Nonparametric Discriminant Analysis Research Articles

Placental abruption is associated with decreased maternal plasma levels of soluble HLA-G.

During pregnancy the fetus represents a semi-allograft. Both membrane-bound and soluble forms of the nonclassic human leukocyte antigen (HLA)-G protect the fetus from maternal immune attack. To assess the relevance of soluble HLA-G (sHLA-G) levels in the maternal circulation for the occurrence of characteristic pregnancy disorders, we analyzed sHLA-G plasma levels of women with normal and pathological pregnancies. Compared to normal pregnancy, significantly increased sHLA-G levels were detected in women delivered preterm because of intrauterine activation (uncontrollable labor, rupture of fetal membranes, cervical insufficiency) and women with Hemolysis, Elevated Liver enzymes, Low Platelet count (HELLP) syndrome. Contrary to these disorders, the sHLA-G levels in women with placental abruption were more than three times lower than in normal pregnancy (p < .0001). Nonparametric discriminant analysis showed that women with sHLA-G levels below 9.95 ng/mL had a relative risk of 7.12 for the development of placental abruption during further course of pregnancy. These results suggest that the occurrence of pregnancy-associated diseases is strongly influenced by maternal sHLA-G plasma levels.

BIODIVERSITY OF CENTRAL ALPINECOREGONUS(SALMONIFORMES): IMPACT OF ONE-HUNDRED YEARS OF MANAGEMENT

Coregonus has been under intense in the Central Alpine region of Europe for more than 100 yr. To assess how this has affected local populations, extant patterns of genotypic and phenotypic diversity were examined within a taxonomic frame- work to identify indigenous and introduced populations, and to provide a perspective on future based on true conservation units. Thirty-three Coregonus populations 17 selected Central Alpine lakes were classified as indigenous, introduced, or uncertain (i.e., status or origin unknown). Using genetic data across six microsatellite DNA loci, individuals of the 19 indigenous populations could be correctly allocated to population with 71% probability in a nonparametric discriminant analysis. The same individuals could be allocated to population with 69% probability using five meristic counts, and but 44% probability using four fin- pigmentation characteristics. Discriminating ability was enhanced to 91% when both meristic and color data were coalesced, and composite use of genetic and phenotypic data provided an average discrimination probability of 79%. Capabilities of the various data sets decreased when applied separately to allocate specimens according to either lake (n = 8) or lake-aggregate (n = 5). Genetic data were then statistically contrasted against four taxonomic hierarchies: Kot- telatt's species arrangement, and Steinmann's depiction of ecotype, natio, and a combi- nation of the two. Genetic data were statistically congruent with Kottelat's depiction of species, and with Steinmann's arrangement of populations into natio (or regions). Results support ar- guments that indigenous populations of Central Alpine Coregonus are distinct, with closest relations within lakes (or lake aggregates). Their evolutionary origin is best described using a species-flock model. Genetic data for 19 indigenous populations were combined with those for 14 populations either introduced or of unknown provenance. Pairwise comparisons of allele and genotype frequencies demonstrated significant genetic differences among populations, sup- porting uniqueness of rare forms, such as alpenrheinfelchen of Lake Konstanz or winter- brienzlig of Lake Brienz, but also revealed genetic divergence of introduced populations their alleged source. Introduced populations clustered within the group containing their pop- ulation of origin but did not associate directly with their source, thus indicating post-introduction genetic divergence. These findings were most remarkable for balchen of Lake Ageri and palee Lake Geneve (stocked lakes Zug and Geneve, respectively). Also, sem- pacherbalchen of Lake Sempach was significantly distinct all other populations, even though it was supposedly stocked from every lake and into every lake. It also clustered with populations in geographic proximity, suggesting that it may still retain historic endemicity. Finally, lavarello and nuova forma Lake Maggiore did not group as expected with forms Lake Konstanz or lakes Neuchatel/Bienne, but instead with those Lake Zug. Nonparametric discriminant analyses over 32 populations, again employing genotypic and phenotypic data, confirmed divergence of introduced populations and clarified status for pop- ulations of uncertain origin. Results of analyses also confirmed that historic signatures still persist in extant populations. However, several examples also demonstrate that indiscriminant and undocumented stocking in the Central Alpine region during the last 100 yr has simply added to the confusion already extant naturally occurring cryptic and sibling species within these lakes. Thus, until species descriptions are forthcoming for all forms, the Central Alpine Coregonus lineage should be viewed as an evolutionarily significant unit (ESU), and each population a specific management unit (MU) within that lineage.

