Standard Discriminant Analysis Research Articles

Chemometrics identification of geographical origin of garlic in Korea using elements concentrations data obtained by ICP-OES and ICP-MS

Discriminant analysis was performed according to the geographical origin of garlic using 60 elements. This study aimed to develop an analytical method for determining the geographical origin of garlic using inductively coupled plasma (ICP) analysis. Statistically significant differences were observed in 25 out of 60 elements. A total of 31 variable meanings in projection were selected from orthogonal partial least square discriminant analysis. The selected elements overlapped with those with significant differences, and those that did not were also included. The prediction of the selected element was confirmed using the area under the curve value of the receiver operating characteristic curve. A heatmap was also used to identify the geographic origin, and discriminant analysis of the geographic origin exhibited 100 % accuracy in standard discriminant analysis. This elemental analysis method exhibits promise as a food and agricultural product analysis tool, and can accurately determine the geographic origin of condiment vegetables other than garlic.

Discrimination of Pineapples Varieties based on Volatile Organic Compounds using Chromatographic and Chemometrics Analysis

This study analyzed the volatile organic compounds (VOCs) of four different pineapple varieties (MD2, Sarawak, Josephine and Morris). Head Space-Solid Phase Micro Extraction (HS-SPME) was used to extract the VOCs of those pineapples using Gas Chromatography-Mass Spectrometry (GC-MS). Analysis of pineapples extracts identified many types of VOCS including esters, alcohols, terpenes, aldehydes, ketones, saturated hydrocarbons and phenols. Thirtyfive selected VOCs were used for varietal discrimination using chemometrics techniques namely principal components analysis (PCA), cluster analysis (CA) and discriminant analysis (DA). The application of PCA and CA was able to group the pineapple samples according to their varieties based on their respective VOCs. Standard mode DA had discriminated the samples with 98.75% correctness using all 35 VOCs. The identification of significant compounds found in the studied samples was successfully confirmed (p<0.05) by PCA. The total variance of PC1 and PC2 is 63.34% exhibiting that the ester compounds show strong and moderate loading values. One of the unique identifiers is the presence of β-Myrcene with a loading value 0.93 found in PC1 where it is described as pleasant terpenes odor and balsamic descriptor. GCMS and chemometric techniques provided meaningful chemically quantitative data.

Large-Dimensional Characterization of Robust Linear Discriminant Analysis

In standard discriminant analysis, data are commonly assumed to follow a Gaussian distribution, a condition which is often violated in practice. In this work, to account for potential spurious or mislabeled observations in the training data, we consider a robust version of regularized linear discriminant analysis (LDA) classifiers. Essential to such robust version of LDA is the design of a robust discriminant rule which relies on a robust estimate of the covariance matrix of the training data. We propose to use a regularized version of M-estimators of covariance matrices belonging to Maronna's class of estimators. In the regime where both the number of variables and the number of training samples are large, building upon recent results from random matrix theory, we show that when the training data are free from outliers, each classifier within the class of proposed robust classifiers is asymptotically equivalent to traditional, non-robust classifiers. Rather surprisingly, this entails that the use of robust estimators does not degrade the performance of LDA, up to a transformation of the regularization parameter that we precisely characterize. We also demonstrate that the proposed robust classifiers lead to a better classification accuracy when the data are corrupted by outliers or random noise. Furthermore, through simulations on the popular MNIST data set and considering different classification tasks, we show that the worse the classification error of traditional methods is, the further gain is to be expected with the use of our proposed method.

The Development of Malaysian Body Somatotype Model using Comprehensive Multivariate Techniques

This study was designed to develop Malaysian body somatotype model among U21 athletes using multivariate analysis. A total of 85 athletes (aged 20.5 ± 5.5 year) were participated in the assessment of anthropometrics measurements. They were from three types of sports which are weightlifter, futsal and Sepak Takraw. These selected sports were represented three categories of body somatotypes namely endomorph, mesomorph and ectomorph respectively. Discriminant Analysis (DA) was used to determine the model and validate the accuracy of these groups classification. As the result, DA obtained 98.8% variability with two factors. First factor (F1) revealed 85.9% discrimination while second factor (F2) revealed 12.9% discrimination as it is related to anthropometrics and the variation of three groups significantly. A body somatotype model was generated using the standardized coefficient of F1. Standard DA showed three discriminated variables (height, sitting height and weight) with 67.06% percentage of correctness. While forward and backward stepwise mode assigned two discriminated variables (weight and height) with 69.41% percentage of correctness. They were established as essential indicators for differentiating body physical category.

