Standard Discriminant Analysis Research Articles

Identification of a host-associated species complex using molecular and morphometric analyses, with the description of Gyrodactylus rugiensoides n. sp. (Gyrodactylidae, Monogenea)

Gyrodactylus rugiensis was originally described as a parasite occurring on the marine gobies Pomatoschistus minutus and Pomatoschistus microps. In our preliminary survey this species was also frequently found on Pomatoschistus pictus and Pomatoschistus lozanoi. Subsequent molecular analysis of the internal transcribed spacers rDNA region revealed that this parasite actually represents a complex of two apparently cryptic species, one restricted to P. microps and the other shared by P. minutus,P. lozanoi and P. pictus. Morphometric analyses were conducted on 17 features of the opisthaptoral hard parts of specimens collected from all four host species. Standard discriminant analysis showed a clear separation of both genotypes by significant differences in marginal hook and ventral bar features. Statistical classifiers (linear discriminant analysis and nearest neighbours) resulted in an estimated misclassification rate of 4.7 and 3.1%, respectively. Based on molecular, morphological and statistical analyses a new species, Gyrodactylus rugiensoides is described. This species seems to display a lower host-specificity than generally observed for Gyrodactylus species as it infects three sympatric host species.However, seasonal and host-dependent morphometric variation is shown for G. rugiensoides collected on P. pictus. Host-switching and gene flow might be important factors preventing speciation on closely related and sympatric host species. The presence of host associated species complexes in this Gyrodactylus-Pomatoschistus system is also confirmed by the presence of two host-dependent genotypes within G. micropsi found on P. minutus and P. lozanoi, and P. microps, respectively. By comparing host and parasite phylogeny, phylogenetic and ecological factors influencing host-specificity are discussed.

Locating the genes underlying a simulated complex disease by discriminant analysis.

The purpose of this study was to propose and evaluate a novel multivariate approach for genetic mapping of complex binary human diseases. This approach uses the application of either of two methods of standard (stepwise) discriminant analysis to detect linkage based on the differential marker identity-by-descent distributions among the three affection groups of sib pairs (concordantly affected, discordant, and concordantly unaffected). One of the advantages of this approach is that it allows for simultaneously testing all markers, as well as other genetic and environmental factors, in a single multivariate setting. We have explored its properties and behaviors via an application to the simulated data in Genetic Analysis Workshop 12.

Novel ‘hybrid’ classification method employing Bayesian networks

Standard statistical discriminant analysis techniques inherently make assumptions about underlying class structures in data, limiting their validity and effectiveness. Other classification methods, such as soft independent modeling of class analogy (SIMCA) or artificial neural networks, replace the disadvantage of making such assumptions with an equally impeding lack of interpretability. The intention of this work was to formulate a classification scheme that avoids these and other obstacles. A new classification technique has been designed that combines the recursive partitioning feature of tree-based classifiers (e.g. classification and regression trees (CART)) with the probabilistic reasoning of Bayesian networks. The proposed hybrid approach benefits from all the advantages of tree-based classifiers and Bayesian networks without experiencing the usual limitations associated with these methods individually. The resulting classifier outperformed several standard methods and has the added benefits of being both statistically and semantically justifiable.

A discriminant analysis extension to mixed models.

Discriminant analysis is commonly used to classify an observation into one of two (or more) populations on the basis of correlated measurements. Classical discriminant analysis approaches require complete data for all observations. Our extension enables the use of all available longitudinal data, regardless of completeness. Traditionally a linear discriminant function assumes a common unstructured covariance matrix for both populations, which may be taken from a multivariate model. Here, we can model the correlated measurements and use a structured covariance in the discriminant function. We illustrate cases in which the estimated covariance structure is either compound symmetric, heterogeneous compound symmetric or heterogeneous autoregressive. Thus a structured covariance is incorporated into the discrimination process in contrast to standard discriminant analysis methodology. Simulations are performed to obtain a true measure of the effect of structure on the error rate. In addition, the usual multivariate expected value structure is altered. The impact on the discrimination process is contrasted when using the multivariate and random-effects covariance structures and expected values. The random-effects covariance structure leads to an improvement in the error rate in small samples. To illustrate the procedure we consider repeated measurements data from a clinical trial comparing two active treatments; the goal is to determine if the treatment could be unblinded based on repeated anxiety score measurements.

Changes in Plasma Lipid Homeostasis Observed in Chronic Fatigue Syndrome Patients

A study of 60 CDC-defined chronic fatigue syndrome (CFS) patients and 39 age- and sex-matched controls was undertaken to determine whether there were any alterations in plasma lipid profiles from CFS patients compared with control subjects. Plasma samples were taken from fasted (12 h) subjects and the lipid components were extracted, saponified and analyzed by capillary gas chromatography-mass spectrometry (GC-MS). It was found that CFS patients had different plasma saponified lipid profiles compared with control subjects (standard discriminant function analysis p < 0.02). The first and second most important factors, discriminating the CFS patients from the controls, were a decrease in trans -9-octadecenoic acid and an increase in octadecenoic acid, respectively. The relative abundance of trans -9-octadecenoic acid in the CFS patients was 0.74% compared with 0.99% in the controls ( p< 0.02) and the trans -9-octadecenoic acid:octadecenoic acid ratio was 0.15 in the CFS patients compared with 0.27 in contro...

