Learning polyhedral classifiers using logistic function

In this paper we propose a new algorithm for learning polyhedral classifiers. In contrast to existing methods for learning polyhedral classifier which solve a constrained optimization problem, our method solves an unconstrained optimization problem. Our method is based on a logistic function based model for the posterior probability function. We propose an alternating optimization algorithm, namely, SPLA1 (Single Polyhedral Learning Algorithm1) which maximizes the loglikelihood of the training data to learn the parameters. We also extend our method to make it independent of any user specified parameter (e.g., number of hyperplanes required to form a polyhedral set) in SPLA2. We show the effectiveness of our approach with experiments on various synthetic and real world datasets and compare our approach with a standard decision tree method (OC1) and a constrained optimization based method for learning polyhedral sets.

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

A note on the von Bertalanffy growth function concerning the allocation of surplus energy to reproduction

We propose an extended form of the von Bertalanffy growth function (VBGF), where the allocation of surplus energy to reproduction is considered. Any function can be used in our model to describe the ratio of energy allocation for reproduction to that for somatic growth. As an example, two models for energy allocation were derived: a step-function and a logistic function. The extended model can jointly describe growth in adult and juvenile stages. The change in growth rate between the two stages can be either gradual or steep; the latter gives a biphasic VBGF. The results of curve fitting indicated that a consideration of reproductive energy is meaningful for model extension. By controlling parameter values, our comprehensive model gives various growth curve shapes ranging from indeterminate to determinate growth. An increase in the number of parameters is unavoidable in practical applications of this new model. Additional information on reproduction will improve the reliability of model estimates.

Knowledge extraction from a mixed transfer function artificial neural network

One of the main problems with Artificial Neural Networks (ANNs) is that their results are not intuitively clear. For example, commonly used hidden neurons with sigmoid activation function can approximate any continuous function, including linear functions, but the coefficients (weights) of this approximation are rather meaningless. To address this problem, current paper presents a novel kind of a neural network that uses transfer functions of various complexities in contrast to mono-transfer functions used in sigmoid and hyperbolic tangent networks. The presence of transfer functions of various complexities in a Mixed Transfer Functions Artificial Neural Network (MTFANN) allow easy conversion of the full model into user-friendly equation format (similar to that of linear regression) without any pruning or simplification of the model. At the same time, MTFANN maintains similar generalization ability to mono-transfer function networks in a global optimization context. The performance and knowledge extraction of MTFANN were evaluated on a realistic simulation of the Puma 560 robot arm and compared to sigmoid, hyperbolic tangent, linear and sinusoidal networks.

Knowledge extraction from a mixed transfer function artificial neural network

One of the big problems with Artificial Neural Networks (ANN) is that their results are not intuitively clear. For example, if we use the traditional neurons, with a sigmoid activation function, we can approximate any function, including linear functions, but the coefficients (weights) in this approximation will be rather meaningless. To resolve this problem, this paper presents a novel kind of ANN with different transfer functions mixed together. The aim of such a network is to i) obtain a better generalization than current networks ii) to obtain knowledge from the networks without a sophisticated knowledge extraction algorithm iii) to increase the understanding and acceptance of ANNs. Transfer Complexity Ratio is defined to make a sense of the weights associated with the network. The paper begins with a review of the knowledge extraction from ANNs and then presents a Mixed Transfer Function Artificial Neural Network (MTFANN). A MTFANN contains different transfer functions mixed together rather than mono-transfer functions. This mixed presence has helped to obtain high level knowledge and similar generalization comparatively to monotransfer function nets in a global optimization context.

Activation function study for wavelet network

The main purpose of this paper is to investigate theoretically and experimentally the use of family of Polynomial Powers of the Sigmoid (PPS) Function Networks applied in speech signal representation and function approximation. This paper carries out practical investigations in terms of approximation fitness (LSE), time consuming (CPU Time), computational complexity (FLOP) and representation power (Number of Activation Function) for different PPS activation functions. We expected that different activation functions can provide performance variations and further investigations will guide us towards a class of mappings associating the best activation function to solve a class of problems under certain criteria.

POLYCHOTOMOUS LOGISTIC REGRESSION ANALYSIS (HYPERTENSION, CORONARY HEART DISEASE)

The history of the logistic function since its introduction in 1838 is reviewed, and the logistic model for a polychotomous response variable is presented with a discussion of the assumptions involved in its derivation and use. Following this, the maximum likelihood estimators for the model parameters are derived along with a Newton-Raphson iterative procedure for evaluation. A rigorous mathematical derivation of the limiting distribution of the maximum likelihood estimators is then presented using a characteristic function approach. An appendix with theorems on the asymptotic normality of sample sums when the observations are not identically distributed, with proofs, supports the presentation on asymptotic properties of the maximum likelihood estimators. Finally, two applications of the model are presented using data from the Hypertension Detection and Follow-up Program, a prospective, population-based, randomized trial of treatment for hypertension. The first application compares the risk of five-year mortality from cardiovascular causes with that from noncardiovascular causes; the second application compares risk factors for fatal or nonfatal coronary heart disease with those for fatal or nonfatal stroke. ^