Technical and tactical performance indicators discriminating winning and losing team in elite Asian beach soccer tournament.

The present study aims to identify the essential technical and tactical performance indicators that could differentiate winning and losing performance in the Asian elite beach soccer competition. A set of 20 technical and tactical performance indicators namely; shot back-third, shot mid-third, shot front-third, pass back-third, pass mid-third, pass front-third, shot in box, shot outbox, chances created, interception, turnover, goals scored 1st period, goals scored 2nd period, goals scored 3rd period, goals scored extra time, tackling, fouls committed, complete save, incomplete save and passing error were observed during the beach soccer Asian Football Confederation tournament 2017 held in Malaysia. A total of 23 matches from 12 teams were notated using StatWatch application in real-time. Discriminant analysis (DA) of standard, backward as well stepwise modes were used to develop a model for the winning (WT) and losing team (LT) whilst Mann-Whitney U test was utilized to ascertain the differences between the WT and LT with respect to the performance indicators evaluated. The standard backward, forward and stepwise discriminates the WT and the LT with an excellent accuracy of 95.65%, 91.30% and 89.13%, respectively. The standard DA model discriminated the teams from seven performance indicators whilst both the backward and forward stepwise identified two performance indicators. The Mann-Whitney U test analysis indicated that the WT is statistically significant from the LT based on the performance indicators determined from the standard mode model of the DA. It was demonstrated that seven performance indicators namely; shot front-third, pass front-third, chances created, goals scores at the 1st period, goals scored at the 2nd period, goals scored at 3rd period were directly linked to a successful performance whilst the incomplete save by the keeper attribute towards the poor performance of the team. The present finding could serve useful to the coaches as well as performance analysts as a measure of profiling successful performance and enables team improvement with respect to the associated performance indicators.

Factor analysis and discriminant analysis of wastewater quality in Vidyaranyapuram sewage treatment plant, Mysore, India: a case study

Wastewater treatment plant monitoring is an essential part of effective wastewater management. The analysis of eight physico-chemical parameters of untreated wastewater was carried out at Vidyaranyapuram sewage treatment plant, Mysore, India. Factor analysis (FA) was applied to the untreated wastewater data matrix, and pollution was found to be the most contributing factor, explaining 22.31% of the total variance (chloride, biochemical oxygen demand, chemical oxygen demand and total dissolved solids). The second most contributing factor was found to be nitrification which explained 21.11% of the total variance (pH and nitrate), whereas the salinization factor contributed 16.98% of the total variance (total solids and total suspended solids). FA regression scores could not satisfactorily classify the data matrix with respect to the seasonal variations. Discriminant analysis (DA) was used to find the seasonal variations in the data matrix, and the standard mode DA explained 66.6% of total variance by grouping the cases with respect to seasons.

Machine vision for crack inspection of biscuits featuring pyramid detection scheme

One of the challenges associated with machine vision inspection of biscuits or baked products with non-uniform colour distributions and textured background is the detection of a small and minute crack. In this study, a pyramid automatic crack detection scheme was proposed. This requires an enhancement method to properly distinguish the crack and intact samples. Canny–Deriche filter was used to emphasis the crack and reduce the noise. In order to segment minute crack pattern with less noise, a unimodal thresholding technique was developed and tested. The detection was based on support vector machine (SVM) featuring Wilk’s λ selection criteria. The accuracy of the system was compared with standard discriminant analysis. It was discovered that the pyramid SVM after Wilk’s λ analysis was more precise in detection compared to other classifiers, resulting in the specificity and sensitivity of 98% and 96% respectively, and average correct classification of consistently more than 97%.

A link-analysis-based discriminant analysis for exploring partially labeled graphs

This letter investigates a link-analysis variant of discriminant analysis for projecting nodes of a (partially) labeled graph in a low-dimensional subspace and extracting discriminant node features. Basically, it corresponds to a kernel discriminant analysis computed from a kernel on a graph together with a class betweenness measure. As for standard discriminant analysis, the projected nodes are maximally separated with respect to the ratio of between-class inertia on total inertia – the distances being computed according to the kernel. The visualization of various graphs shows that the resulting display conveys useful information. Moreover, semi-supervised classification experiments indicate that the discriminant analysis indeed extracts relevant node features that are able to classify unlabeled nodes with competing performance.

