ID3 [69,72] or, better an algorithm for inducing regression trees, such as CART [17] Initialization of RBFNs by means of decision trees has been proposed by [5] and extensively analysed by Kubat [51]. 3.0.0.5 Weights Linear Optimization. Both equations (1) and (2) are linear in the weights w i hence, given the parameters c i and Q i of the basis functions it is possible to use a linear optimization method for finding the values of the w i , that minimize the cost function computed on the ....

M. Kubat. Decision trees can initialize radial-basis function networks. IEEE Transactions on neural networks, 9(5):813--821, September 1998.

.... extended with a model pruning method in [17] Because feedforward neural networks are expensive to train, and the abundance of their parameters can render the training procedure inefficient if the training set is small, instead of feedforward networks, radial basis functions were initialized in [18]. This method is based on the placement of radial bases functions to the center or the edge of the rectangular regions defined by the DT. The complexity of the resulted model is controlled by the complexity of the decision tree [18] or by the number of the added basis functions [19] As radial ....

....feedforward networks, radial basis functions were initialized in [18] This method is based on the placement of radial bases functions to the center or the edge of the rectangular regions defined by the DT. The complexity of the resulted model is controlled by the complexity of the decision tree [18] or by the number of the added basis functions [19] As radial basis functions are functionally equivalent to fuzzy inference systems [20] this approach is identical to LOLIMOT that initializes fuzzy models from regression trees [21] A similar approach is the simple fuzzification of the ....

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M. Kubat. (1998) Decision Trees Can Initialize Radial-Basis-Function Networks. IEEE Transactions on Neural Networks, 9, 813--821.

.... On the other hand, the result of AdaBoost is a linear combination of the predictions of the base classi ers, and if the base classi ers are RBFs, then the result of boosting is a RBF Network [15, 16] This work is also related with the methods for constructing RBFNs from decision trees [14]. These works share the idea of constructing the network from a symbolic machine learning method. For instance, the selection of each RBF is based on the one for the split of a node in a decision tree. A di erence with that methods is that in the case of the decision trees there are two steps: ....

Miroslav Kubat. Decision trees can initialize radial-basis function networks. IEEE Transactions on Neural Networks, 9:813-821, 1998.

....already investigated by some researcher. In [10] a decision tree was mapped into a feedforward neural network. A variation of this method is given in [11] where the decision tree was used for the input domains discretization only. This approach was extended with a model pruning method in [12] In [13], the decision tree was applied to initialize radial basis functions for a neural network, because feedforward neural networks are expensive to train, and the abundance of their parameters may render the training procedure ine#cient if the training set is small. This method was based on the ....

....procedure ine#cient if the training set is small. This method was based on the placement of radialbasis functions to the center or the edge of the rectangular regions defined by the decision tree. The complexity of the resulted model can be controlled by the complexity of the decision tree [13] or by the number of the added basis functions [14] As radial basis functions are functionally equivalent to fuzzy inference systems [15,16] this approach is identical to LOLIMOT [17] that initializes fuzzy models from regression trees. A similar approach is the simple fuzzification of the ....

[Article contains additional citation context not shown here]

M. Kubat, Decision trees can initialize radial-basis-function networks, IEEE Trans. NN 9 (1998) 813--821.

....the centers of the RBFs typically unsupervised or supervised training procedures from clustering or vector quantization are used [8, 11] and the output weights were determined using the pseudo inverse matrix approach. Initialising RBF networks using decision trees was introduced by Kubat in 1998 [6]. He was the first who suggested such a combination; Orr addressed this topic in [9] In this initialisation technique at first a decision tree is calculated using for example the C4.5 software package. From this decision tree the regions defined by the leaves of the tree are transformed into the ....

....defined by a path through the tree starting at the root and terminating in a leaf. The number of leaves in the classification tree determines the number of hidden RBF neurons in the network. In the C4.5 software the size of the tree (model complexity) can be controlled by a pruning parameter (c) [6, 9]. The parameter m does something similar. It specifies the number of data points to create a region and helps to prevent the influence of noisy feature vectors in huge data sets. 4 RBF Network Training In multilayer perceptron all parameters are usually trained simultaneously at the same time ....

M. Kubat. Decision trees can initialize radial-basis-function networks. IEEE Trans. Neural Networks, 9:813--821, 1998.

....while the number of Gaussian units is predetermined. The mixing coe# cients are then discarded and the output weights are determined by the pseudo inverse method. Determining the complexity of the basis layer in a direct step, using information theoretic considerations, was proposed by Kubat [17]. A decision tree [30] is used to partition the instance space into relatively pure regions. The basis layer is then determined by setting a basis function into the center of this region and training the output weights thereafter. This method appears an attractive method to standard clustering ....

M. Kubat. Decision trees can initialize radial-basis function networks. IEEE Transactions on Neural Networks, 9(5):813--821, 1998.