Phenotyping novel stay-green traits to capture genetic variation in senescence dynamics

Stay-green plants retain green leaves longer after anthesis and can have improved yield, particularly under water limitation. As senescence is a dynamic process, genotypes with different senescence patterns may exhibit similar final normalised difference vegetative index (NDVI). By monitoring NDVI from as early as awn emergence to maturity, we demonstrate that analysing senescence dynamics improves insight into genotypic stay-green variation. A senescence evaluation tool was developed to fit a logistic function to NDVI data and used to analyse data from three environments for a wheat (Triticum aestivum L.) population whose lines contrast for stay-green. Key stay-green traits were estimated including, maximum NDVI, senescence rate and a trait integrating NDVI variation after anthesis, as well as the timing from anthesis to onset, midpoint and conclusion of senescence. The integrative trait and the timing to onset and mid-senescence exhibited high positive correlations with yield and a high heritability in the three studied environments. Senescence rate was correlated with yield in some environments, whereas maximum NDVI was associated with yield in a drought-stressed environment. Where resources preclude frequent measurements, we found that NDVI measurements may be restricted to the period of rapid senescence, but caution is required when dealing with lines of different phenology. In contrast, regular monitoring during the whole period after flowering allows the estimation of senescence dynamics traits that may be reliably compared across genotypes and environments. We anticipate that selection for stay-green traits will enhance genetic progress towards high-yielding, stay-green germplasm.

Clays Can Decrease Gaseous Nutrient Losses from Soil-Applied Livestock Manures

Clays could underpin a viable agricultural greenhouse gas (GHG) abatement technology given their affinity for nitrogen and carbon compounds. We provide the first investigation into the efficacy of clays to decrease agricultural nitrogen GHG emissions (i.e., N2O and NH3). Via laboratory experiments using an automated closed-vessel analysis system, we tested the capacity of two clays (vermiculite and bentonite) to decrease N2O and NH3 emissions and organic carbon losses from livestock manures (beef, pig, poultry, and egg layer) incorporated into an agricultural soil. Clay addition levels varied, with a maximum of 1:1 to manure (dry weight). Cumulative gas emissions were modeled using the biological logistic function, with 15 of 16 treatments successfully fitted (P < 0.05) by this model. When assessing all of the manures together, NH3 emissions were lower (×2) at the highest clay addition level compared with no clay addition, but this difference was not significant (P = 0.17). Nitrous oxide emissions were significantly lower (×3; P < 0.05) at the highest clay addition level compared with no clay addition. When assessing manures individually, we observed generally decreasing trends in NH3 and N2O emissions with increasing clay addition, albeit with widely varying statistical significance between manure types. Most of the treatments also showed strong evidence of increased C retention with increasing clay additions, with up to 10 times more carbon retained in treatments containing clay compared with treatments containing no clay. This preliminary assessment of the efficacy of clays to mitigate agricultural GHG emissions indicates strong promise.

Volume Change behaviour in Calcitic Soil influenced with Sulphuric Acid using Artificial Neural Networks

This paper elucidates the methodology of applying artificial neural network model (ANNM) to predict the percent swell of calcitic soil in sulphuric acid solutions, a complex phenomenon involving many parameters. Swell data required for modelling is experimentally obtained using conventional oedometer tests under nominal surcharge. The phases in ANN include optimal design of architecture, operation and training of architecture. The designed optimal neural model (3-5-1) is a fully connected three layer feed forward network with symmetric sigmoid activation function and trained by the back propagation algorithm to minimize a quadratic error criterion.The used model requires parameters such as duration of interaction, calcite mineral content and acid concentration for prediction of swell. The observed strong correlation coefficient (R2 = 0.9979) between the values determined by the experiment and predicted using the developed model demonstrates that the network can provide answers to complex problems in geotechnical engineering.

An environmentally based growth model that uses finite difference calculus with maximum likelihood method: its application to the brackish water bivalve Corbicula japonica in Lake Abashiri, Japan

We present a growth analysis model that combines large amounts of environmental data with limited amounts of biological data and apply it to Corbicula japonica. The model uses the maximum-likelihood method with the Akaike information criterion, which provides an objective criterion for model selection. An adequate distribution for describing a single cohort is selected from available probability density functions, which are expressed by location and scale parameters. Daily relative increase rates of the location parameter are expressed by a multivariate logistic function with environmental factors for each day and categorical variables indicating animal ages as independent variables. Daily relative increase rates of the scale parameter are expressed by an equation describing the relationship with the daily relative increase rate of the location parameter. Corbicula japonica grows to a modal shell length of 0.7 mm during the first year in Lake Abashiri. Compared with the attain-able maximum size of about 30 mm, the growth of juveniles is extremely slow because their growth is less susceptible to environmental factors until the second winter. The extremely slow growth in Lake Abashiri could be a geographical genetic variation within C. japonica.

