Upper bound on pattern storage in feedforward networks

Narasimha, Pramod Lakshmi; Manry, M.T.; Galindo, Francisco

doi:10.1016/j.neucom.2008.04.014

Cited by 8 publications

(6 citation statements)

References 22 publications

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“…To evaluate the performance among the two classifiers (SFLN, ELM) using the scaled training data, five statistical indices (RMSE, CO, PE, RSQ, and R 2 ) were calculated for different numbers of hidden nodes for Scenario 1 (note: result figures are not shown here). SLFN's learning capacity is governed bỹ N ≤ N ≤ (1 + n/m)Ñ [55], so the lower bound of the number of hidden nodes is N/(1 + n/m) = 28/(1 + 3/1) = 7 for this experiment. This indicates that SLFN with nine hidden nodes can be used for prediction because its RMSE of training error is small.…”

Section: ) Comparison Of Elm and Slfnmentioning

confidence: 99%

Ensemble Learning via Higher Order Singular Value Decomposition for Integrating Data and Classifier Fusion in Water Quality Monitoring

Sun

Chang

Chen

et al. 2021

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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Current multimodal learning in smart feature extraction and classification has reshaped the landscape of remote sensing. The recent developments in smart feature extraction mainly rely on different machine learning and data mining algorithms as powerful classifiers to improve prediction accuracy. This article presents an innovative ensemble learning algorithm for integrated data and classifier fusion via higher order singular value decomposition (IDCF-HOSVD). Based on the fused data, different analytical, semiempirical, and empirical classifiers can be selected and applied to perform information retrieval that can be further synergized via a tensor flow based feature extraction scheme over the classifier space. When preserving core fused image patterns via HOSVD, the final step of IDCF-HOSVD helps rank the contributions from different classifiers via nonlinear correlation information entropy. Practical implementation of the IDCF-HOSVD algorithm was assessed through its application to map the seasonal water quality conditions in Lake Nicaragua, Central America.

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Section: ) Comparison Of Elm and Slfnmentioning

confidence: 99%

Ensemble Learning via Higher Order Singular Value Decomposition for Integrating Data and Classifier Fusion in Water Quality Monitoring

Sun

Chang

Chen

et al. 2021

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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show abstract

“…In this context, two scenarios of four include only the detected known teleconnection patterns for monthly and seasonal scale; the other two scenarios contain both known and unknown teleconnection patterns for monthly and seasonal scale. Note that the neural network capacity test associated with hidden layers was applied to check the potential overfitting of the proposed forecasting models (Narasimha et al, 2008;Sheela andDeepa, 2013, Wang et al, 2014).…”

Section: Mapping the Teleconnection Patterns Or Index Regions-pixel-wisementioning

confidence: 99%

Multi-scale quantitative precipitation forecasting using nonlinear and nonstationary teleconnection signals and artificial neural network models

Chang

Yang

Imen

et al. 2017

Journal of Hydrology

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Global sea surface temperature (SST) anomalies are observed to have a significant effect on terrestrial precipitation patterns throughout the United States. SST variations have been correlated with terrestrial precipitation via ocean-atmospheric interactions known as climate teleconnections. This study demonstrates how the scale effect could affect the forecasting accuracy with or without the inclusion of those newly discovered unknown teleconnection signals between Adirondack precipitation and SST anomaly in the Atlantic and Pacific oceans. Unique SST regions of both known and unknown telecommunication signals were extracted from the wavelet analysis and used as input variables in an artificial neural network (ANN) forecasting model. Monthly and seasonal scales were considered with respect to a host of long-term (30-year) nonlinear and nonstationary teleconnection signals detected locally at the study site of Adirondack. Similar intraannual time-lag effects of SST on precipitation variability are salient at both time scales. Sensitivity analysis of four scenarios reveals that more improvements of the forecasting accuracy of the ANN model can be observed by including both known and unknown teleconnection patterns at both time scales, although such improvements are not salient. Research findings also highlight the importance of choosing the forecasting model at the seasonal scale to predict more accurate peak values and global trends of terrestrial precipitation in response to teleconnection signals. The scale shift from monthly to seasonal may improve results by 17% and 17 mm/day in terms of R squared and root of mean square error values, respectively, if both known and unknown SST regions are considered for forecasting.