.... was extended with a model pruning method in [12] Because feedforward neural networks are expensive to train and the abundance of their parameters can render the training procedure inefficient if the training set is small, instead of feedforward networks, radial basis functions were initialized in [13]. This method is based on the placement of radial bases functions to the center or the edge of the rectangular regions defined by the DT. The complexity of the resulted model is controlled by the complexity of the decision tree [13] or by the number of the added basis functions [14] As radial ....

....feedforward networks, radial basis functions were initialized in [13] This method is based on the placement of radial bases functions to the center or the edge of the rectangular regions defined by the DT. The complexity of the resulted model is controlled by the complexity of the decision tree [13] or by the number of the added basis functions [14] As radial basis functions are functionally equivalent to fuzzy inference systems [15, 16] this approach is identical to LOLIMOT [17] that initializes fuzzy models from regression trees. A similar approach is the simple fuzzification of the ....

[Article contains additional citation context not shown here]

M. Kubat, "Decision trees can initialize radialbasis -function networks," IEEE Trans. NN, vol. 9, pp. 813--821, 1998.

....Tsukuba, Ibaraki 305 8666, Japan Tom Leonard Dept. of Mathematics and Statistics, University of Edinburgh, Edinburgh, Scotland Abstract We describe a method for nonparametric regression which combines regression trees with radial basis function networks. The method is similar to that of Kubat [1998], who was first to suggest such a combination, but has some significant improvements. We demonstrate the features of the new method, compare its performance with other methods on DELVE data sets and apply it to a real world problem involving the classification of soybean plants from digital ....

....selected centre locations. 2 1. 3 Combining the Two Methods The combination of trees and RBF networks was first suggested by Kubat and Ivanova [1995] in the context of classification rather than regression (although the two tasks raise similar issues) Further elaboration of the idea appeared in Kubat [1998]. Essentially, each terminal node of the classification tree contributes one unit to the RBF network, the centre and radius of which are determined by the position and size of the corresponding hyperrectangle. Thus the regression tree sets the number, positions and sizes of all RBF centres in the ....

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M. Kubat. Decision trees can initialize radial-basis function networks. IEEE Transactions on Neural Networks, 9(5):813--821, 1998.

....and used to generate the RBF network which the Matlab function returns. Regression Trees and RBF Networks 15 4 Regression Trees and RBF Networks 4. 1 Introduction This section is about a novel method for nonparametric regression involving a combination between regression trees and RBF networks [8]. The basic idea of a regression tree is to recursively partition the input space in two and approximate the function in each half by the average output value of the samples it contains [4] Each split is parallel to one of the axes so it can be expressed by an inequality involving one of the ....

....Finally we show some results and summarise our conclusions. 4. 2 The Basic Idea The combination of trees and RBF networks was first suggested by [9] in the context of classification rather than regression (though the two cases are very similar) Further elaboration of the idea appeared in [8]. Essentially, each terminal node of the classification tree contributes one hidden unit to the RBF network, the centre and radius of which are determined by the position and size of the corresponding hyperrectangle. Thus the tree sets the number, positions and sizes of all RBFs in the network. ....

[Article contains additional citation context not shown here]

M. Kubat. Decision trees can initialize radial-basis function networks. IEEE Transactions on Neural Networks, 9(5):813--821, 1998.

....do not pose any major challenge, the main difficulty is presented by the centers i . Existing methods associate these vectors with the gravity centers of data clusters (Moody and Darken, 1989; Musavi et al. 1992) with hyperrectangles defined on the instance space by decision tree induction (Kubat, 1998), or with vectors determined by AI search techniques (Chen, Cowan, and Grant, 1991; Cheng and Lin, 1994) A method that adds one neuron at a time with subsequent tuning of the centers was developed by Fritzke (1993, 1994) Techniques to adjust the centers by learning have been studied also by ....

.... we used) initialization by selected training examples gave better results than the more expensive clustering technique suggested by Moody and Darken, 1989) and Musavi et al. 1992) On the other hand, the achieved performance does not seem to reach the classification accuracies reported by Kubat (1998) for his decision tree based initialization. However, a great advantage of SELEX is the compactness of the resulting network. In the decision tree based approach, a typical network contained dozens of neurons. The encouraging results suggest that exampleselecting techniques (used in RBF ....

Kubat, M. (1998). Decision Trees Can Initialize RadialBasis Function Networks. IEEE Transactions on Neural Networks, 9, pp. 813--821.

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M. Kubat. Decision trees can initialize radialbasis function networks. IEEE Transactions on Neural Networks, 9:813--821, 1998. http://www.cacs.usl.edu/~mkubat/ publications/dtrbf.ps.

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M. Kubat. Decision trees can initialize radial basis function networks. IEEE Transactions on Neural Networks, 9(5):813-821, 1998.

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