Main Factors Affecting the Consumer Acceptance of Argentinean Fermented Sausages

AbstractMicrobiological, physicochemical and sensory characteristics of most popular Argentinean fermented sausages were evaluated in order to detect drivers of consumer liking. As a first step, a detailed description of instrumental parameters and consumer liking for fermented sausages was carried out. Furthermore, two multivariate mappings were performed: (1) cluster analysis to identify accepted fermented sausages based on overall acceptance and liking of appearance, aroma, taste and texture and (2) standard discriminant analysis to graphically recognize instrumental parameters that better described acceptance clusters. From these results, three fermented sausages groups with different acceptance patterns were segmented; taste and texture emerged as key sensory parameters and water activity, lightness, total protein, molds and enterococci among the physicochemical and microbiological variables were correlated with consumer liking.Practical ApplicationsGetting insight into the factors involved in the consumer liking is a relevant task for food scientists who want to establish official standards in terms of sensory quality. From the results obtained herein, instrumental parameters linked to consumer acceptance can be proposed as quality criteria. These guidelines could be profited by manufacturers and technologists to improve fermented sausage production.

Gender Assignment of Westland Petrels (Procellaria westlandica) Using Linear Discriminant Function Analysis

Abstract Rapid classification of a study subject's gender is critical for many ecological, behavioral, and conservation projects. We evaluated sexual-size dimorphism of adult Westland Petrels (Procellaria westlandica), a large nocturnal colony-nesting seabird, using linear discriminant function analysis and compared our results to birds classified using standard DNA gender identification techniques. The results revealed a strong pattern of sexual dimorphism (Wilks' Lambda = 0.43, F7,29 = 5.6, P < 0.001) in the standard discriminant function analysis despite an unbalanced sex ratio in our sample of adults captured at the breeding colony. Minimum bill depth and head length, of the seven morphometric characters we measured, successfully assigned the correct gender to 95% of all individuals sampled (n = 37). We provide a canonical classification function of morphological traits that may be used in the field to rapidly differentiate adult females and males of this rare petrel species.

Discriminant analysis for compositional data and robust parameter estimation

Compositional data, i.e. data including only relative information, need to be transformed prior to applying the standard discriminant analysis methods that are designed for the Euclidean space. Here it is investigated for linear, quadratic, and Fisher discriminant analysis, which of the transformations lead to invariance of the resulting discriminant rules. Moreover, it is shown that for robust parameter estimation not only an appropriate transformation, but also affine equivariant estimators of location and covariance are needed. An example and simulated data demonstrate the effects of working in an inappropriate space for discriminant analysis.

Support vector machine approach to real-time inspection of biscuits on moving conveyor belt

An intelligent system for colour inspection of biscuit products is proposed. In this system, the state-of-the-art classification techniques based on Support Vector Machines (SVM) and Wilk's λ analysis were used to classify biscuits into one of four distinct groups: under-baked, moderately baked, over-baked, and substantially over-baked. The accuracy of the system was compared with standard discriminant analysis using both direct and multi-step classifications. It was discovered that the radial basis SVM after Wilk's λ was more precise in classification compared to other classifiers. Real-time implementation was achieved by means of multi-core processor with advanced multiple-buffering and multithreading algorithms. The system resulted in correct classification rate of more than 96% for stationary and moving biscuits at 9 m/min. It was discovered that touching and non-touching biscuits did not significantly interfere with accurate assessment of baking. However, image processing of touching biscuits was considerably slower compared to non-touching biscuits, averaging at 36.3 ms and 9.0 ms, respectively. The decrease in speed was due to the complexity of the watershed-based algorithm used to segment touching biscuits. This image computing platform can potentially support the requirements of the high-volume biscuit production.

Multi-class colour inspection of baked foods featuring support vector machine and Wilk’s λ analysis

Abstract An automated, intelligent system for the colour inspection of biscuit products is proposed. In this system, advanced classification techniques featuring Support Vector Machines (SVM) and Wilk’s λ analysis were used to classify biscuits into one of eight distinct groups, corresponding to different degrees of baking. The results of the analyses were compared using standard discriminant analysis employing direct and multi-step classifications. It was discovered that the directed acyclic graph (DAG) and the balanced binary tree (BBT) after Wilk’s λ were more precise in the classification, as compared to other classifiers. In all cases, these methods resulted in the correct classification rate of 87.25% and 86.75% for DAG and BBT, respectively. Since the algorithm was implemented using software, the system could be programmed to inspect other bakery products.

