Evolutionary product unit based neural networks for regression.

This paper presents a new method for regression based on the evolution of a type of feed-forward neural networks whose basis function units are products of the inputs raised to real number power. These nodes are usually called product units. The main advantage of product units is their capacity for implementing higher order functions. Nevertheless, the training of product unit based networks poses several problems, since local learning algorithms are not suitable for these networks due to the existence of many local minima on the error surface. Moreover, it is unclear how to establish the structure of the network since, hitherto, all learning methods described in the literature deal only with parameter adjustment. In this paper, we propose a model of evolution of product unit based networks to overcome these difficulties. The proposed model evolves both the weights and the structure of these networks by means of an evolutionary programming algorithm. The performance of the model is evaluated in five widely used benchmark functions and a hard real-world problem of microbial growth modeling. Our evolutionary model is compared to a multistart technique combined with a Levenberg-Marquardt algorithm and shows better overall performance in the benchmark functions as well as the real-world problem.

Hybridization of evolutionary algorithms and local search by means of a clustering method.

This paper presents a hybrid evolutionary algorithm (EA) to solve nonlinear-regression problems. Although EAs have proven their ability to explore large search spaces, they are comparatively inefficient in fine tuning the solution. This drawback is usually avoided by means of local optimization algorithms that are applied to the individuals of the population. The algorithms that use local optimization procedures are usually called hybrid algorithms. On the other hand, it is well known that the clustering process enables the creation of groups (clusters) with mutually close points that hopefully correspond to relevant regions of attraction. Local-search procedures can then be started once in every such region. This paper proposes the combination of an EA, a clustering process, and a local-search procedure to the evolutionary design of product-units neural networks. In the methodology presented, only a few individuals are subject to local optimization. Moreover, the local optimization algorithm is only applied at specific stages of the evolutionary process. Our results show a favorable performance when the regression method proposed is compared to other standard methods.

Logistic regression by means of evolutionary radial basis function neural networks.

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.

Patient tolerance during outpatient flexible cystoscopy--a prospective, randomized, double-blind study comparing plain lubrication and lidocaine gel.

OBJECTIVE: To compare the tolerance of flexible cystoscopy with topical anesthetic versus simple lubrication when the assigned lubricant is instilled 5 min before the exploration. MATERIAL AND METHODS: A total of 185 consecutive patients were randomly assigned either to simple lubrication (Group 1) or to lidocaine hydrochloride gel (Group 2). Thirteen patients had some kind of difficulty during exploration (stenosis) that required additional manipulation or electrocoagulation for small relapses and were excluded from the final analysis, leaving 172 patients suitable for inclusion. After the intervention, all patients were surveyed regarding their discomfort and pain levels using a verbal scale and a visual analog scale ranging from zero to 10. A chi2 analysis was performed for comparison of qualitative covariables, and quantitative covariables were compared using Student's t-test. RESULTS: The 172 patients were evenly distributed between the two groups. Of those in Group 1, 89% noted little or no discomfort, compared to 84% in Group 2. Some pain or intense pain was noted by 10% and 16% in Groups 1 and 2, respectively (p > 0.05). The average value on the visual analog scale was 2.10 and 1.97 in Groups 1 and 2, respectively (p > 0.05). CONCLUSION: There are no differences in the perception of discomfort and pain by patients when anesthetic lubricant or simple lubrication are used if the waiting time before the exploration is 5 min.