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“…. , NRL(i)} in (17) are the links with repeated weight A iq for the qth MF of x i . Theorem 2: The gradient components of the F-CONFIS in the premise part should be summed NRL(i) times for fuzzy variable x i .…”

Section: B Special Learning Algorithm For the Fuzzy Neural Network Via A Fully Connected Neural Fuzzy Inference Systemmentioning

confidence: 99%

“…Furthermore, it has been shown in [17] that the upper bound for the capacity of feed-forward networks with arbitrary hidden unit activation functions can be found. For a feed-forward network (without bias) with N inputs, M outputs, L hidden units, and arbitrary hidden activation functions, the number of patterns P that can be memorized with no error is less than or equal to L(N + M), divided by the number of outputs M .…”

Section: Capacity Of Fuzzy Neural Network or Fully Connected Neural Fuzzy Inference Systemmentioning

confidence: 99%

“…This is to say that the FNN designed for certain applications by human expert must have constraints, such as the maximum number of input and output samples it can approximate or memorize. Similar to the discussions of the capacity of multilayer NNs [17], the capacity of the FNN is thus defined as the maximum number of arbitrary distinct input samples that can be mapped to desired output samples with a zero error. The overcapacity may lead training process to diverge in the FNN.…”

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confidence: 99%

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The Bounded Capacity of Fuzzy Neural Networks (FNNs) Via a New Fully Connected Neural Fuzzy Inference System (F-CONFIS) With Its Applications

Wang

Chen

2014

IEEE Trans. Fuzzy Syst.

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In this paper, a fuzzy neural network (FNN) is transformed into an equivalent three-layer fully connected neural inference system (F-CONFIS). This F-CONFIS is a new type of a neural network whose links are with dependent and repeated weights between the input layer and hidden layer. For these special dependent repeated links of the F-CONFIS, some special properties are revealed. A new learning algorithm with these special properties is proposed in this paper for the F-CONFIS. The F-CONFIS is therefore applied for finding the capacity of the FNN. The lower bound and upper bound of the capacity of the FNN can be found from a new theorem proposed in this paper. Several examples are illustrated with satisfactory simulation results for the capacity of the F-CONFIS (or the FNN). These include "within capacity training of the FNN," "over capacity training of the FNN," "training by increasing the capacity of the FNN," and "impact of the capacity of the FNN in clustering Iris Data." It is noted that the finding of the capacity of the F-CONFIS, or FNN, has its emerging values in all engineering applications using fuzzy neural networks. This is to say that all engineering applications using FNN should not exceed the capacity of the FNN to avoid unexpected results. The clustering of Iris data using FNN illustrated in this paper is one of the most relevant engineering applications in this regards. Index Terms-Capacity of neural networks, fuzzy neural networks (FNNs), fuzzy system, Iris data, neural networks. I. INTRODUCTIONI N the past decade, fuzzy neural networks (FNNs) have been widely used in many kinds of subject areas and engineering applications for problem solving, such as pattern recognition, intelligent adaptive control, regression or density estimation, and so on [1]-[6]. The FNN possesses the characteristics of linguistic information and the learning of a neural Manuscript

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Upper bound on pattern storage in feedforward networks

Cited by 8 publications

References 22 publications

Ensemble Learning via Higher Order Singular Value Decomposition for Integrating Data and Classifier Fusion in Water Quality Monitoring

Ensemble Learning via Higher Order Singular Value Decomposition for Integrating Data and Classifier Fusion in Water Quality Monitoring

Multi-scale quantitative precipitation forecasting using nonlinear and nonstationary teleconnection signals and artificial neural network models

The Bounded Capacity of Fuzzy Neural Networks (FNNs) Via a New Fully Connected Neural Fuzzy Inference System (F-CONFIS) With Its Applications

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