Multivariate Discriminant Techniques Research Articles

Socio-Economic and Cultural Context in the Development of Early Mathematical Competencies: A Comparative Study of Specific Educational Contexts in Chile and Spain.

This research presents the findings of a comparative study of mathematical competence among 130 students (M = 54.08months; SD = 2.57) from vulnerable school contexts in Chile and the Spanish public school system. The study analyses a set of general and specific domain precursors for which evidence of socioeconomic background exists. Using multivariate regression and discriminant analysis techniques, we calculated similarities and differences between groups by comparing these precursors. Significant differences were found between the Spanish and Chilean groups (p < .05); however, no differences were observed in non-symbolic comparison and receptive vocabulary. Possible reasons for the existence and extent of these differences are discussed in terms of socio-cultural and educational contexts.

Use of discriminant statistical procedures for an early detection of persistent lactations in dairy cows

With the development of precision dairy farming, data on individual daily milk production are easily available in many herds. The aim of the present research was to develop an algorithm able to early detect dairy cows with a potential persistent lactation using daily production data. In this study, 2295 lactations belonging to primiparous (1015) and multiparous (1280) Holstein cows from two different farms equipped with the Afimilk system were used. Based on daily milk yield at 305 days in milk (DIM), animals were grouped into three production classes: low (LC) with milk yield <20 kg, middle (MC) with milk yield between 20 kg and 32 kg, and high (HC) with milk yield >32 kg, respectively. Lactations of MC or HC were considered as suitable for becoming long lactations. Four different models (Wood, Ali & Schaeffer, Legendre polynomials and 4th degree polynomials) were fitted to individual lactations by using the first 90, 120 and 150 DIM. Estimated model parameters were considered as variables in two multivariate discriminant techniques. The canonical discriminant analysis was used to test for possible differences between the extreme classes LC and HC. The discriminant analysis was performed to assign animals to the two production classes. The canonical discriminant analysis significantly separated LC from HC both for primiparous and multiparous cows. Among the different lactation models, the 4th degree polynomial was the most precise when the discriminant analysis was used to assign animals to the two production classes. In particular, by using the data of the first 150 DIM, the percentage of LC lactations incorrectly assigned to HC was 5% for primiparous and 7% for multiparous. Errors slightly increased when data of 120 (6% and 8% for primiparous and multiparous) and 90 (7% and 12% for primiparous and multiparous) DIM were used.The entire procedure could be automated by implementing, for example, the Afifarm’s report with a statistical computer software and it could be applied at farm level or using data from different associated farms. In practice, a historical database with previous complete lactations should be firstly created. As a new lactation proceeds, the recorded milk production data are fitted by using the 4th degree polynomial model and the estimated parameters submitted to the discriminant analysis. The lactation will be assigned to LC or HC.

Rapid measures of user's adherence to vaginal drug products using attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) and multivariate discriminant techniques.

BackgroundThe topical HIV prevention (microbicides) field is in acute need of a method to rapidly and objectively measure adherence to product use in clinical trials. Infrared (IR) spectroscopy has been used in many pharmaceutical and forensic applications but has yet to be applied to adherence monitoring. In this study, we report on efforts to test the feasibility of using IR spectroscopy as a means to measure residual active or placebo vaginal product, semen exposure and vaginal insertion from a single swab.MethodsA portable IR spectrometer equipped with diamond attenuated total reflectance (ATR) was used to capture spectra of unused vs. vaginally-used swabs, vaginal swabs containing semen, and vaginal swabs to which either tenofovir-containing or matching placebo products (vaginal gel or insert) were added. Spectral data obtained from swabs placed directly on the spectrometer were divided into calibration and testing sets for developing and validating discriminant models set up to provide yes/no predictions of: vaginal vs. non-vaginal use, presence vs. no presence of each test product, and presence vs. no presence of semen. Further validation of models was performed using vaginal swabs collected from a clinical study evaluating vaginally administered placebo insert formulations.ResultsFor each discriminant model developed to predict vaginal vs. non-vaginal use, presence vs. no presence of each test product, and presence vs. no presence of semen, classified validation samples not included in the model development were correctly identified into their respective classes with minimal prediction error. Clinically obtained vaginal swabs collected 15–60 minutes after placebo insert use were also correctly identified, further validating the models.ConclusionOur findings demonstrate the proof of concept that IR spectroscopy can be a method for rapid detection and characterization of microbicide products and biological fluids present in vaginal swabs. This novel method has potential to support real-time, on-site adherence monitoring in clinical or field settings.