Probabilistic description of metocean parameters by means of kernel density models 1. Theoretical background and first results

In the present work a general kernel density model (KDM) has been introduced and assessed for the analytic representation of any empirical distribution function (univariate or multivariate) of metocean parameters. This model is based on the concept of kernel density function, which has been first introduced in the context of non-parametric discriminant analysis by Fix and Hodges [Nonparametric discrimination: consistency properties, 1951], and generalised to the multivariate case by Cacoulos [Ann Inst Math 18 (1966) 178]. In its standard form, the kernel density estimators are applied to given samples of observations, producing analytical (yet non-parametric) estimations of the unknown (underlying) probability density functions. Motivated by the fact that, in many practical applications, metocean data are available only in the form of histograms (grouped data), the present KDM is implemented in a way permitting to obtain analytical estimates of the underlying probability distributions on the basis of grouped data. The main features of the proposed KDM are: (i) it can treat multivariate data with very reasonable computational cost, (ii) it is flexible enough to represent quite general distribution patterns both in the univariate and in the multivariate case, (iii) with an appropriate selection of the bandwidth, results in very satisfactory representations, avoiding local pathologies, (iv) it is marginally consistent, i.e. any marginal distribution calculated by integration from the multivariate model is identical with the corresponding marginal KDM, obtained directly from the marginal data. First numerical results are presented herein, showing that the performance of the present model is very satisfactory for all the wave parameters studied, univariate, bivariate, the trivariate ( H S, T m, Θ m), and conditionals. A more detailed investigation, also including applications to other metocean parameters, will be presented as a second part.

A new nonparametric discriminant analysis algorithm accounting for bounded data errors

In a statistical pattern recognition context, discriminant analysis is designed to classify, when possible, objects into predefined categories. Because this method requires precise input data, uncertainties cannot be propagated in the classifying process. In real case studies, this could lead to drastic misinterpretations of objects. A new nonparametric algorithm based on interval arithmetic has thus been developed to propagate interval-form data. They consist in calculating interval conditional probability density functions and interval posterior probabilities. Objects are eventually assigned to a subset of classes, consistent with the data and their uncertainties. The classifying model is thus less precise, but more realistic than the standard one, which we prove on a real case study.

Nondestructive indices of trace element exposure in squamate reptiles

Compared with birds, mammals, fish, and even amphibians, very little is known about the effects of contaminants on reptiles. Recent evidence that many reptile populations may be declining has stimulated demand for toxicological studies of reptiles as well as development of nondestructive sampling techniques useful for assessing and monitoring contaminant exposure. The current study experimentally evaluated the utility of shed skins, tail clips, and blood samples as nondestructive indices of trace element exposure in banded water snakes, Nerodia fasciata. For 13.5 months, snakes were either fed fish from a coal ash-contaminated site or uncontaminated food from a reference site. Snakes fed contaminated prey accumulated As, Cd, Se, Sr, and V in various organs (i.e. liver, kidney, and/or gonads). Moreover, non-parametric discriminant function analysis revealed that snakes could be placed in two groups that reliably reflected their experimental diet based upon Se, Sr, and As concentrations in tail clips, blood, and/or shed skins. We suggest that nondestructive sampling techniques, particularly analyses of blood and tail clips, may be easily applied in evaluations of contaminant exposure in the field and laboratory and may prevent excessive destructive sampling of potentially threatened reptile species.

