Three learning phases for radial-basis-function networks

Schwenker, Friedhelm; Kestler, Hans A.; Palm, Günther

doi:10.1016/s0893-6080(01)00027-2

Cited by 456 publications

(214 citation statements)

References 32 publications

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“…It then propagates this error backwards through the network, and updates the weights in each layer through gradient descent. Although backpropagation is usually associated with artificial neural networks that use sigmoid or hyperbolic activation functions, the algorithm is also applicable to radial basis function networks (Poggio and Girosi, 1990;Schwenker et al, 2001a).…”

Section: Algorithm: Backpropagationmentioning

confidence: 99%

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Many regression algorithms, one unified model: A review

2015

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Regression is the process of learning relationships between inputs and continuous outputs from example data, which enables predictions for novel inputs. The history of regression is closely related to the history of artificial neural networks since the seminal work of Rosenblatt (1958). The aims of this paper are to provide an overview of many regression algorithms, and to demonstrate how the function representation whose parameters they regress fall into two classes: a weighted sum of basis functions, or a mixture of linear models. Furthermore, we show that the former is a special case of the latter. Our ambition is thus to provide a deep understanding of the relationship between these algorithms, that, despite being derived from very different principles, use a function representation that can be captured within one unified model. Finally, step-by-step derivations of the algorithms from first principles and visualizations of their inner workings allow this article to be used as a tutorial for those new to regression.

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Section: Algorithm: Backpropagationmentioning

confidence: 99%

“…A complementary analysis comes from Widrow et al (2013), who examine under which conditions training a network benefits from backpropagation or not. Schwenker et al (2001a) use a combination of both least squares batch learning and incremental backpropagation.…”

Section: Backpropagation For Slfnsmentioning

confidence: 99%

Many regression algorithms, one unified model: A review

2015

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“…The final transformation should be able to extract desired information form this image. If the final transformation is linear Y = k+1 X = T k+1 ( k X; k W) parameters k W are either determined in an iterative procedure simultaneously with all other parameters W from previous transformations (as in the backpropagation algorithms [36]), or sequentially determined by calculating the pseudoinverse transformation, as is frequently practiced in the two-phase RBF learning [91]. Simultaneous adaptation of all parameters (RBF centers, scaling parameters, output layer weights) in experiments on more demanding data gives better results.…”

Section: Transformation-based Meta-learningmentioning

confidence: 99%

“…This is basically equivalent to random initialization of feedforward neural networks with linear transfer functions only. Such methods are used to start a twophase RBF learning [91]. For simple data random projections work rather well [97], but one should always check results of linear discrimination in the original feature space, as it may not be significantly worse.…”

Section: Transformation-based Meta-learningmentioning

confidence: 99%

Optimal Support Features for Meta-Learning

Duch

Maszczyk

Grochowski

2011

Studies in Computational Intelligence

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Meta-learning has many aspects, but its final goal is to discover in an automatic way many interesting models for a given data. Our early attempts in this area involved heterogeneous learning systems combined with a complexity-guided search for optimal models, performed within the framework of (dis)similarity based methods to discover "knowledge granules". This approach, inspired by neurocognitive mechanisms of information processing in the brain, is generalized here to learning based on parallel chains of transformations that extract useful information granules and use it as additional features. Various types of transformations that generate hidden features are analyzed and methods to generate them are discussed. They include restricted random projections, optimization of these features using projection pursuit methods, similarity-based and general kernel-based features, conditionally defined features, features derived from partial successes of various learning algorithms, and using the whole learning models as new features. In the enhanced feature space the goal of learning is to create image of the input data that can be directly handled by relatively simple decision processes. The focus is on hierarchical methods for generation of information, starting from new support features that are discovered by different types of data models created on similar tasks and successively building more complex features on the enhanced feature spaces. Resulting algorithms facilitate deep learning, and also enable understanding of structures present in the data by visualization of the results of data transformations and by creating logical, fuzzy and prototype-based rules based on new features. Relations to various machine-learning approaches, comparison of results, and neurocognitive inspirations for meta-learning are discussed.

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“…In this case the method for linear SVM training could be applied. The Gaussian radial basis function is one of this kernels, so the support vector learning could be applied as learning method for radial basis function network with support vectors being the centers of radial basis functions [7,8]. Paper [9] provides the idea of the extension of the support vector machine algorithm to the multiclass classification problem with usage of different weights for different outputs and selection of the class which produces the maximum value.…”

mentioning

confidence: 99%

Heart Disease Diagnosis Based on Deep Radial Basis Function Kernel Machine

Alsalamah¹,

Amin²,

Palade³

2018

ICST Transactions on Ambient Systems

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Over the years Radial Basis Function (RBF) Kernel Machines have been used in Machine Learning tasks, but there are certain flaws that prevent their usage in some up-to-date applications (e.g., some Kernel Machines suffer from fast growth number of learning parameters whilst predicting data with large number of variations). Besides, Kernel Machines with single hidden layer have no mechanisms for features selection in multidimensional data space, and machine-learning task becomes intractable with enlargement of the data available for analysis. To address these issues, this paper investigates the usage of a framework for "deep learning" architecture composed of multilayered adaptive non-linear components -Multilayer RBF Kernel Machine. To be precise, three different approaches of features selection and dimensionality reduction to train RBF based on Multilayer Kernel Learning are explored, and comparisons between them in terms of accuracy, performance and computational complexity are made. As opposed to the "shallow learning" algorithm with usually single layer architecture, results show that the multilayered system produces better results with large and highly varied data. In particular, features selection and dimensionality reduction, as a class of the multilayer method, shows results that are more accurate. This paper proposes a novel scheme based on deep Multilayer RBF Kernel Machine learning for sleep apnea detection and quantification using statistical features of ECG signals. The results obtained show that the newly proposed approach provides significant accuracy improvements compared to state-of-the-art methods. Because of its noninvasive and low-cost nature, this algorithm has the potential for numerous applications in sleep medicine.

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Three learning phases for radial-basis-function networks

Cited by 456 publications

References 32 publications

Many regression algorithms, one unified model: A review

Many regression algorithms, one unified model: A review

Optimal Support Features for Meta-Learning

Heart Disease Diagnosis Based on Deep Radial Basis Function Kernel Machine

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