Relating discriminant analysis and data envelopment analysis to one another

Two techniques that have received a great deal of attention recently are Discriminant Analysis (DA) and Data Envelopment Analysis (DEA). While these are two apparently unrelated methods, they do share some noteworthy commonalities. Both can be described as methods for evaluating performance of a group of similar units or observations using linear programming. In each, a set of factors has been measured for all units and a weighting scheme is sought for these factors to differentiate between the successful and the unsuccessful units. These similarities between DA and DEA raise the question of whether some useful middle ground might exist between the two methods, or whether each method might learn something from the other. Exploring these possibilities along with examining the differences and similarities between DA and DEA is the purpose of this paper. The comparison of the two methods in itself provides insight into both methods and provides the taxonomy from which several alternatives to standard DA and DEA are proposed. Two of these methods are developed and discussed in greater detail and appear to have potential usefulness.

Effect of some modifications in standard discriminant analysis

In this paper, the results of three simulation studies about discrimination are described. The first study investigates the use of James–Stein estimators in Fisher's discriminant function. The second compares the Anderson-Bahadur minimax linear discriminant function with the quadratic discriminant function and the last one deals with the choice of an unweighted between groups sum of squares and sum of products matrix instead if the usual between groups matrix

Forecasting Tropical Cyclone Recurvature. Part II. An Objective Technique Using an Empirical Orthogonal Function Representation of Vorticity Fields

Abstract An empirical orthogonal function (EOF) representation of relative vorticity is used to forecast recurvature (change in storm heading from west through north to cast of 360°) of western North Pacific tropical cyclones. A pattern recognition approach is adapted in which the synoptic conditions at recurvature time and each 12-h interval up to 96 h prior to recurvature are to be distinguished from the synoptic pattern for straight-mover storms. Synoptic descriptors are defined in terms of the time-dependent principal components of the vorticity fields for the individual maps. A standard discriminant analysis approach using 250-mb vorticity fields correctly identifies recurvers and straight movers in 80% and 66%, respectively, of the 782 cases. For a specific discriminant analysis that is derived to separate recurvers (74% correct) from straight movers (81% correct), the accuracy is higher than for the operational track prediction techniques and the official forecasts considered in Part I of this stud...

A robust methodology for discriminant analysis based on least‐absolute‐value estimation

AbstractMany important real‐world discriminant problems require application of linear discriminant analysis to data that are contaminated with outliers and do not approximate the assumptions required for the near‐optimal performance of the standard statistical model. A robust diagnostic methodology is developed based on least‐absolute‐value estimation which addresses both descriptive and classification objectives of discriminant analysis. When used in conjunction with standard discriminant analysis this methodology allows the assessment of the impact of contamination on standard discriminant analysis and identification of possible assumption violations and contaminating data points through an informal graphical display. An application to the mortgage loan‐granting problem is used as a basis for demonstrating the methodology.

BEAGLE—A DARWINIAN APPROACH TO PATTERN RECOGNITION

BEAGLE (Biological Evolutionary Algorithm Generating Logical Expressions) is a computer package for producing decision‐rules by induction from a database. It works on the principle of “Naturalistic Selection” whereby rules that fit the data badly are “killed off” and replaced by “mutations” of better rules or by new rules created by “mating” two better adapted rules. The rules are Boolean expressions represented by tree structures. The software consists of two Pascal programs, HERB (Heuristic Evolutionary Rule Breeder) and LEAF (Logical Evaluator And Forecaster). HERB improves a given starting set of rules by running over several simulated generations. LEAF uses the rules to classify samples from a database where the correct membership may not be known. Preliminary tests on three different databases have been carried out—on hospital admissions (classing heart patients as deaths or survivors), on athletic physique (classing Olympic finalists as long‐distance runners or sprinters) and on football results (categorizing games into draws and non‐draws). It appears from the tests that the method works better than the standard discriminant analysis technique based on a linear discriminant function, and hence that this long‐neglected approach warrants further investigation.

A Discriminant Analysis Approach to the Identification of Human Chromosomes

The identification of the various types of the 46 chromosomes in a normal human cell is formulated as a discriminant analysis problem. Derived are expressions for posterior probabilities, and rules are given for identification where the number of chromosomes of each type is exactly known. The resulting model is applied to experimental data from chromosomes of the Denver B-group. The results using the developed model compare favorably with those of the standard discriminant analysis approach.