Statistical modelling and prediction of atmospheric pollution by particulate material: two nonparametric approaches

Atmospheric particles are one of the main factors of air pollution in Santiago, Chile. Inhalation of particulate material is known to lead to serious health problems, including respiratory illness and complications related thereto. Vehicular traffic, industrial activity and street dust are important sources of atmospheric particles. The public authorities in Santiago have been monitoring air pollution by means of a network of semi-automatic sampling stations. At one of these stations, located near the city centre close to Government House, both PM2.5 and PM10 particulate material concentrations have been measured continuously for several years. Here PM2.5 refers to particles having a diameter smaller than 2.5 microns and PM10 corresponds to particles smaller than 10 microns. Hourly averages of the concentrations are available. For the present work, hourly data recorded at intervals of 12 hours have been used. The aim is to describe and forecast these variables with satisfactory precision, including critical pollution episodes, both as a function of previous behaviour and of a set of meteorological variables, comprising wind speed and direction, ambient temperature and relative air humidity. Both non-parametric discriminant analysis and multivariate adaptive regression splines procedures have been applied. Highly satisfactory classification as well as forecasting results were achieved with these approaches, respectively. Copyright © 2001 John Wiley & Sons, Ltd.

The psychometric properties of the English language version of the Aachen Aphasia Test (EAAT)

This article reports results of a standardization study of the English language version of the Aachen aphasia test (EAAT). The EAAT was administered to 135 speakers with and 93 without aphasia. Aphasic speakers were divided into four groups (n =30) representing EAAT standard syndrome groups (global, amnestic, Broca's and Wernicke's aphasia), and 15 speakers who could not be classified into the standard groups. Without aphasia were 24 nonhospitalized and 41 hospitalized speakers with no history of neurological illness or speech-language disorder and 28 speakers with a history of neurological illness, but no aphasia. Hierarchical cluster analysis (complete linkage) demonstrated the validity of the linguistically motivated construction of the EAAT. This was further confirmed for the main subtests through nonmetric multidimensional scaling (smallest space analysis). The property of increasing complexity across subparts of subtests was also confirmed. Nonparametric discriminant analyses showed the high differential validity of the EAAT for distinguishing between aphasia-no aphasia and acceptably high validity for separating out subgroups of speakers. Consistency coefficients (Cronbach's f) illustrate the high to very high internal consistency of the subtests. We argue for the applicability to the EAAT of the original German reliability studies which showed retest and inter- and intra-rater reliability to be high. We conclude that the EAAT amply meets criterion levels for a psychometrically robust test.

Multivariate analysis of the adjustment of the colour duplex unit for the differential diagnosis of lymph node alterations.

Intranodal angioarchitecture was used as criterion for the differential diagnosis of lymph node alterations by colour duplex sonography. The influence of the adjustment of the duplex unit on the diagnostic accuracy and on the rate of lymph nodes with detectable intranodal flow signals was tested. A total of 243 superficial lymph nodes in 127 patients were included in a retrospective study. Diagnoses were approved by histopathology (n = 173) or clinical follow-ups (n = 70 reactive lymph nodes). The intranodal angioarchitecture and sonomorphology were assessed. We used nonparametric discriminant analysis in order to define appropriate settings for transducer frequency, flow mode, power and threshold which result in the best diagnostic quality. Of the lymph nodes, 87 % displayed flow signals using a threshold of >/= 13 and the flow modes low or medium. Vascularisation was detected only in 47 % of the nodes assessed with different adjustments. Diagnostic accuracy dropped from 94 to 68-84 % if threshold was < 13 or power was less than -11 dB. An insufficient adjustment of the colour duplex unit decreases the chance of detecting intranodal flow signals and impairs the diagnostic quality of colour duplex sonography. Flow mode, power and threshold are the most important parameters which have to be adjusted properly.

Predicting fault-prone modules with case-based reasoning

Software quality classification models seek to predict quality factors such as whether a module will be fault prone, or not. Case based reasoning (CBR) is a modeling technique that seeks to answer new questions by identifying similar cases from the past. When applied to software reliability, the working hypothesis of our approach is this: a module currently under development is probably fault prone if a module with similar product and process attributes in an earlier release was fault prone. The contribution of the paper is application of case based reasoning to software quality modeling. To the best of our knowledge, this is the first time that case based reasoning has been used to identify fault prone modules. A case study illustrates our approach and provides evidence that case based reasoning can be the basis for useful software quality classification models that are competitive with discriminant models. The case study revisits data from a previously published nonparametric discriminant analysis study. The Type II misclassification rate of the CBR model was substantially better than that of the discriminant model. Although the Type I misclassification rate was slightly greater and the overall misclassification rate was only slightly less, the CBR model was preferred when costs of misclassification were considered.