A comparison of multivariate signal discrimination techniques

This paper investigates several techniques to discriminate two multivariate stationary signals. The methods considered include Gaussian likelihood ratio tests for variance equality, a chi-squared time-domain test, and a spectral-based test. The latter two tests assess equality of the multivariate autocovariance function of the two signals over many different lags. The Gaussian likelihood ratio test is perhaps best viewed as principal component analyses (PCA) without dimension reduction aspects; it can be modified to consider covariance features other than variances via dimension augmentation tactics. A simulation study is constructed that shows how one can make inappropriate conclusions with PCA tests, even when dimension augmentation techniques are used to incorporate non-zero lag autocovariances into the analysis. The various discrimination methods are first discussed. A simulation study then illuminates the various properties of the methods. In this pursuit, calculations are needed to identify several multivariate time series models with specific autocovariance properties. To demonstrate the applicability of the methods, nine US and Canadian weather stations from three distinct regions are clustered. Here, the spectral clustering perfectly identified distinct regions, the chi-squared test performed marginally, and the PCA/likelihood ratio method did not perform well.

Search for a Higgs boson in the diphoton final state using the full CDF data set from [formula omitted] collisions at [formula omitted

A search for a narrow Higgs boson resonance in the diphoton mass spectrum is presented based on data corresponding to 10 fb−1 of integrated luminosity collected by the CDF experiment from proton–antiproton collisions at s=1.96 TeV. To increase the sensitivity of the search, we employ a multivariate discriminant technique for the first time in this channel at CDF. No evidence of signal is observed, and upper limits are set on the cross section times branching ratio of the resonant state as a function of the Higgs boson mass. The limits are interpreted in the context of the standard model with an expected (observed) limit on the cross section times branching ratio of 9.9 (17.0) times the standard model prediction at the 95% credibility level for a Higgs boson mass of 125 GeV/c2. Moreover, a Higgs boson with suppressed couplings to fermions is excluded for masses below 114 GeV/c2 at the 95% credibility level.

Search forWHassociated production inpp¯collisions ats=1.96 TeV

This report describes a search for associated production of $W$ and Higgs bosons based on data corresponding to an integrated luminosity of $\cal{L}$$ \approx 5.3 \rm fb^{-1}$ collected with the D0 detector at the Fermilab Tevatron $p\bar{p}$ Collider. Events containing a $W\rightarrow \ell \nu$ candidate (with $\ell$ corresponding to $e$ or $\mu$) are selected in association with two or three reconstructed jets. One or two of the jets are required to be consistent with having evolved from a $b$ quark. A multivariate discriminant technique is used to improve the separation of signal and backgrounds. Expected and observed upper limits are obtained for the product of the $WH$ production cross section and branching ratios and reported in terms of ratios relative to the prediction of the standard model as a function of the mass of the Higgs boson ($M_{H}$). The observed and expected 95% C.L. upper limits obtained for an assumed $M_{H}=115 \rm GeV$ are, respectively, factors of 4.5 and 4.8 larger than the value predicted by the standard model.