Extension of model-based classification for binary data when training and test populations differ

Standard discriminant analysis supposes that both the training sample and the test sample are derived from the same population. When these samples arise from populations differing in their descriptive parameters, a generalization of discriminant analysis consists of adapting the classification rule related to the training population to another rule related to the test population, by estimating a link map between both populations. This paper extends an existing work in the multinormal context to the case of binary data. In order to solve the problem of defining a link map between the two binary populations, it is assumed that the binary data result from the discretization of latent Gaussian data. An estimation method and a robustness study are presented, and two applications in a biological context illustrate this work.

Mathematical Programming Approaches to Classification Problems

Discriminant Analysis (DA) is widely applied in many fields. Some recent researches raise the fact that standard DA assumptions, such as a normal distribution of data and equality of the variance-covariance matrices, are not always satisfied. A Mathematical Programming approach (MP) has been frequently used in DA and can be considered a valuable alternative to the classical models of DA. The MP approach provides more flexibility for the process of analysis. The aim of this paper is to address a comparative study in which we analyze the performance of three statistical and some MP methods using linear and nonlinear discriminant functions in two-group classification problems. New classification procedures will be adapted to context of nonlinear discriminant functions. Different applications are used to compare these methods including the Support Vector Machines- (SVMs-) based approach. The findings of this study will be useful in assisting decision-makers to choose the most appropriate model for their decision-making situation.

Development of a geographical distribution model of Rhodnius pallescens Barber, 1932 using environmental data recorded by remote sensing

Rhodnius pallescens, main vector of Trypanosoma cruzi in Panama and secondary vector in Colombia, Costa Rica and Nicaragua, represents an important epidemiological risk in those countries. It occupies sylvatic ecotopes, and because of this its distribution and abundance could be conditioned by environmental factors. In this work, we integrated environmental variables recorded by remote sensing and data of R. pallescens presence in the countries mentioned above in order to know the environmental variables with better capacity to describe the insects’ distribution, which will help to entomological surveillance and control. Standard discriminant analysis (DA) was used to determine if there is a significant difference in the environmental variation between the presence and the absence sites of R. pallescens. Forward stepwise discriminant analysis (fDA) was used to determine the environmental variables which better discriminated between presence and absence sites, and to construct a predictive map of geographical distribution. Univariate analyses were used to determine the discriminatory power of individual variables. The model derived from DA showed 89% of sensitivity and 92.8% of specificity. Multivariate and univariate analyses showed the vapor pressure deficit minimum as the principal variable among the nine most important to describe the distribution of the species, which is in agreement with the R. pallescens stenohydric status. Map shows insects’ distribution predicted by environmental variables, and moreover includes the distribution of most species belonging to Rhodnius genus, except R. domesticus, R. nasutus and R. neglectus. We interpreted these results as a reflection of the common evolution of the most Rhodnius species, except for the last ones that probably evolved isolated due to particular environmental conditions. In conclusion, this study showed that a reduced number of environmental variables can predict the distribution of R. pallescens and related species. This methodology can be very useful to make critical decisions for vectorial surveillance and control of Chagas disease vectors.

Quantitative Digital and Palmar Dermatoglyphics among Sardinian Linguistic Groups