An Analysis of the Influence of Annual Thermal Variables on the Occurrence of Fifteen Warmwater Fishes

Abstract Multisource fish-sampling data and U.S. Geological Survey temperature data from streams throughout the United States were used to investigate the influence of derived thermal regime variables on the presence or absence of 15 common warmwater fish species. The 3-year average annual thermal regime was calculated for streams where presence or absence was known for these 15 species. Six variables estimated to be of biological importance to the winter and summer survival and recruitment of a species, including measures of feeding and nonfeeding periods, were calculated from these thermal regimes. Stepwise discriminant analysis and multiple regression were used to select optimal variables for creating multivariate models. Parametric and nonparametric multivariate discriminant analyses were then performed to test our ability to correctly classify presence or absence using the thermal variables. These statistical empirical models were able to correctly predict presence or absence with greater than 90% ac...

Mineral Favorability Mapping: A Comparison of Artificial Neural Networks, Logistic Regression, and Discriminant Analysis

A Probabilistic Neural Network (PNN) was trained to classify mineralized and nonmineralized cells using eight geological, geochemical, and geophysical variables. When applied to a second (validation) set of well-explored cells that had been excluded from the training set, the trained PNN generalized well, giving true positive percentages of 86.7 and 93.8 for the mineralized and nonmineralized cells, respectively. All artifical neural networks and statistical models were analyzed and compared by the percentages of mineralized cells and barren cells that would be retained and rejected correctly respectively, for specified cutoff probabilities for mineralization. For example, a cutoff probability for mineralization of 0.5 applied to the PNN probabilities would have retained correctly 87.66% of the mineralized cells and correctly rejected 93.25% of the barren cells of the validation set. Nonparametric discriminant analysis, based upon the Epanechnikov Kernel performed better than logistic regression or parametric discriminant analysis. Moreover, it generalized well to the validation set of well-explored cells, particularly to those cells that were mineralized. However, PNN performed better overall than nonparametric discriminant analysis in that it achieved higher percentages of correct retention and correct rejection of mineralized and barren cells, respectively. Although the generalized regression neural network (GRNN) is not designed for a binary—presence or absence of mineralization— dependent variable, it also performed well in mapping favorability by an index valued on the interval [0, 1]. However, PNN outperformed GRNN in correctly retaining mineralized cells and rejecting barren cells of the validation set.

A generalized wilcoxon-mann-whitney statistic

We develop a simple but useful generalization of the classical Wilcoxon-Mann-Whitney statistic. A normal approximation and a recurrence for the exact distribution of this generalization are available. The statistic has potential application in nonparametric discriminant analysis.

A Comparative Study of Ordering and Classification of Fault-ProneSoftware Modules

Software quality models can predict the quality of modules early enough for cost-effective prevention of problems. For example, software product and process metrics can be the basis for predicting reliability. Predicting the exact number of faults is often not necessary; classification models can identify fault-prone modules. However, such models require that ’’fault-prone‘‘ be defined before modeling, usually via a threshold. This may not be practical due to uncertain limits on the amount of reliability-improvement effort. In such cases, predicting the rank-order of modules is more useful. A module-order model predicts the rank-order of modules according to a quantitative quality factor, such as the number of faults. This paper demonstrates how module-order models can be used for classification, and compares them with statistical classification models. Two case studies of full-scale industrial software systems compared nonparametric discriminant analysis with module-order models. One case study examined a military command, control, and communications system. The other studied a large legacy telecommunications system. We found that module-order models give management more flexible reliability enhancement strategies than classification models, and in these case studies, yielded more accurate results than corresponding discriminant models.

Multivariate Discrimination of Colorado PlateauGilaspp.: The “Art of Seeing Well” Revisited

