A New Accelerated Fixed-Point Algorithm for Classification and Convex Minimization Problems in Hilbert Spaces with Directed Graphs

Janngam, Kobkoon; Wattanataweekul, Rattanakorn

doi:10.3390/sym14051059

Cited by 2 publications

(1 citation statement)

References 39 publications

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“…In the past decade, many researchers introduced algorithms for finding the fixed points of G-nonexpansive mappings; see [11][12][13][14]. Recently, Janngam et al [15][16][17] introduced fixed-point algorithms in Hilbert spaces with directed graphs and applied these results to classification and image recovery.…”

Section: Introductionmentioning

confidence: 99%

An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems

Janngam

Suantai

2022

Mathematics

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In this paper, we propose a new accelerated common fixed-point algorithm for two countable families of G-nonexpansive mappings. Weak convergence results are obtained in the context of directed graphs in real Hilbert spaces. As applications, we apply the obtained results to solving some convex minimization problems and employ our proposed algorithm to solve the data classification of Breast Cancer, Heart Diseases and Ionosphere. Moreover, we also compare the performance of our proposed algorithm with other algorithms in the literature and it is shown that our algorithm has a better convergence behavior than the others.

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Section: Introductionmentioning

confidence: 99%

An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems

Janngam

Suantai

2022

Mathematics

Self Cite

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Training of an Extreme Learning Machine Autoencoder Based on an Iterative Shrinkage-Thresholding Optimization Algorithm

2022

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Orthogonal transformations, proper decomposition, and the Moore–Penrose inverse are traditional methods of obtaining the output layer weights for an extreme learning machine autoencoder. However, an increase in the number of hidden neurons causes higher convergence times and computational complexity, whereas the generalization capability is low when the number of neurons is small. One way to address this issue is to use the fast iterative shrinkage-thresholding algorithm (FISTA) to minimize the output weights of the extreme learning machine. In this work, we aim to improve the convergence speed of FISTA by using two fast algorithms of the shrinkage-thresholding class, called greedy FISTA (G-FISTA) and linearly convergent FISTA (LC-FISTA). Our method is an exciting proposal for decision-making involving the resolution of many application problems, especially those requiring longer computational times. In our experiments, we adopt six public datasets that are frequently used in machine learning: MNIST, NORB, CIFAR10, UMist, Caltech256, and Stanford Cars. We apply several metrics to evaluate the performance of our method, and the object of comparison is the FISTA algorithm due to its popularity for neural network training. The experimental results show that G-FISTA and LC-FISTA achieve higher convergence speeds in the autoencoder training process; for example, in the Stanford Cars dataset, G-FISTA and LC-FISTA are faster than FISTA by 48.42% and 47.32%, respectively. Overall, all three algorithms maintain good values of the performance metrics on all databases.

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A New Accelerated Fixed-Point Algorithm for Classification and Convex Minimization Problems in Hilbert Spaces with Directed Graphs

Cited by 2 publications

References 39 publications

An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems

An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems

Training of an Extreme Learning Machine Autoencoder Based on an Iterative Shrinkage-Thresholding Optimization Algorithm

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