Cross-validated structure selection for neural networks

Schenker, B.; Agarwal, Mukul

doi:10.1016/0098-1354(95)00013-r

Cited by 56 publications

(30 citation statements)

References 7 publications

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“…With weight decay, an additional term is added to the error function that is proportional to the sizes of the weights associated with each factor entering the models. Early stopping is a popular alternative to weight decay that is often employed when the number of parameters/number of samples ratio is significantly greater than unity (3,20,47,54,60). Early stopping is a nonconvergent technique that terminates training before the ANN is finished fitting the training data.…”

Section: Discussionmentioning

confidence: 99%

“…For this study, the values of ␣ selected for nirS, nirK, dsrAB 1 , and dsrAB 2 were 1.0, 0.35, 1.0, and 0.001, respectively. K-fold cross-validation is a well-established method of using an entire data set for both training and testing (7,54,58). We performed onefold, also known as leave-one-out, cross-validation in which one sample was withheld from training and used to test the model fitted to the remaining data.…”

Section: Molecular Methodsmentioning

confidence: 99%

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Coupling of Functional Gene Diversity and Geochemical Data from Environmental Samples

Palumbo

Schryver

Bagwell

et al. 2004

Appl Environ Microbiol

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Genomic techniques commonly used for assessing distributions of microorganisms in the environment often produce small sample sizes. We investigated artificial neural networks for analyzing the distributions of nitrite reductase genes (nirS and nirK) and two sets of dissimilatory sulfite reductase genes (dsrAB 1 and dsrAB 2 ) in small sample sets. Data reduction (to reduce the number of input parameters), cross-validation (to measure the generalization error), weight decay (to adjust model parameters to reduce generalization error), and importance analysis (to determine which variables had the most influence) were useful in developing and interpreting neural network models that could be used to infer relationships between geochemistry and gene distributions. A robust relationship was observed between geochemistry and the frequencies of genes that were not closely related to known dissimilatory sulfite reductase genes (dsrAB 2 ). Uranium and sulfate appeared to be the most related to distribution of two groups of these unusual dsrAB-related genes. For the other three groups, the distributions appeared to be related to pH, nickel, nonpurgeable organic carbon, and total organic carbon. The models relating the geochemical parameters to the distributions of the nirS, nirK, and dsrAB 1 genes did not generalize as well as the models for dsrAB 2 . The data also illustrate the danger (generating a model that has a high generalization error) of not using a validation approach in evaluating the meaningfulness of the fit of linear or nonlinear models to such small sample sizes.One of the goals of microbial ecology is to understand which abiotic factors control the abundance and distribution of microorganisms in the environment. Environmental microbial ecology is beginning to achieve this goal in a wide range of habitats (6,8,30,59) with the advent of molecular techniques that allow a significant part of the indigenous populations to be identified to some phylogenetic or functional level. For example, microbial distributions and diversity have been examined in relation to spatial factors (1), freshwater and ocean environments (51), and soil type (48, 50). Distribution or diversity has also been linked to dominant environmental characteristics or seasonal variations (29,43,57,63,68). To identify the critical factors that influence population distribution in complex environments, sophisticated data analysis techniques are needed to model the relationships between microbial distributions and environmental characteristics (14, 66).Cloning and sequencing of functional genes from environmental samples are powerful methods for investigating the ecology of microorganisms. These techniques have advanced our understanding of the types of microorganisms and degradation capabilities found in various habitats (6,12,15,43,51). However, relating the population data generated by these techniques to environmental characteristics, such as geochemical measurements, can be challenging. One problem is the small sample size that is typical in thes...

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Section: Discussionmentioning

confidence: 99%

Section: Molecular Methodsmentioning

confidence: 99%

Coupling of Functional Gene Diversity and Geochemical Data from Environmental Samples

Palumbo

Schryver

Bagwell

et al. 2004

Appl Environ Microbiol

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“…The leave-one-out cross-validation procedure [36] was adopted to test the performance of the network in a reliable manner, taking into account the limited number of cases available in the classes, and in the same time achieving an acceptable generalization in the classification and avoiding overtraining.…”

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confidence: 99%

Classification of Event-Related Potentials Associated with Response Errors in Actors and Observers Based on Autoregressive Modeling

Vasios¹

2010

TOMINFOJ

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Event-Related Potentials (ERPs) provide non-invasive measurements of the electrical activity on the scalp related to the processing of stimuli and preparation of responses by the brain. In this paper an ERP-signal classification method is proposed for discriminating between ERPs of correct and incorrect responses of actors and of observers seeing an actor making such responses. The classification method targeted signals containing error-related negativity (ERN) and error positivity (Pe) components, which are typically associated with error processing in the human brain. Feature extraction consisted of Multivariate Autoregressive modeling combined with the Simulated Annealing technique. The resulting information was subsequently classified by means of an Artificial Neural Network (ANN) using back-propagation algorithm under the "leave-one-out cross-validation" scenario and the Fuzzy C-Means (FCM) algorithm. The ANN consisted of a multi-layer perceptron (MLP). The approach yielded classification rates of up to 85%, both for the actors' correct and incorrect responses and the corresponding ERPs of the observers. The electrodes needed for such classifications were situated mainly at central and frontal areas. Results provide indications that the classification of the ERN is achievable. Furthermore, the availability of the Pe signals, in addition to the ERN, improves the classification, and this is more pronounced for observers' signals. The proposed ERP-signal classification method provides a promising tool to study error detection and observational-learning mechanisms in performance monitoring and joint-action research, in both healthy and patient populations.

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“…In a comparison of CV with two other MLP architecture selection strategies in a recent paper [20] CV was found to be the best at choosing the optimal network architecture, at least on the data sets tested. However, the comparison was based on only a single type of artificial data and did not look at any real world problem domains.…”

Section: Cross Validation (Cv)mentioning

confidence: 99%