Fishery managers have long been troubled by phenotypic variation within and among Colorado Plateau Gila. The problem is twofold. From an historical perspective, there was reticence to investigate fishes long considered as “undesirable.” In a taxonomic sense, there is confusion over within- and among-species variability. We document the former, then clarify the latter by applying discriminant analysis to meristic and morphometric data collected from museum specimens. We test three hypotheses: roundtail chub G. robusta humpback chub G. cypha and bonytail G. elegans are morphologically indistinguishable; juveniles are assignable to species based upon adult characters; and putative hybrids are morphologically intermediate between parental forms. Through the use of meristic characters in a nonparametric discriminant analysis, over 95% of all adults were segregated to species. By using morphometric characters, 97% could be allocated to species. Gila robusta was easily separated from G. cypha and G. elegans. The latter were most difficult of all species-pairs to discriminate, yet field characters still segregated them at better than 95%. A discriminant function, based upon five morphometric characters, will allocate unknowns to species. Juvenile G. robusta were easily discriminated (>97%), but juveniles of G. cypha and G. elegans were often misidentified as G. robusta. Putative hybrids were generally assigned to one or the other parental form; thus, hybrid intermediacy could not be rejected. However, paucity of hybrids weakened the test. We conclude that factors most important in segregating these species are character selection, adequate analyses, and “the art of seeing well.”

Classification of Fault-Prone Software Modules: Prior Probabilities,Costs, and Model Evaluation

Software quality models can give timely predictions of reliability indicators, for targeting software improvement efforts. In some cases, classification techniques are sufficient for useful software quality models. The software engineering community has not applied informed prior probabilities widely to software quality classification modeling studies. Moreover, even though costs are of paramount concern to software managers, costs of misclassification have received little attention in the software engineering literature. This paper applies informed prior probabilities and costs of misclassification to software quality classification. We also discuss the advantages and limitations of several statistical methods for evaluating the accuracy of software quality classification models. We conducted two full-scale industrial case studies which integrated these concepts with nonparametric discriminant analysis to illustrate how they can be used by a classification technique. The case studies supported our hypothesis that classification models of software quality can benefit by considering informed prior probabilities and by minimizing the expected cost of misclassifications. The case studies also illustrated the advantages and limitations of resubstitution, cross-validation, and data splitting for model evaluation.

Helminth parasites as biological tags in population studies of Greenland halibut (Reinhardtius hippoglossoides(Walbaum)), in the north-west Atlantic

As part of a stock identification study, the parasite fauna of 608 Greenland halibut, Reinhardtius hippoglossoides (Walbaum) from six areas in the north-west Atlantic was examined. New records of parasite species for the Greenland area have been added by this study. No significant diVerences in prevalence were found between sexes or age groups of Greenland halibut. Three digeneans (Brachyphallus crenatus, Steganoderma formosum and Stenakron vetustum) and three nematodes (Anisakis simplex, Ascarophis sp., andContracaecumsp.) showed irregularities in spatial infestation pattern and were therefore chosen as biological tags. Nonparametric discriminant analyses of the prevalence of these parasites indicated strong similarities between components oV Labrador, Davis Strait, and in the fjords of Umanak at West Greenland. Greenland halibut in south-west Greenland fjords appeared to be isolated, as does the component in the Denmark Strait. This general pattern adds further support to previous investigations on stock structure of Greenland halibut in the North-west Atlantic. ? 1997 International Council for the Exploration of the Sea

Prediction of the outcome of growth at 2 years of age in neonates with intra-uterine growth retardation

The aim of the study was to identify at birth, in infants showing intra-uterine growth retardation (IUGR), any parameters correlative with the increase in height SDS during the first 2 years of life and with short stature at 2 years of age, and to determine whether the sensitivity and specificity of such parameters would permit their use as predictors of short stature at 2 years of age. Two cohorts of children born with IUGR with birth weight < 3rd percentile, were studied. In the first group of 317 children selected at birth, 224 were effectively followed up to 2 years of age (group 1) and the second group of 48 children was evaluated at 2 years of age for short stature related to IUGR (group 2). Perinatal history, auxological data at birth and parental height were monitored in a prospective study for the group 1 children and in a retrospective study for the group 2 children. By 2 years of age, 8% of the 224 children followed (group 1), presented short stature (< or = 2 SDS). In a multiple linear regression model, gestational age, birth length (SDS), target height (SDS) and maternal tobacco consumption were found to be the strongest predictors of the magnitude of the height gain (SDS) during the first 2 years of life. Using these parameters 47% of the variability of the height gain (SDS) during the first 2 years of life could be explained at birth. Moreover, logistic regression analysis showed three risk factors at birth for short stature by 2 years of age: reduced gestational age due to premature birth (adjusted odd ratio (O.R.) = 2.10; 95% C.I. = 1.06-4.14), the greater the difference (for each S.D.) between birth length (SDS) and target height (SDS) (O.R. = 1.93; 95% C.I. = 1.40-2.66) and although as a borderline significant factor, maternal tobacco consumption (O.R. = 1.58; C.I. 95% = 0.81-3.07). Non-parametric discriminant analysis was used to investigate whether short (< or = -2 SDS) or normal stature (> -2 SDS) at 2 years could be predicted at birth using gestational age (weeks), birth length (SDS), target height (SDS) and maternal tobacco consumption as discriminant variables. We found that this discriminant model correctly predicted at birth the short stature of 57 of 59 children at 2 years of age (sensitivity 97%) and the normal stature of 142 of 159 children at 2 years of age (specificity 89%). In conclusion, an accurate prediction of short stature by 2 years of age is feasible at birth in the IUGR neonate.

