Reducing the number of support vectors of SVM classifiers using the smoothed separable case approximation.

In this brief, we propose a new method to reduce the number of support vectors of support vector machine (SVM) classifiers. We formulate the approximation of an SVM solution as a classification problem that is separable in the feature space. Due to the separability, the hard-margin SVM can be used to solve it. This approach, which we call the separable case approximation (SCA), is very similar to the cross-training algorithm explained in , which is inspired by editing algorithms . The norm of the weight vector achieved by SCA can, however, become arbitrarily large. For that reason, we propose an algorithm, called the smoothed SCA (SSCA), that additionally upper-bounds the weight vector of the pruned solution and, for the commonly used kernels, reduces the number of support vectors even more. The lower the chosen upper bound, the larger this extra reduction becomes. Upper-bounding the weight vector is important because it ensures numerical stability, reduces the time to find the pruned solution, and avoids overfitting during the approximation phase. On the examined datasets, SSCA drastically reduces the number of support vectors.

Coupled simulated annealing.

We present a new class of methods for the global optimization of continuous variables based on simulated annealing (SA). The coupled SA (CSA) class is characterized by a set of parallel SA processes coupled by their acceptance probabilities. The coupling is performed by a term in the acceptance probability function, which is a function of the energies of the current states of all SA processes. A particular CSA instance method is distinguished by the form of its coupling term and acceptance probability. In this paper, we present three CSA instance methods and compare them with the uncoupled case, i.e., multistart SA. The primary objective of the coupling in CSA is to create cooperative behavior via information exchange. This aim helps in the decision of whether uphill moves will be accepted. In addition, coupling can provide information that can be used online to steer the overall optimization process toward the global optimum. We present an example where we use the acceptance temperature to control the variance of the acceptance probabilities with a simple control scheme. This approach leads to much better optimization efficiency, because it reduces the sensitivity of the algorithm to initialization parameters while guiding the optimization process to quasioptimal runs. We present the results of extensive experiments and show that the addition of the coupling and the variance control leads to considerable improvements with respect to the uncoupled case and a more recently proposed distributed version of SA.

Cluster synchronization in oscillatory networks.

Synchronous behavior in networks of coupled oscillators is a commonly observed phenomenon attracting a growing interest in physics, biology, communication, and other fields of science and technology. Besides global synchronization, one can also observe splitting of the full network into several clusters of mutually synchronized oscillators. In this paper, we study the conditions for such cluster partitioning into ensembles for the case of identical chaotic systems. We focus mainly on the existence and the stability of unique unconditional clusters whose rise does not depend on the origin of the other clusters. Also, conditional clusters in arrays of globally nonsymmetrically coupled identical chaotic oscillators are investigated. The design problem of organizing clusters into a given configuration is discussed.

A possible role of the cytochrome P450c17alpha gene (CYP17) polymorphism in the pathobiology of uterine leiomyomas from black South African women: a pilot study.

BACKGROUND: To investigate the role of the CYP17 gene promoter polymorphism in the pathobiology of uterine leiomyomas in African and Caucasian women. METHODS: During a 6-month period, 145 Caucasian and black South African women undergoing hysterectomy were included prospectively. Blood samples were obtained for DNA analysis. Factors modifying the risk for uterine leiomyoma growth such as age, parity, age at last birth, weight, body mass index, menopausal status, cigarette smoking and oral contraceptive use were determined. RESULTS: The risk for leiomyoma development among black South African homozygous carriers of the CYP17 A2 allele was shown to be significantly increased when compared to women homozygous for the CYP17 A1 allele or to heterozygous women. Logistic regression analysis disclosed age, parity and CYP17 polymorphism to have an impact on the presence of uterine leiomyomas (p-values are, respectively, 0.0006, 0.0001 and 0.03) in black South African women. However, among Caucasian women, logistic regression analysis showed only intake of oral contraceptives to influence the formation of uterine leiomyomas (p = 0.03). CONCLUSION: This exploratory trial suggests that among African women, homozygous carriers of the CYP17 A2 allele expose their myometrium to a stronger estrogenic stimulation contributing to the pathobiology of uterine leiomyomas.

Embedding recurrent neural networks into predator-prey models.

We study changes of coordinates that allow the embedding of ordinary differential equations describing continuous-time recurrent neural networks into differential equations describing predator-prey models-also called Lotka-Volterra systems. We transform the equations for the neural network first into quasi-monomial form (Brenig, L. (1988). Complete factorization and analytic solutions of generalized Lotka-Volterra equations. Physics Letters A, 133(7-8), 378-382), where we express the vector field of the dynamical system as a linear combination of products of powers of the variables. In practice, this transformation is possible only if the activation function is the hyperbolic tangent or the logistic sigmoid. From this quasi-monomial form, we can directly transform the system further into Lotka-Volterra equations. The resulting Lotka-Volterra system is of higher dimension than the original system, but the behavior of its first variables is equivalent to the behavior of the original neural network. We expect that this transformation will permit the application of existing techniques for the analysis of Lotka-Volterra systems to recurrent neural networks. Furthermore, our results show that Lotka-Volterra systems are universal approximators of dynamical systems, just as are continuous-time neural networks.

NL(q) Theory: A Neural Control Framework with Global Asymptotic Stability Criteria.

In this paper a framework for model-based neural control design is presented, consisting of nonlinear state space models and controllers, parametrized by multilayer feedforward neural networks. The models and closed-loop systems are transformed into so-called NL(q) system form. NL(q) systems represent a large class of nonlinear dynamical systems consisting of q layers with alternating linear and static nonlinear operators that satisfy a sector condition. For such NL(q)s sufficient conditions for global asymptotic stability, input/output stability (dissipativity with finite L(2)-gain) and robust stability and performance are presented. The stability criteria are expressed as linear matrix inequalities. In the analysis problem it is shown how stability of a given controller can be checked. In the synthesis problem two methods for neural control design are discussed. In the first method Narendra's dynamic backpropagation for tracking on a set of specific reference inputs is modified with an NL(q) stability constraint in order to ensure, e.g., closed-loop stability. In a second method control design is done without tracking on specific reference inputs, but based on the input/output stability criteria itself, within a standard plant framework as this is done, for example, in H( infinity ) control theory and &mgr; theory. Copyright 1997 Elsevier Science Ltd.