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.

High-breakdown linear discriminant analysis

The classification rules of linear discriminant analysis are defined by the true mean vectors and the common covariance matrix of the populations from which the data come. Because these true parameters are generally unknown, they are commonly estimated by the sample mean vector and covariance matrix of the data in a training sample randomly drawn from each population. However, these sample statistics are notoriously susceptible to contamination by outliers, a problem compounded by the fact that the outliers may be invisible to conventional diagnostics. High-breakdown estimation is a procedure designed to remove this cause for concern by producing estimates that are immune to serious distortion by a minority of outliers, regardless of their severity. In this article we motivate and develop a high-breakdown criterion for linear discriminant analysis and give an algorithm for its implementation. The procedure is intended to supplement rather than replace the usual sample-moment methodology of discriminant analysis either by providing indications that the dataset is not seriously affected by outliers (supporting the usual analysis) or by identifying apparently aberrant points and giving resistant estimators that are not affected by them.

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 studyof tephrochrology. In this paper, DFA is applied to compositional datasets of twodifferent types of tephras from Mountain Ruapehu in New Zealand and MountainRainier in USA. The canonical variables from the analysis are further investigated witha statistical methodology of change-point problems in order to gain a betterunderstanding of the change in compositional pattern over time. Finally, a special caseof segmented regression has been proposed to model both the time of change and thechange in pattern. This model can be used to estimate the age for the unknown tephrasusing Bayesian statistical calibration

Discriminant analysis of skull morphometric characters in Apodemus sylvaticus, A-flavicollis, and A-alpicola (Mammalia; Rodentia) from the Alps

A total of 108 Apodemus skulls from Switzerland, Austria, Italy, France and Germany was studied to determine morphological characteristics useful in identifying individuals as Apodemus sylvaticus (Linnaeus, 1758), A. flavicollis (Melchior, 1834) or A. alpicola Heinrich, 1952. The original assignment of the samples to the three species was based on molar cusp morphology, body proportions, pelage coloration, and allozyme analysis. The 24 measured cranial characters used together accurately discriminated between the three species and correctly classified 100% of the individuals to species. A stepwise discriminant function analysis showed that 6 cranial characters are sufficient to differentiate between the three species, with a correct classification above 97%. Fisher's linear discriminant function coefficients can be used directly for classification of unknown specimens.

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

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.

Identification of species of the Euterpe genus by rare earth elements using inductively coupled plasma mass spectrometry and linear discriminant analysis

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

A robustness verification system for mobile phone authentication based on gestures using Linear Discriminant Analysis

This article evaluates an authentication technique for mobiles based on gestures. Users create a remindful identifying gesture to be considered as their in-air signature. This work analyzes a database of 120 gestures of different vulnerability, obtaining an Equal Error Rate (EER) of 9.19% when robustness of gestures is not verified. Most of the errors in this EER come from very simple and easily forgeable gestures that should be discarded at enrollment phase. Therefore, an in-air signature robustness verification system using Linear Discriminant Analysis is proposed to infer automatically whether the gesture is secure or not. Different configurations have been tested obtaining a lowest EER of 4.01% when 45.02% of gestures were discarded, and an optimal compromise of EER of 4.82% when 19.19% of gestures were automatically rejected.

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

Issued Apr. 1980.

Maximization of a Linear Utility Function over the Set of the Housing Market Short-Term Equilibria

AMS subject classification: 90C05, 90A14.

Prediction of Golgi Type II membrane proteins based on their transmembrane domains

Motivation: A major issue in cell biology today is how distinct intracellular regions of the cell, like the Golgi Apparatus, maintain their unique composition of proteins and lipids. The cell differentially separates Golgi resident proteins from proteins that move through the organelle to other subcellular destinations. We set out to determine if we could distinguish these two types of transmembrane proteins using computational approaches. Results: A new method has been developed to predict Golgi membrane proteins based on their transmembrane domains. To establish the prediction procedure, we took the hydrophobicity values and frequencies of different residues within the transmembrane domains into consideration. A simple linear discriminant function was developed with a small number of parameters derived from a dataset of Type II transmembrane proteins of known localization. This can discriminate between proteins destined for Golgi apparatus or other locations (post-Golgi) with a success rate of 89.3% or 85.2%, respectively on our redundancy-reduced data sets.

Computational differentiation of N-terminal signal peptides and transmembrane helices

Signal peptides and transmembrane helices both contain a stretch of hydrophobic amino acids. This common feature makes it difficult for signal peptide and transmembrane helix predictors to correctly assign identity to stretches of hydrophobic residues near the N-terminal methionine of a protein sequence. The inability to reliably distinguish between N-terminal transmembrane helix and signal peptide is an error with serious consequences for the prediction of protein secretory status or transmembrane topology. In this study, we report a new method for differentiating protein N-terminal signal peptides and transmembrane helices. Based on the sequence features extracted from hydrophobic regions (amino acid frequency, hydrophobicity, and the start position), we set up discriminant functions and examined them on non-redundant datasets with jackknife tests. This method can incorporate other signal peptide prediction methods and achieve higher prediction accuracy. For Gram-negative bacterial proteins, 95.7% of N-terminal signal peptides and transmembrane helices can be correctly predicted (coefficient 0.90). Given a sensitivity of 90%, transmembrane helices can be identified from signal peptides with a precision of 99% (coefficient 0.92). For eukaryotic proteins, 94.2% of N-terminal signal peptides and transmembrane helices can be correctly predicted with coefficient 0.83. Given a sensitivity of 90%, transmembrane helices can be identified from signal peptides with a precision of 87% (coefficient 0.85). The method can be used to complement current transmembrane protein prediction and signal peptide prediction methods to improve their prediction accuracies. (C) 2003 Elsevier Inc. All rights reserved.

Echocardiographic detection of congestive heart failure in postinfarction rats

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Aplicativo computacional para obtenção de probabilidades a priori de classificação errônea em experimentos agronômicos

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