Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Multidimensional polynomial powers of sigmoid (PPS) Wavelet neural networks

Wavelet functions have been used as the activation function in feedforward neural networks. An abundance of R&D has been produced on wavelet neural network area. Some successful algorithms and applications in wavelet neural network have been developed and reported in the literature. However, most of the aforementioned reports impose many restrictions in the classical backpropagation algorithm, such as low dimensionality, tensor product of wavelets, parameters initialization, and, in general, the output is one dimensional, etc. In order to remove some of these restrictions, a family of polynomial wavelets generated from powers of sigmoid functions is presented. We described how a multidimensional wavelet neural networks based on these functions can be constructed, trained and applied in pattern recognition tasks. As an example of application for the method proposed, it is studied the exclusive-or (XOR) problem.

Human face verification based on multidimensional Polynomial Powers of Sigmoid (PPS)

In this paper, we described how a multidimensional wavelet neural networks based on Polynomial Powers of Sigmoid (PPS) can be constructed, trained and applied in image processing tasks. In this sense, a novel and uniform framework for face verification is presented. The framework is based on a family of PPS wavelets,generated from linear combination of the sigmoid functions, and can be considered appearance based in that features are extracted from the face image. The feature vectors are then subjected to subspace projection of PPS-wavelet. The design of PPS-wavelet neural networks is also discussed, which is seldom reported in the literature. The Stirling Universitys face database were used to generate the results. Our method has achieved 92 % of correct detection and 5 % of false detection rate on the database.

Schur-SzegA composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Genetic effects of the animal and its dam and maternal permanent environmental effects were modelled by random regressions on Legendre polynomials of age at recording. Changes in direct permanent environmental effect variances were modelled by a polynomial variance function, together with a parametric correlation function to account for correlations between ages. Stationary and nonstationary models were used to model within-animal correlations between different ages. Residual variances were considered homogeneous or heterogeneous, with changes modelled by a step or polynomial function of age at recording. Based on Bayesian information criterion, a model with a cubic variance function combined with a nonstationary correlation function for permanent environmental effects, with 49 parameters to be estimated, fitted best. Modelling within-animal correlations through a parametric correlation structure can describe the variation pattern adequately. Moreover, the number of parameters to be estimated can be decreased substantially compared to a model fitting random regression on Legendre polynomial of age. © 2004 Elsevier B.V. All rights reserved.

Classification of masses in mammographic image using wavelet domain features and polynomial classifier

Breast cancer is the most common cancer among women. In CAD systems, several studies have investigated the use of wavelet transform as a multiresolution analysis tool for texture analysis and could be interpreted as inputs to a classifier. In classification, polynomial classifier has been used due to the advantages of providing only one model for optimal separation of classes and to consider this as the solution of the problem. In this paper, a system is proposed for texture analysis and classification of lesions in mammographic images. Multiresolution analysis features were extracted from the region of interest of a given image. These features were computed based on three different wavelet functions, Daubechies 8, Symlet 8 and bi-orthogonal 3.7. For classification, we used the polynomial classification algorithm to define the mammogram images as normal or abnormal. We also made a comparison with other artificial intelligence algorithms (Decision Tree, SVM, K-NN). A Receiver Operating Characteristics (ROC) curve is used to evaluate the performance of the proposed system. Our system is evaluated using 360 digitized mammograms from DDSM database and the result shows that the algorithm has an area under the ROC curve Az of 0.98 ± 0.03. The performance of the polynomial classifier has proved to be better in comparison to other classification algorithms. © 2013 Elsevier Ltd. All rights reserved.

Random regression models using different functions to model milk flow in dairy cows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Schur-Szegö composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Learning kernels for support vector machines with polynomial powers of sigmoid

In the pattern recognition research field, Support Vector Machines (SVM) have been an effectiveness tool for classification purposes, being successively employed in many applications. The SVM input data is transformed into a high dimensional space using some kernel functions where linear separation is more likely. However, there are some computational drawbacks associated to SVM. One of them is the computational burden required to find out the more adequate parameters for the kernel mapping considering each non-linearly separable input data space, which reflects the performance of SVM. This paper introduces the Polynomial Powers of Sigmoid for SVM kernel mapping, and it shows their advantages over well-known kernel functions using real and synthetic datasets.

Estimates of covariance functions for growth from birth to 630 days of age in Nelore cattle

Weight records of Brazilian Nelore cattle, from birth to 630 d of age, recorded every 3 mo, were analyzed using random regression models. Independent variables were Legendre polynomials of age at recording. The model of analysis included contemporary groups as fixed effects and age of dam as a linear and quadratic covariable. Mean trends were modeled through a cubic regression on orthogonal polynomials of age. Up to four sets of random regression coefficients were fitted for animals' direct and maternal, additive genetic, and permanent environmental effects. Changes in measurement error variances with age were modeled through a variance function. Orders of polynomial fit from three to six were considered, resulting in up to 77 parameters to be estimated. Models fitting random regressions modeled the pattern of variances in the data adequately, with estimates similar to those from corresponding univariate analysis. Direct heritability estimates decreased after birth and tended to be lowest at ages at which maternal effect estimates tended to be highest. Maternal heritability estimates increased after birth to a peak around 110 to 120 d of age and decreased thereafter. Additive genetic direct correlation estimates between weights at standard ages (birth, weaning, yearling, and final weight) were moderate to high and maternal genetic and environmental correlations were consistently high.

Construction of polynomial spline spaces over quadtree and octree T-meshes

[EN]We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. ..

A simple strategy for defining polynomial spline spaces over hierarchical T-meses

[EN]We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision scheme. The proposed technique includes some simple rules for inferring local knot vectors to define C 2 -continuous cubic tensor product spline blending functions. Our conjecture is that these rules allow to obtain, for a given T-mesh, a set of linearly independent spline functions with the property that spaces spanned by nested T-meshes are also nested, and therefore, the functions can reproduce cubic polynomials. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0- balanced mesh...

Construction of polynomial spline spaces over quadtree and octree T-meshes

[EN]We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. ..

A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.

Legendre Polynomials, Dipole Moments, Generating Functions, etc..

A standard treatment of aspects of Legendre polynomials is treated here, including the dipole moment expansion, generating functions, etc..