A novel self-constructing Radial Basis Function Neural-Fuzzy System

Yang, Yansong; Sun, Tsung-Ying; Huo, Chih-Li; Yu, Yu-Hsiang; Liu, Chan-Cheng; Tsai, Cheng-Han

doi:10.1016/j.asoc.2013.01.023

Cited by 46 publications

(30 citation statements)

References 28 publications

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“…Proof: By injecting (16) in (17), we get min ξ κ(x i ,x i )− κ \{i} (x i ) ⊤ ξ ≥ δ 2 , for any i = 1, 2, . .…”

Section: Approximation Measurementioning

confidence: 99%

Analyzing Sparse Dictionaries for Online Learning With Kernels

Honeiné

2015

IEEE Trans. Signal Process.

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Many signal processing and machine learning methods share essentially the same linear-in-the-parameter model, with as many parameters as available samples as in kernel-based machines. Sparse approximation is essential in many disciplines, with new challenges emerging in online learning with kernels. To this end, several sparsity measures have been proposed in the literature to quantify sparse dictionaries and constructing relevant ones, the most prolific ones being the distance, the approximation, the coherence and the Babel measures. In this paper, we analyze sparse dictionaries based on these measures. By conducting an eigenvalue analysis, we show that these sparsity measures share many properties, including the linear independence condition and inducing a well-posed optimization problem. Furthermore, we prove that there exists a quasi-isometry between the parameter (i.e., dual) space and the dictionary's induced feature space. Index Terms-Sparse approximation, adaptive filtering, kernelbased methods, Gram matrix, machine learning, pattern recognition. Paul Honeine (M'07) was born in Beirut, Lebanon, on October 2, 1977. He received the Dipl.-Ing. degree in mechanical engineering in 2002 and the M.Sc. degree in industrial control in 2003, both from the Faculty of Engineering, the Lebanese University, Lebanon. In 2007, he received the Ph.D. degree in Systems Optimisation and Security from the University of Technology of Troyes, France, and was a Postdoctoral Research associate with the Systems Modeling and Dependability Laboratory, from 2007 to 2008. Since September 2008, he has been an assistant Professor at the University of Technology of Troyes, France. His research interests include nonstationary signal analysis and classification, nonlinear and statistical signal processing, sparse representations, machine learning. Of particular interest are applications to (wireless) sensor networks, biomedical signal processing, hyperspectral imagery and nonlinear adaptive system identification. He is the co-author (with C. Richard) of the 2009 Best Paper Award at the IEEE Workshop on Machine Learning for Signal Processing. Over the past 5 years, he has published more than 100 peerreviewed papers.

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“…Proof: By injecting (16) in (17), we get min ξ κ(x i ,x i )− κ \{i} (x i ) ⊤ ξ ≥ δ 2 , for any i = 1, 2, . .…”

Section: Approximation Measurementioning

confidence: 99%

Analyzing Sparse Dictionaries for Online Learning With Kernels

Honeiné

2015

IEEE Trans. Signal Process.

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“…Proof: To prove this result, we use the quadratic approximation error given in expression (14) where, for the particular case of β j = sign(κ(x t ,x j )), we get…”

Section: A Approximation Error Of Discarded Samplesmentioning

confidence: 99%

“…The most widely investigated criteria are the distance and the coherence criteria, as well as the Babel criterion. The distance criterion, introduced by Platt in [4] to control the complexity of resource-allocating networks in radial-basis-function networks, retains the most mutually distant samples ; see also [13], [14] for recent advances. The coherence criterion, introduced by Honeine, Richard, and Bermudez in [15], [16] with the recent advances in compressed sensing [17], [18], retains samples that are mutually least coherent.…”

Section: Introductionmentioning

confidence: 99%

Approximation Errors of Online Sparsification Criteria

Honeiné

2015

IEEE Trans. Signal Process.

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Abstract-Many machine learning frameworks, such as resource-allocating networks, kernel-based methods, Gaussian processes, and radial-basis-function networks, require a sparsification scheme in order to address the online learning paradigm. For this purpose, several online sparsification criteria have been proposed to restrict the model definition on a subset of samples. The most known criterion is the (linear) approximation criterion, which discards any sample that can be well represented by the already contributing samples, an operation with excessive computational complexity. Several computationally efficient sparsification criteria have been introduced in the literature, such as the distance, the coherence and the Babel criteria. In this paper, we provide a framework that connects these sparsification criteria to the issue of approximating samples, by deriving theoretical bounds on the approximation errors. Moreover, we investigate the error of approximating any feature, by proposing upper-bounds on the approximation error for each of the aforementioned sparsification criteria. Two classes of features are described in detail, the empirical mean and the principal axes in the kernel principal component analysis.

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“…The incoming vectors are being mapped by the radial basis functions in each hidden node. The output layer yields a vector by linear combination of the outputs of the hidden nodes to produce the final output [39]. The structure of an inputs and outputs RBFNN is depicted as…”

Section: Gaussian Rbfmentioning

confidence: 99%

Non-Gaussian Hybrid Transfer Functions: Memorizing Mine Survivability Calculations

Ansong

Huang

Yeboah

et al. 2015

Mathematical Problems in Engineering

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Hybrid algorithms and models have received significant interest in recent years and are increasingly used to solve real-world problems. Different from existing methods in radial basis transfer function construction, this study proposes a novel nonlinear-weight hybrid algorithm involving the non-Gaussian type radial basis transfer functions. The speed and simplicity of the non-Gaussian type with the accuracy and simplicity of radial basis function are used to produce fast and accurate on-the-fly model for survivability of emergency mine rescue operations, that is, the survivability under all conditions is precalculated and used to train the neural network. The proposed hybrid uses genetic algorithm as a learning method which performs parameter optimization within an integrated analytic framework, to improve network efficiency. Finally, the network parameters including mean iteration, standard variation, standard deviation, convergent time, and optimized error are evaluated using the mean squared error. The results demonstrate that the hybrid model is able to reduce the computation complexity, increase the robustness and optimize its parameters. This novel hybrid model shows outstanding performance and is competitive over other existing models.

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A novel self-constructing Radial Basis Function Neural-Fuzzy System

Cited by 46 publications

References 28 publications

Analyzing Sparse Dictionaries for Online Learning With Kernels

Analyzing Sparse Dictionaries for Online Learning With Kernels

Approximation Errors of Online Sparsification Criteria

Non-Gaussian Hybrid Transfer Functions: Memorizing Mine Survivability Calculations

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