Thrust allocation with linear constrained quadratic cost function

In this paper, a method of thrust allocation based on a linearly constrained quadratic cost function capable of handling rotating azimuths is presented. The problem formulation accounts for magnitude and rate constraints on both thruster forces and azimuth angles. The advantage of this formulation is that the solution can be found with a finite number of iterations for each time step. Experiments with a model ship are used to validate the thrust allocation system.

Acoustic identification of 12 species of echolocating bat by discriminant function analysis and artificial neural networks

We recorded echolocation calls from 14 sympatric species of bat in Britain. Once digitised, one temporal and four spectral features were measured from each call. The frequency-time course of each call was approximated by fitting eight mathematical functions, and the goodness of fit, represented by the mean-squared error, was calculated. Measurements were taken using an automated process that extracted a single call from background noise and measured all variables without intervention. Two species of Rhinolophus were easily identified from call duration and spectral measurements. For the remaining 12 species, discriminant function analysis and multilayer back-propagation perceptrons were used to classify calls to species level. Analyses were carried out with and without the inclusion of curve-fitting data to evaluate its usefulness in distinguishing among species. Discriminant function analysis achieved an overall correct classification rate of 79% with curve-fitting data included, while an artificial neural network achieved 87%. The removal of curve-fitting data improved the performance of the discriminant function analysis by 2 %, while the performance of a perceptron decreased by 2 %. However, an increase in correct identification rates when curve-fitting information was included was not found for all species. The use of a hierarchical classification system, whereby calls were first classified to genus level and then to species level, had little effect on correct classification rates by discriminant function analysis but did improve rates achieved by perceptrons. This is the first published study to use artificial neural networks to classify the echolocation calls of bats to species level. Our findings are discussed in terms of recent advances in recording and analysis technologies, and are related to factors causing convergence and divergence of echolocation call design in bats.

Acoustic identification of twelve species of echolocating bat by discriminant function analysis and artificial neural networks

We recorded echolocation calls from 14 sympatric species of bat in Britain. Once digitised, one temporal and four spectral features were measured from each call. The frequency-time course of each call was approximated by fitting eight mathematical functions, and the goodness of fit, represented by the mean-squared error, was calculated. Measurements were taken using an automated process that extracted a single call from background noise and measured all variables without intervention. Two species of Rhinolophus were easily identified from call duration and spectral measurements. For the remaining 12 species, discriminant function analysis and multilayer back-propagation perceptrons were used to classify calls to species level. Analyses were carried out with and without the inclusion of curve-fitting data to evaluate its usefulness in distinguishing among species. Discriminant function analysis achieved an overall correct classification rate of 79% with curve-fitting data included, while an artificial neural network achieved 87%. The removal of curve-fitting data improved the performance of the discriminant function analysis by 2 %, while the performance of a perceptron decreased by 2 %. However, an increase in correct identification rates when curve-fitting information was included was not found for all species. The use of a hierarchical classification system, whereby calls were first classified to genus level and then to species level, had little effect on correct classification rates by discriminant function analysis but did improve rates achieved by perceptrons. This is the first published study to use artificial neural networks to classify the echolocation calls of bats to species level. Our findings are discussed in terms of recent advances in recording and analysis technologies, and are related to factors causing convergence and divergence of echolocation call design in bats.

Examining the Effectiveness of Discriminant Function Analysis and Cluster Analysis in Species Identification of Male Field Crickets Based on Their Calling Songs

Traditional taxonomy based on morphology has often failed in accurate species identification owing to the occurrence of cryptic species, which are reproductively isolated but morphologically identical. Molecular data have thus been used to complement morphology in species identification. The sexual advertisement calls in several groups of acoustically communicating animals are species-specific and can thus complement molecular data as non-invasive tools for identification. Several statistical tools and automated identifier algorithms have been used to investigate the efficiency of acoustic signals in species identification. Despite a plethora of such methods, there is a general lack of knowledge regarding the appropriate usage of these methods in specific taxa. In this study, we investigated the performance of two commonly used statistical methods, discriminant function analysis (DFA) and cluster analysis, in identification and classification based on acoustic signals of field cricket species belonging to the subfamily Gryllinae. Using a comparative approach we evaluated the optimal number of species and calling song characteristics for both the methods that lead to most accurate classification and identification. The accuracy of classification using DFA was high and was not affected by the number of taxa used. However, a constraint in using discriminant function analysis is the need for a priori classification of songs. Accuracy of classification using cluster analysis, which does not require a priori knowledge, was maximum for 6-7 taxa and decreased significantly when more than ten taxa were analysed together. We also investigated the efficacy of two novel derived acoustic features in improving the accuracy of identification. Our results show that DFA is a reliable statistical tool for species identification using acoustic signals. Our results also show that cluster analysis of acoustic signals in crickets works effectively for species classification and identification.

On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the study of tephrochrology. In this paper, DFA is applied to compositional datasets of two different types of tephras from Mountain Ruapehu in New Zealand and Mountain Rainier in USA. The canonical variables from the analysis are further investigated with a statistical methodology of change-point problems in order to gain a better understanding of the change in compositional pattern over time. Finally, a special case of segmented regression has been proposed to model both the time of change and the change in pattern. This model can be used to estimate the age for the unknown tephras using Bayesian statistical calibration

Intake, the discriminant function : a report on the national study on social services for children and their families /

Issued Apr. 1980.

