Contour Plots of Objective Functions for Feed-Forward Neural Networks

Oh, Sang-Hoon

doi:10.5392/ijoc.2012.8.4.030

Cited by 3 publications

(5 citation statements)

References 19 publications

(27 reference statements)

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“…And, nCE error function with n=4 shows the optimal output more flat than CE and nCE with n=2 cases. The two-dimensional contour plots of CE and nCE error functions also show the same property [17]. So, we can argue that the property of divergence measures derived from CE and nCE coincides with the two-dimensional contour plot of CE and nCE error function in [17] and optimal outputs in [6] and [18].…”

Section: New Divergenc Measure From the N-th Order Extension Of Crosssupporting

confidence: 56%

Deriving a New Divergence Measure from Extended Cross-Entropy Error Function

Wakuya²,

Park³

et al. 2015

International Journal of Contents

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Relative entropy is a divergence measure between two probability density functions of a random variable. Assuming that the random variable has only two alphabets, the relative entropy becomes a cross-entropy error function that can accelerate training convergence of multi-layer perceptron neural networks. Also, the n-th order extension of cross-entropy (nCE) error function exhibits an improved performance in viewpoints of learning convergence and generalization capability. In this paper, we derive a new divergence measure between two probability density functions from the nCE error function. And the new divergence measure is compared with the relative entropy through the use of three-dimensional plots.

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Section: New Divergenc Measure From the N-th Order Extension Of Crosssupporting

confidence: 56%

Deriving a New Divergence Measure from Extended Cross-Entropy Error Function

Wakuya²,

Park³

et al. 2015

International Journal of Contents

Self Cite

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show abstract

“…Since the path prediction in this paper is realized through the chain prediction between nodes, every prediction can actually be regarded as a classification problem. By comparing common cost functions such as mean squared error, root mean squared error, mean absolute error and cross entropy [ 57 , 58 , 59 ], the cross entropy, which is appropriate for solving classification problems, is selected as the cost function:

where, N represents the total number of samples, p ( x ) refers to the probability of the true distribution, and q ( x ) refers to the probability estimate calculated through the model. The performance of cost function is affected by the total number of the samples, which should be taken into account for accurate result.…”

Section: Methodsmentioning

confidence: 99%

“…Since the path prediction in this paper is realized through the chain prediction between nodes, every prediction can actually be regarded as a classification problem. By comparing common cost functions such as mean squared error, root mean squared error, mean absolute error and cross entropy [57][58][59], the cross entropy, which is appropriate for solving classification problems, is selected as the cost function:…”

Section: Path Planning Applying Bp Neural Networkmentioning

confidence: 99%

BIM and Computer Vision-Based Framework for Fire Emergency Evacuation Considering Local Safety Performance

Deng

Zhang

et al. 2021

Sensors

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Fire hazard in public buildings may result in serious casualties due to the difficulty of evacuation caused by intricate interior space and unpredictable development of fire situations. It is essential to provide safe and reliable indoor navigation for people trapped in the fire. Distinguished from the global shortest rescue route planning, a framework focusing on the local safety performance is proposed for emergency evacuation navigation. Sufficiently utilizing the information from Building Information Modeling (BIM), this framework automatically constructs geometry network model (GNM) through Industry Foundation Classes (IFC) and integrates computer vision for indoor positioning. Considering the available local egress time (ALET), a back propagation (BP) neural network is applied for adjusting the rescue route according to the fire situation, improving the local safety performance of evacuation. A campus building is taken as an example for proving the feasibility of the framework proposed. The result indicates that the rescue route generated by proposed framework is secure and reasonable. The proposed framework provides an idea for using real-time images only to implement the automatic generation of rescue route when a fire hazard occurs, which is passive, cheap, and convenient.

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“…For real applications of FNNs, how to train FNNs is still a challenging problem and various objective functions have been proposed to improve the performance of FNNs [5]- [8]. Since these objective functions have peculiar properties, they can be compared by diverse ways [9]- [13].…”

Section: Introductionmentioning

confidence: 99%

“…These results show the reason why some objective functions have problems of over-fitting and slow convergence of learning. Also, the contours of objective functions were derived in a two-dimensional space [9], which can give us more informative comparison results for training of FNNs.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Objective Functions for Feed-forward Neural Network Classifiers Using Receiver Operating Characteristics Graph

Wakuya²

2014

International Journal of Contents

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When developing a classifier using various objective functions, it is important to compare the performances of the classifiers. Although there are statistical analyses of objective functions for classifiers, simulation results can provide us with direct comparison results and in this case, a comparison criterion is considerably critical. A Receiver Operating Characteristics (ROC) graph is a simulation technique for comparing classifiers and selecting a better one based on a performance. In this paper, we adopt the ROC graph to compare classifiers trained by mean-squared error, cross-entropy error, classification figure of merit, and the n-th order extension of cross-entropy error functions. After the training of feed-forward neural networks using the CEDAR database, the ROC graphs are plotted to help us identify which objective function is better.

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Contour Plots of Objective Functions for Feed-Forward Neural Networks

Abstract: Error surfaces provide us with very important information for training of feed-forward neural networks (FNNs

Cited by 3 publications

References 19 publications

Deriving a New Divergence Measure from Extended Cross-Entropy Error Function

Deriving a New Divergence Measure from Extended Cross-Entropy Error Function

BIM and Computer Vision-Based Framework for Fire Emergency Evacuation Considering Local Safety Performance

Comparison of Objective Functions for Feed-forward Neural Network Classifiers Using Receiver Operating Characteristics Graph

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