Demarking and identifying points-reliable criteria for determination of sex from external ear

Introduction: The anatomy of the external ear is clinically and surgically important as it is related to the vital structures in the neck. The morphometric measurements of the external ear were undertaken to determine the sex of an individual. These findings also suggest that this study will have a role in plastic and reconstructive surgery; identification of dysmorphic features in various chromosomal disorders. Aim: The present study will enlighten us to determine the sex from the external ear and provide an insight in determining the variations in sex from the external ear with 100% accuracy. It may also serve as a guideline before surgical intervention in otoplasty so as to resculpt or reshape the ear. Materials and Methods: The subjects were 100 healthy male and 100 healthy female medical students of age group 18-25 years of Goa Medical College, Bambolim, Goa, having no history of any diseases or other genetic disorder or heredity diseases. The anatomical landmarks used for this research study were the right and left a) ear length b) ear length above tragus c) ear length below tragus d) tragus length e) ear breadth f) concha length g) concha breadth h) lobule height i) lobule width of the external ear. Results: The measurement procedure proved to be easy and it did not show any discomfort to the participants. Ear length below tragus, lobule height and lobule width were larger in females than males. This method was made applicable to all the parameters except for ear length below tragus, lobule height and lobule widths since these parameters were greater in females than males. Conclusion: In this study, we could determine the sex from the external ear in a large percentage. The parameters were of little value when subjected to demarking point analyses. However, for a larger population the mean values for the above parameters from different regions will have significantly different values and hence, DPs are to be worked out separately for the different regions. These DPs are much simpler to apply than multivariate discriminant functional techniques for identification of sex with certainty.

PDE-Foam—A probability density estimation method using self-adapting phase-space binning

Probability density estimation (PDE) is a multi-variate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this paper, we present a modification of the PDE method that uses a self-adapting binning method to divide the multi-dimensional phase space in a finite number of hyper-rectangles (cells). The binning algorithm adjusts the size and position of a predefined number of cells inside the multi-dimensional phase space, minimising the variance of the signal and background densities inside the cells. The implementation of the binning algorithm (PDE-Foam) is based on the MC event-generation package Foam. We present performance results for representative examples (toy models) and discuss the dependence of the obtained results on the choice of parameters. The new PDE-Foam shows improved classification capability for small training samples and reduced classification time compared to the original PDE method based on range searching.

Multivariate discrimination technique based on the Bayesian theory

A multivariate discrimination technique was established based on the Bayesian theory. Using this technique, P/S ratios of different types (e.g., Pn/Sn, Pn/Lg, Pg/Sn or Pg/Lg) measured within different frequency bands and from different stations were combined together to discriminate seismic events in Central Asia. Major advantages of the Bayesian approach are that the probability to be an explosion for any unknown event can be directly calculated given the measurements of a group of discriminants, and at the same time correlations among these discriminants can be fully taken into account. It was proved theoretically that the Bayesian technique would be optimal and its discriminating performance would be better than that of any individual discriminant as well as better than that yielded by the linear combination approach ignoring correlations among discriminants. This conclusion was also validated in this paper by applying the Bayesian approach to the above-mentioned observed data.

Smoothed multi-variate histogrammed PDEs, and [formula omitted] optimisation

With increasing requirements from particle physics for effective multi-variate discrimination techniques, a number of alternative probability density estimate (PDE) methods have appeared in recent years. These relatively advanced methods attempt to form effective PDEs in the presence of low statistics where a simple histogramming method does not perform well. In this paper a multi-variate histogrammed PDE method is presented. The method incorporates a simple Laplace smoothing procedure and χ 2 -triggered optimisation that results in the automatic selection of near-optimal binning and greatly improved PDE performance at low statistics. The performance of the smoothed histogrammed PDE is compared to a theoretically ideal PDE, and to results from a kernel PDE and a neural network.

A multi-variate discrimination technique based on range-searching

We present a fast and transparent multi-variate event classification technique, called PDE-RS, which is based on sampling the signal and background densities in a multi-dimensional phase space using range-searching. The employed algorithm is presented in detail and its behaviour is studied with simple toy examples representing basic patterns of problems often encountered in High Energy Physics data analyses. In addition an example relevant for the search for instanton-induced processes in deep-inelastic scattering at HERA is discussed. For all studied examples, the new presented method performs as good as artificial Neural Networks and has furthermore the advantage to need less computation time. This allows to carefully select the best combination of observables which optimally separate the signal and background and for which the simulations describe the data best. Moreover, the systematic and statistical uncertainties can be easily evaluated. The method is therefore a powerful tool to find a small number of signal events in the large data samples expected at future particle colliders.