Copper complexation by fulvic acid affects copper toxicity to the larvae of the polychaete Hydroides elegans

Copper toxicity is influenced by a variety of environmental factors including dissolved organic matter (DOM). We examined the complexation of copper by fulvic acid (FA), one of the major components of DOM, by measuring the decline in labile copper by anodic stripping voltammetrically (ASV). The data were described using a one-site ligand binding model, with a ligand concentration of 0.19 mu mol site mg(-1) C, and a logK' of 6.2. The model was used to predict labile copper concentration in a bioassay designed to quantify the extent to which Cu-FA complexation affected copper toxicity to the larvae of marine polychaete Hydroides elegans. The toxicity data, when expressed as labile copper concentration causing abnormal development, were independent of FA concentration and could be modeled as a logistic function, with a 48-h EC50 of 58.9 mu g 1(-1). However, when the data were expressed as a function of total copper concentration, the toxicity was dependent on FA concentration, with a 48-h EC50 ranging from 55.6 mu g 1(-1) in the no-FA control to 137.4 mu g 1(-1) in the 20 mg 1(-1) FA treatment. Thus, FA was protective against copper toxicity to the larvae, and such an effect was caused by the reduction in labile copper due to Cu-FA complexation. Our results demonstrate the potential of ASV as a useful tool for predicting metal toxicity to the larvae in coastal environment where DOM plays an important role in complexing metal ions. (c) 2007 Elsevier Ltd. All rights reserved.

Models for the analysis of growth curves for rearing tinamous (Rhynchotus rufescens) in captivity

Growth curves models provide a visual assessment of growth as a function of time, and prediction body weight at a specific age. This study aimed at estimating tinamous growth curve using different models, and at verifying their goodness of fit. A total number 11,639 weight records from 411 birds, being 6,671 from females and 3,095 from males, was analyzed. The highest estimates of a parameter were obtained using Brody (BD), von Bertalanffy (VB), Gompertz (GP,) and Logistic function (LG). Adult females were 5.7% heavier than males. The highest estimates of b parameter were obtained in the LG, GP, BID, and VB models. The estimated k parameter values in decreasing order were obtained in LG, GP, VB, and BID models. The correlation between the parameters a and k showed heavier birds are less precocious than the lighter. The estimates of intercept, linear regression coefficient, quadratic regression coefficient, and differences between quadratic coefficient of functions and estimated ties of quadratic-quadratic-quadratic segmented polynomials (QQQSP) were: 31.1732 +/- 2.41339; 3.07898 +/- 0.13287; 0.02689 +/- 0.00152; -0.05566 +/- 0.00193; 0.02349 +/- 0.00107, and 57 and 145 days, respectively. The estimated predicted mean error values (PME) of VB, GP, BID, LG, and QQQSP models were, respectively, 0.8353; 0.01715; -0.6939; -2.2453; and -0.7544%. The coefficient of determination (RI) and least square error values (MS) showed similar results. In conclusion, the VB and the QQQSP models adequately described tinamous growth. The best model to describe tinamous growth was the Gompertz model, because it presented the highest R-2 values, easiness of convergence, lower PME, and the easiness of parameter biological interpretation.

Heritability estimates and genetic correlations for body weight and scrotal circumference adjusted to 12 and 18 months of age for male Nellore cattle

Heritability estimates and genetic correlations were obtained for body weight and scrotal circumference, adjusted, respectively, to 12 (BW12 and SC12) and 18 (BW18 and SC18) months of age, for 10 742 male Nellore cattle. The adjustments to SC12 and SC18 were made using a nonlinear logistic function, while BW12 and BW18 were obtained by linear adjustment. The contemporary groups (CGs) were defined from animals born on the same farm, in the same year and birth season. The mean heritability estimates obtained using the restricted maximum likelihood method in bi-trait analysis were 0.25, 0.25, 0.29 and 0.42 for BW12 BW18, SC12 and SC18, respectively. The genetic correlations were 0.30 +/- 0.11, 0.21 +/- 0.13, 0.21 +/- 0.11, -0.08 +/- 0.15, 0.16 +/- 0.12 and 0.89 +/- 0.04 between the traits BW12 and BW18; BW12 and SC12; BW12 and SC18; BW18 and SC12; BW18 and SC18; and SC12 and SC18. The heritability for SC18 was considerably greater than for SC12 suggesting that this should be included as a selection criterion. The genetic correlation between BW18 and SC12 was close to zero, indicating that these traits did not influence each other The contrary occurred between SC12 and SC18, indicating that selection using one of these could alter the other Because of the mean magnitudes of heritabilities in the various measurements of weight and scrotal perimeter it is suggested that the practice of individual selection for these traits is possible.