This paper proposes a framework for constructing and training radial basis function (RBF) neural networks. The proposed growing radial basis function (GRBF) network begins with a small number of prototypes, which determine the locations of radial basis functions. In the process of training, the GRBF network gross by splitting one of the prototypes at each growing cycle. Two splitting criteria are proposed to determine which prototype to split in each growing cycle. The proposed hybrid learning scheme provides a framework for incorporating existing algorithms in the training of GRBF networks. These include unsupervised algorithms for clustering and learning vector quantization, as well as learning algorithms for training single-layer linear neural networks. A supervised learning scheme based on the minimization of the localized class-conditional variance is also proposed and tested. GRBF neural networks are evaluated and tested on a variety of data sets with very satisfactory results.
This paper presents an axiomatic approach for constructing radial basis function (RBF) neural networks. This approach results in a broad variety of admissible RBF models, including those employing Gaussian RBF's. The form of the RBF's is determined by a generator function. New RBF models can be developed according to the proposed approach by selecting generator functions other than exponential ones, which lead to Gaussian RBF's. This paper also proposes a supervised learning algorithm based on gradient descent for training reformulated RBF neural networks constructed using the proposed approach. A sensitivity analysis of the proposed algorithm relates the properties of RBF's with the convergence of gradient descent learning. Experiments involving a variety of reformulated RBF networks generated by linear and exponential generator functions indicate that gradient descent learning is simple, easily implementable, and produces RBF networks that perform considerably better than conventional RBF models trained by existing algorithms.
Presents a systematic approach for constructing reformulated radial basis function (RBF) neural networks, which was developed to facilitate their training by supervised learning algorithms based on gradient descent. This approach reduces the construction of radial basis function models to the selection of admissible generator functions. The selection of generator functions relies on the concept of the blind spot, which is introduced in the paper. The paper also introduces a new family of reformulated radial basis function neural networks, which are referred to as cosine radial basis functions. Cosine radial basis functions are constructed by linear generator functions of a special form and their use as similarity measures in radial basis function models is justified by their geometric interpretation. A set of experiments on a variety of datasets indicate that cosine radial basis functions outperform considerably conventional radial basis function neural networks with Gaussian radial basis functions. Cosine radial basis functions are also strong competitors to existing reformulated radial basis function models trained by gradient descent and feedforward neural networks with sigmoid hidden units.
This letter derives a new interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c-means and fuzzy learning vector quantization. These algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning. Derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent. A close relationship between the resulting algorithms and fuzzy c-means is revealed by investigating the functionals involved. It is also shown that the fuzzy c-means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition.
Summary: Purpose:The main objective of this research is the development of automated video processing and analysis procedures aimed at the recognition and characterization of the types of neonatal seizures. The long-term goal of this research is the integration of these computational procedures into the development of a stand-alone automated system that could be used as a supplement in the neonatal intensive care unit (NICU) to provide 24-h per day noninvasive monitoring of infants at risk for seizures.Methods: We developed and evaluated a variety of computational tools and procedures that may be used to carry out the three essential tasks involved in the development of a seizure recognition and characterization system: the extraction of quantitative motion information from video recordings of neonatal seizures in the form of motion-strength and motor-activity signals, the selection of quantitative features that convey some unique behavioral characteristics of neonatal seizures, and the training of artificial neural networks to distinguish neonatal seizures from random infant behaviors and to differentiate between myoclonic and focal clonic seizures.Results: The methods were tested on a set of 240 video recordings of 43 patients exhibiting myoclonic seizures (80 cases), focal clonic seizures (80 cases), and random infant movements (80 cases). The outcome of the experiments verified that opticalflow methods are promising computational tools for quantifying neonatal seizures from video recordings in the form of motionstrength signals. The experimental results also verified that the robust motion trackers developed in this study outperformed considerably the motion trackers based on predictive block matching in terms of both reliability and accuracy. The quantitative features selected from motion-strength and motor-activity signals constitute a satisfactory representation of neonatal seizures and random infant movements and seem to be complementary. Such features lead to trained neural networks that exhibit performance levels exceeding the initial goals of this study, the sensitivity goal being ≥80% and the specificity goal being ≥90%.Conclusions: The outcome of this experimental study provides strong evidence that it is feasible to develop an automated system for the recognition and characterization of the types of neonatal seizures based on video recordings. This will be accomplished by enhancing the accuracy and improving the reliability of the computational tools and methods developed during the course of the study outlined here.
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