Business failure prediction using the UTADIS multicriteria analysis method

Business failure prediction is one of the most essential problems in the field of financial management. The research on developing quantitative business failure prediction models has been focused on building discriminant models to distinguish among failed and non-failed firms. Several researchers in this field have proposed multivariate statistical discrimination techniques. This paper explores the applicability of multicriteria analysis to predict business failure. Four preference disaggregation methods, namely the UTADIS method and three of its variants, are compared to three well-known multivariate statistical and econometric techniques, namely discriminant analysis, logit and probit analyses. A basic (learning) sample and a holdout (testing) sample are used to perform the comparison. Through this comparison, the relative performance of all the aforementioned methods is investigated regarding their discriminating and predicting ability.

Volatile Compounds of Bovine Milk as Related to the Stage of the Estrous Cycle

Previous reports on behavioral assays with trained dogs suggested that milk samples from cows at diestrus, proestrus, and estrus had different odors. To identify the odor differences, volatile compounds in milk were isolated and analyzed by gas chromatography and mass spectrometry. About 80 peaks were detected in each chromatogram, of which 59 were present in all samples, and 23 were tentatively identified. The major identified compounds included the following six structurally distinct classes: ester, aldehyde, ketone, alcohol, fatty acid, and lactone. Although no unique peaks were found to be specific to samples taken at diestrus, proestrus, or estrus, 36 compounds exhibited significant differences in concentration among the three reproductive stages. These quantitative differences may account for the variation of milk odors during the estrous cycle.In order to investigate the quantitative differences systematically, multivariate discriminant techniques were used to relate the gas chromatographic profiles with the three stages of the estrous cycle. Stepwise discriminant analysis indicated that 15 of the 59 peaks in each chromatogram could best be used to reveal the differences among milk samples taken at diestrus, proestrus, and estrus stages. The discriminant function based on the 15 key peaks could classify all of the samples into their original categories at a total accuracy of 97.9%. Canonical analysis indicated that milk samples from different stages were clearly separated from each other in a two-dimensional space.

Seasonal Prediction Models for North Atlantic Basin Hurricane Location

Using multivariate discriminant analysis techniques, statistically significant and skillful models are developed for making extended-range forecasts of hurricane activity within specific locations of the North Atlantic basin. These forecasts predict the presence or absence of hurricane activity and not the actual number of storms that will occur within a region. Successful models are developed for predicting intense hurricane activity in both the Gulf of Mexico and the Caribbean subbasins separately. Extended-range forecasts of all hurricane activity are also possible within the Caribbean Sea. More significantly, lead-time forecasts of landfalling hurricanes on the southeastern Atlantic coast of the United States are possible and show a substantial improvement over climatology. Extended-range forecasts of hurricane activity for the northeastern United States and for the Gulf of Mexico are not feasible due, respectively, to the relative lack and abundance of hurricane activity. Crossvalidated forecast accuracies range from 78% to 81% for the regions in which successful models can be developed. An all-possible subsets selection algorithm is used to identify the predictor models, while bootstrap techniques are used to assess model significance. Statistical tests using normal approximations are employed to compare cross-validated (hindcast) forecast accuracy to climatology.

Multivariate Discrimination Methods for Top Quark Analysis

Multivariate discrimination techniques are being considered as alternatives to many data-analysis methods conventionally used in experimental high-energy physics. In this article, the applications of four different methods—a quadratic classifier, kernel discriminant analysis, a feedforward neural network, and multivariate adaptive regression splines—are compared for the detection of the top quark. Simulated particle-collision data that correspond to two classes, a rare signal and a dominant background, are used.

