Analysis of input-output clustering for determining centers of RBFN

Uykan, Zekeriya; Güzeliş, Cüneyt; Çelebi, M.E.; Koivo, H.N.

doi:10.1109/72.857766

Cited by 137 publications

(47 citation statements)

References 22 publications

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“…For instance, the number and position of the RBFs may be fixed and defined a priori [12], or they may be determined by conducting a clustering analysis of the training dataset and allocate one hidden unit for each cluster. Algorithms differ by the clustering algorithm employed: k-means clustering, fuzzy k-means clustering, hierarchical clustering and self-organizing map NNs, [13], or also inputoutput clustering [14].…”

Section: Related Workmentioning

confidence: 99%

Logistic Regression by Means of Evolutionary Radial Basis Function Neural Networks

Gutiérrez

Hervás-Martı́nez

Martínez-Estudillo

2011

IEEE Trans. Neural Netw.

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Abstract-This paper proposes a hybrid multilogistic methodology, named logistic regression using initial and radial basis function (RBF) covariates. The process for obtaining the coefficients is carried out in three steps. First, an evolutionary programming (EP) algorithm is applied, in order to produce an RBF neural network (RBFNN) with a reduced number of RBF transformations and the simplest structure possible. Then, the initial attribute space (or, as commonly known as in logistic regression literature, the covariate space) is transformed by adding the nonlinear transformations of the input variables given by the RBFs of the best individual in the final generation. Finally, a maximum likelihood optimization method determines the coefficients associated with a multilogistic regression model built in this augmented covariate space. In this final step, two different multilogistic regression algorithms are applied: one considers all initial and RBF covariates (multilogistic initial-RBF regression) and the other one incrementally constructs the model and applies cross validation, resulting in an automatic covariate selection [simplelogistic initial-RBF regression (SLIRBF)]. Both methods include a regularization parameter, which has been also optimized. The methodology proposed is tested using 18 benchmark classification problems from well-known machine learning problems and two real agronomical problems. The results are compared with the corresponding multilogistic regression methods applied to the initial covariate space, to the RBFNNs obtained by the EP algorithm, and to other probabilistic classifiers, including different RBFNN design methods [e.g., relaxed variable kernel density estimation, support vector machines, a sparse classifier (sparse multinomial logistic regression)] and a procedure similar to SLIRBF but using product unit basis functions. The SLIRBF models are found to be competitive when compared with the corresponding multilogistic regression methods and the RBFEP method. A measure of statistical significance is used, which indicates that SLIRBF reaches the state of the art.

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Section: Related Workmentioning

confidence: 99%

Logistic Regression by Means of Evolutionary Radial Basis Function Neural Networks

Gutiérrez

Hervás-Martı́nez

Martínez-Estudillo

2011

IEEE Trans. Neural Netw.

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“…The output layer is linear, and it produces the predicted class labels based on the response of the hidden units. Theoretical and empirical studies showed that the performance of the RBF network highly depends on the number and initial locations of the hidden units [1], [2]. However, no well defined procedure exists how to tackle this cumbersome step.…”

Section: Introductionmentioning

confidence: 99%

A Supervised Clustering Algorithm for the Initialization of RBF Neural Network Classifiers

Çevikalp

Larlus

Jurie

2007

2007 IEEE 15th Signal Processing and Communications Applications

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ÖzetçeBu bildiride RBF sinir ağlarındaki saklı katman öğelerinin sayısını ve başlangıç yerlerini bulmak için tektürel topaklandırma algoritması adını verdiğimiz yeni bir yöntem önerdik. Bu amaçla kullanılan diğer yöntemlerin aksine, önerdiğimiz yöntem sınıfların etiket bilgisini kullanan bir yaklaşım olup, aranan parametreler sınıflar arasındaki örtüşmelere göre belirlenir. Önerilen yöntemin ardındaki temel fikir, içinde sadece tek bir sınıfa ait elemanlar bulunan tektürel topaklar oluşturmaktır. Önerilen yöntemi RBF sinir ağları sınıflandırıcısıyla birlikte Graz02 nesne veri tabanı ve ORL yüz veri tabanı üzerinde test ettik. Deneysel sonuçlar önerdiğimiz yöntemle başlatılan RBF sınıflandırıcının k-enyakın-merkez topaklandırma yöntemiyle başlatılan RBF sınıflandırıcıdan çok daha iyi sonuçlar verdiğini göstermektedir. Aynı zamanda elde edilen tanıma oranları Graz02 nesne veri tabanı için literatürde yayınlanan en iyi tanıma oranlarını geçmekte ve ORL yüz veri tabanı için de benzer sonuçlar üretmektedir. Bu da bu çalışmada sunulan topaklandırma yönteminin saklı katman öğelerinin sayısını ve başlangıç yerlerini bulmada oldukça başarılı olduğunu göstermektedir. AbstractIn this paper, we propose a new supervised clustering algorithm, coined as the Homogeneous Clustering (HC), to find the number and initial locations of the hidden units in Radial Basis Function (RBF) neural network classifiers. In contrast to the traditional clustering algorithms introduced for this goal, the proposed algorithm is a supervised procedure where the number and initial locations of the hidden units are determined based on split of the clusters having overlaps among the classes. The basic idea of the proposed approach is to create class specific homogenous clusters where the corresponding samples are closer to their mean than the means of rival clusters belonging to other class categories. We tested the proposed clustering algorithm along with the RBF network classifier on the Graz02 object database and the ORL face database. The experimental results show that the RBF network classifier performs better when it is initialized with the proposed HC algorithm than an unsupervised k-means algorithm. Moreover, our recognition results exceed the best published results on the Graz02 database and they are comparable to the best results on the ORL face database indicating that the proposed clustering algorithm initializes the hidden unit parameters successfully.

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“…Some of the steps in the proofs of Appendices A and B are partly inspired by the analysis in [22,23]. Examining the average SNR functionθ a (·) in (2), we prove in Appendix A that theθ a (·) has a global Lipschitz constant…”

Section: A Appendixmentioning

confidence: 99%

Composite vector quantization for optimizing antenna locations

Uykan

Jäntti²

2018

Turk J Elec Eng & Comp Sci

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Abstract:In this paper, we study the location optimization problem of remote antenna units (RAUs) in generalized distributed antenna systems (GDASs). We propose a composite vector quantization (CVQ) algorithm that consists of unsupervised and supervised terms for RAU location optimization. We show that the CVQ can be used i) to minimize an upper bound to the cell-averaged SNR error for a desired/demanded location-specific SNR function, and ii) to maximize the cell-averaged effective SNR. The CVQ-DAS includes the standard VQ, and thus the well-known squared distance criterion (SDC) as a special case. Computer simulations confirm the findings and suggest that the proposed CVQ-DAS outperforms the SDC in terms of cell-averaged "effective SNR".

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Analysis of input-output clustering for determining centers of RBFN

Cited by 137 publications

References 22 publications

Logistic Regression by Means of Evolutionary Radial Basis Function Neural Networks

Logistic Regression by Means of Evolutionary Radial Basis Function Neural Networks

A Supervised Clustering Algorithm for the Initialization of RBF Neural Network Classifiers

Composite vector quantization for optimizing antenna locations

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