Discriminant analysis of normal and malignant breast tissue based upon INAA investigation of elemental concentration

Discriminant analysis of six trace element concentrations measured by instrumental neutron activation analysis (INAA) in 26 paired-samples of malignant and histologically normal human breast tissues shows the technique to be a potentially valuable clinical tool for making malignant-normal classification. Nonparametric discriminant analysis is performed for the data obtained. Linear and quadratic discriminant analyses are also carried out for comparison. For this data set a formal analysis shows that the elements which may be useful in distinguishing between malignant and normal tissues are Ca, Rb and Br, providing correct classification for 24 out of 26 normal samples and 22 out of 26 malignant samples.

Parasites of Lake Herring (Coregonus artedi) from Lake Superior, with special reference to use of parasites as markers of stock structure

We examined parasites of 152 lake herring (Coregonus artedi) collected from three locations in Wisconsin waters of Lake Superior in 1994, four locations in Wisconsin waters in 1996, and one location in Minnesota waters in 1996 to determine; 1) the species composition and relative abundances of parasites in lake herring, 2) the differences in parasite relative abundances across locations sampled, and 3) the utility of parasite relative abundances as markers of stock structure. Parasites from 19 taxa infected lake herring collected in 1994 and 1996; Henneguya zschokkei, Chloromyxum sp., and Cyatho-cephalus truncatus were reported in fishes from Lake Superior for the first time, and Clinostomum mar-ginatum was reported in lake herring for the first time. Significant differences in abundances of eight parasite taxa were found across locations sampled in 1996, with most of the differences occurring between fish from Minnesota and Wisconsin waters. Nonparametric discriminant function analyses correctly classified 105 of the 108 fish (97%) from Wisconsin waters in 1994 and 1996 and also correctly classified 9 of the 13 fish (69%) from the one location in Minnesota waters. This indicated that little mixing of lake herring from those regions occurred and that the potential exists to use parasite abundances as a marker of lake herring stock structure. This was the first time that multivariate analysis of parasites have been used in the Great Lakes to assess stock structure of fishes. Because the technique was highly successful at classifying locations of our samples, we recommend that parasite abundances in lake herring from all areas of the lake be analyzed as part of a larger study to determine whether lake herring from populations throughout the lake can be as accurately classified as were fish in our study.

Vascular patterns in reactive and malignant lymphadenopathy.

A total of 130 superficial lymph nodes were evaluated using color Doppler flow imaging (CDFI) in order to differentiate benign from malignant lymphadenopathy. The patterns of intranodal flow signals detected at standardized conditions by CDFI were classified using eight self-defined criteria and were correlated with the histopathological or clinical diagnosis. Nonparametric discriminant analysis showed that four vascular were suspicious of malignancy: (a) avascular areas, (b) displacement of intranodal vessels, (c) accessory peripheral vessels and (d) aberrant course of central vessels. Of the neoplastic lymph nodes (n = 73), 96% showed at least one pathological vascular pattern. Malignancy could be excluded in 95% of 57 reactive lymph nodes using these four criteria. Most reactive lymph nodes in contrast demonstrated a vascular hilus and/or vessels running at the long axis of the lymph node with branches to the cortex. There was a diagnostic accuracy of 41-82% in the additionally evaluated sonomorphological (size, shape, echogenicity) and Doppler (increased Pourcelot's or pulsatility indices) criteria. The definitive interpretation of the promising results of this retrospective study requires confirmation of examiner independency as well as a prospective evaluation.