Multivariate Discrimination Methods for Top Quark Analysis

Multivariate discrimination techniques are being considered as alternatives to many data-analysis methods conventionally used in experimental high-energy physics. In this article, the applications of four different methods—a quadratic classifier, kernel discriminant analysis, a feedforward neural network, and multivariate adaptive regression splines—are compared for the detection of the top quark. Simulated particle-collision data that correspond to two classes, a rare signal and a dominant background, are used.

Environment of deposition of the sandstones of Lower Vindhyans of parts of Durg district, Madhya Pradesh, India

Present paper attempts to establish the environment of deposition of the sandstones belonging to the Chandarpur Group exposed in parts of the Durg district, Madhya Pradesh (India). Grain size and shape analyses of the sandstones are carried out. Vertical variations of the different grain size statistics of the fluvial and beach sediments are also studied. A multivariate linear discriminant technique was adopted for discriminating the sediments of these two environments. The palaeocurrents are towards north, northeast and southeast.&#x0D; Petrographic studies and provenance analysis of the sandstones show that the beach environment is richer in quartz and poorer in matrix as compared to the fluvial ones. The sandstones have been clearly differentiated with the help of multivariate discriminant analysis using thin section modal constituents like quartz, feldspars, iron oxide, matrix, etc. Results of the lithostratigraphic, grain size and petrographic studies fairly tally with each other suggesting that the sandstones under study were deposited under two very different fluvial and beach environments.

Discrimination of Organic Solvents Using an Infrared-Emitting Diode-Based Analyzer. Part I: Feasibility

This report demonstrates the feasibility of discriminating organic solvents on the basis of short-wave near-infrared spectra (from 0.7 to 1.1 μm). Both library searching and multivariate statistical methods were applied to 8-cm−1 spectra and to spectra de-resolved to the point achievable with an analyzer using discrete infrared-emitting diode sources. Library searching performed satisfactorily if the unknown and library spectra were collected under reasonably similar conditions, but performed poorly if the temperature of hydrogen-bonding solvents was varied. A multivariate discrimination technique based on Mahalanobis distance computation was capable of discriminating between several alcohols while allowing for a temperature variation of 20°C. These results indicate that a very low resolution (on the order of 100 cm−1) short-wave near-infrared analyzer can achieve successful discrimination between similar solvents under variable conditions.

Machine Vision for Color Inspection of Potatoes and Apples

A machine vision system was trained to distinguish between good and greened potatoes and yellow and green Golden Delicious apples. The method of using the HSI (Hue, Saturation, and Intensity) color system proved highly effective for color evaluation and image processing. The vision system achieved over 90% accuracy in inspection of potatoes and apples by representing features with hue histograms and applying multivariate discriminant techniques. Reducing the number of hue bins by selecting significant features only or by summing groups of hue bins increased misclassification by the vision system. Color classification represents an important quality feature evaluation method that needs to be integrated into an overall automated quality inspection and grading system.

Application of discriminant analysis to interpret the behaviour of photochemical oxidants in an urban area

The seasonal variation and monthly hourly cycles were studied from the 0 3 , NO and N0 2 hourly mean data obtained in Valladolid. The hourly patterns obtained each month revealed one diurnal 0 3 and two NO and NO 2 , peaks, in the early morning and in the evening, respectively, all of them affected by a seasonal variation. An early morning peak at rush hour followed by an NO 2 increase and subsequent 0 3 formation were the common features observed in all periods of the year. The early morning N02 peak-time occurrence was, however, poorly defined, and NO conversion to NO 2 , its associated lag and its participation in 0 3 formation, were not well understood from the experimental data. In order to obtain information about NO conversion to NO 2 a multivariate discriminant analysis technique was applied both to the summer and winter periods data series of maxima 0 3 , NO and N02 diurnal concentrations, their peak-time occurrence in the morning and the common meteorological variables. The selection of an urban atmospheric stability scheme as a discriminant variable gave a satisfactory clustering for the summer data series and a poorer resolution for the winter data series. The comparison of the composition of the centroids allows us to conclude the important influence of wind speed, solar radiation and atmospheric stability on 0 3 pollution levels and precursors and on the photochemical conversion of NO to N0 2 in the city.