Exact Discriminant Function Design Using Some Optimization Techniques

Some aspects of design of the discriminant functions that in the best way separate points of predefined final sets are considered. The concept is introduced of the nested discriminant functions which allow to separate correctly points of any of the final sets. It is proposed to apply some methods of non-smooth optimization to solve arising extremal problems efficiently.

Aplicativo computacional da função discriminante quadrática para utilização em ciências experimentais

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Quadratic Lyapunov functions for linear systems Journal

The paper deals with the existence of a quadratic Lyapunov function V = x′P(t)x for an exponentially stable linear system with varying coefficients described by the vector differential equation S0305004100044777_inline1 The derivative dV/dt is allowed to be strictly semi-(F) and the locus dV/dt = 0 does not contain any arc of the system trajectory. It is then shown that the coefficient matrix A(t) of the exponentially stable sy

B-Spline potential function for maximum a-posteriori image reconstruction in fluorescence microscopy

An iterative image reconstruction technique employing B-Spline potential function in a Bayesian framework is proposed for fluorescence microscopy images. B-splines are piecewise polynomials with smooth transition, compact support and are the shortest polynomial splines. Incorporation of the B-spline potential function in the maximum-a-posteriori reconstruction technique resulted in improved contrast, enhanced resolution and substantial background reduction. The proposed technique is validated on simulated data as well as on the images acquired from fluorescence microscopes (widefield, confocal laser scanning fluorescence and super-resolution 4Pi microscopy). A comparative study of the proposed technique with the state-of-art maximum likelihood (ML) and maximum-a-posteriori (MAP) with quadratic potential function shows its superiority over the others. B-Spline MAP technique can find applications in several imaging modalities of fluorescence microscopy like selective plane illumination microscopy, localization microscopy and STED. (C) 2015 Author(s).

Automatic classification of field-collected dinoflagellates by artificial neural network

Automatic taxonomic categorisation of 23 species of dinoflagellates was demonstrated using field-collected specimens. These dinoflagellates have been responsible for the majority of toxic and noxious phytoplankton blooms which have occurred in the coastal waters of the European Union in recent years and make severe impact on the aquaculture industry. The performance by human 'expert' ecologists/taxonomists in identifying these species was compared to that achieved by 2 artificial neural network classifiers (multilayer perceptron and radial basis function networks) and 2 other statistical techniques, k-Nearest Neighbour and Quadratic Discriminant Analysis. The neural network classifiers outperform the classical statistical techniques. Over extended trials, the human experts averaged 85% while the radial basis network achieved a best performance of 83%, the multilayer perceptron 66%, k-Nearest Neighbour 60%, and the Quadratic Discriminant Analysis 56%.

A function to predict the risk for death in the neonatal sepsis

This was a prospective study of 43 septic neonates at the NICU of the School of Medicine of Botucatu, São Paulo State University. Clinical and laboratory data of sepsis were analyzed based on outcome divided into two groups, survival and death. We calculated the discriminatory power of the relevant variables for the diagnosis of sepsis in each group, and using software for Discriminant Analysis, a function was proposed. There were 43 septic cases with 31 survivals and 12 deaths. The variables that had the highest discriminatory power were: n(o) of compromised systems, the SNAP, FiO2, and (A-a)O2. The study of these and others variables, such as birth weight, n(o) of risk factors, and pH using a Linear Discriminant Function(LDF) allowed us to identify the high-risk neonates for death with a low error rate (8.33%). The LDF was: F = 0.00043 (birth weight) + 0.30367 (n(o) of risk factors) - 0.1171 (n(o) of compromised systems) + 0.33223 (SNAP) + 2.27972 (pH) - 14.96511 (FiO2) + 0.01814 ((A-a)O2). If F > 22.77 there was high risk of death. This study suggests that the LDF at the onset of sepsis is useful for the early identification of the high-risk neonates that need special clinical and laboratory surveillance.

Statnote 29:discriminant analysis

Discriminant analysis (also known as discriminant function analysis or multiple discriminant analysis) is a multivariate statistical method of testing the degree to which two or more populations may overlap with each other. It was devised independently by several statisticians including Fisher, Mahalanobis, and Hotelling ). The technique has several possible applications in Microbiology. First, in a clinical microbiological setting, if two different infectious diseases were defined by a number of clinical and pathological variables, it may be useful to decide which measurements were the most effective at distinguishing between the two diseases. Second, in an environmental microbiological setting, the technique could be used to study the relationships between different populations, e.g., to what extent do the properties of soils in which the bacterium Azotobacter is found differ from those in which it is absent? Third, the method can be used as a multivariate ‘t’ test , i.e., given a number of related measurements on two groups, the analysis can provide a single test of the hypothesis that the two populations have the same means for all the variables studied. This statnote describes one of the most popular applications of discriminant analysis in identifying the descriptive variables that can distinguish between two populations.

Interactive Stepwise Discriminant Analysis in Matlab

2000 Mathematics Subject Classification: 62-04, 62H30, 62J20