Discriminant analyses of 23 digital and 15 palmar quantitative dermatoglyphic variables of 1364 Sardinians, 689 males and 675 females, were performed to identify biological relationships among five Sardinian linguistic groups of both sexes. By various subsets of dermatoglyphic variables (23 and 20 digital, 15 and 14 palmar, 4 summary traits) MANOVA revealed high intergroup heterogeneity among the groups of both sexes and within each sex. In the latter case the males are an exception when 15 and 14 (MLI removed) palmar variables are used. Standard discriminant analysis of the 23 digital variables, i.e. the radial and ulnar ridge counts on each of the 10 fingers plus total finger ridge count (TFRC), absolute finger ridge count (AFRC) and pattern intensity (PI), resulted in imperfect separation of males and females and an unclear picture of the biological relationships among the groups. In contrast, standard discriminant analysis of 20 digital variables (TFRC, AFRC and PI were removed from the analysis) resulted in separation of the sexes and a pattern of relationships among the populations consistent with their ethno-historical backgrounds. Standard discriminant analysis of 15 palmar dermatoglyphic variables failed to provide separation of the sexes and produced a pattern of relationships in disagreement with both the linguistic and ethno-historical backgrounds, even removing MLI (Main Line Index). Standard discriminant analysis of 4 summary dermatoglyphic variables (TFRC, AFRC, PI and MLI) yielded imperfect separation of males and females and an unclear pattern of relationships. By stepwise discriminant analysis with p < or = 0.01 as F-to-enter and p < or = 0.05 as F-to-remove, only 4 of the 38 digital and palmar variables were in the model (URC R5, RRC L5, RRC R5, URC R4). The pattern of inter-population biological relationships was conceptually similar to the one produced by the 20 digital variables. It showed a clear separation of the Gallurian group (both males and females), which speaks an Italian dialect. The properly Sardinian linguistic groups (Campidanian and Logudorian), the Sassarian group (which speaks an Italian dialect) and the Alghero group (which speaks Catalan) were close to one another. This picture agrees with the ethno-historical background rather than with the linguistic one.

Morphometric comparison of three members of the Gyrodactylus nemachili-like species group (Monogenea: Gyrodactylidae) on Barbatula barbatula L. in the Czech Republic, with a reinstatement of G. papernai Ergens &amp; Bychowsky, 1967

The Gyrodactylus nemachili-like species complex, parasitising stone loach Barbatula barbatula L. in the Czech Republic, was investigated based on the detailed morphometric analysis of its haptoral hard parts. The existence of two species, G. jiroveci Ergens & Bychowsky, 1967 and G. pseudonemachili Ergens & Bychowsky, 1967 was confirmed. A standard discriminant analysis of the morphometric data showed a clear separation between specimens of G. jiroveci and another species or variant. Based on the morphology of the haptoral hard parts, this third species was more similar to G. jiroveci than to G. pseudonemachili. The differences between G. jiroveci and the third species were mainly in the morphology of the marginal hook sickle, but included the total length of the marginal hook, the length of the hamulus point, the length of the marginal hook sickle, the width of the ventral bar, and the width of the dorsal bar. Based on comparison with the original material, the third species was identified as G. papernai Ergens & Bychowsky, 1967, which has recently been considered a synonym of G. jiroveci. These analyses provided sufficient evidence for the restoration of G. papernai as a valid taxon. Partial sequences of the internal transcribed spacer rRNA genes (ITS rDNA) verified the validity of all three Gyrodactylus species studied.

Peritoneal fluid cytokines and sICAM-1 in minimal endometriosis: search for discriminating factors between infertility and/or endometriosis

Objective:To evaluate cytokine levels (IL-1β, TNF-α, IL-6, IL-8), soluble intercellular adhesion molecule-1 (sICAM-1) and number of macrophages in peritoneal fluid (PF) of women with no minimal endometriosis and associated (or not) infertility in order to discriminate between infertility and/or endometriosis. Study design:Cytokines and sICAM-1 were measured by using quantitative enzyme-linked immunosorbent assay (ELISA) while the macrophages were identified by May-Grunwald-Giemsa and non-specific esterase staining and presented as medians. The measurements were performed in 78 women belonging to four selected subgroups according to their endometriosis and/or infertility status. Statistical analysis was performed using Kruskal–Wallis non-parametric ANOVA test. Additionally, discriminant function analyses were performed. Results:We have found the most elevated macrophage numbers in the groups of women with endometriosis. IL-1β did not present any statistically significant values differentiating the analysed subgroups. IL-6 (110.0pg/ml) and TNF-α exhibited the highest concentrations (statistically significant) in a group of fertile women with endometriosis. IL-8 clearly differentiated between the subgroups with infertility and sICAM-1 was statistically significantly elevated in the subgroups of infertile women. In the forward discriminant analysis, when subdividing the studied population according to its infertility status (we considered macrophages, IL-8 and IL-6 in order of probability values), we have found striking probability value of 92% for the correct classification into an infertile population. Conclusion:Out of the range of the analysed factors we have found only the sICAM-1 to be singled out between the standard discriminant analysis and the forward one. However, this important flagging molecule might be of considerable value for discrimination between different types of pathology at the level of immune effector function. The increased levels of TNF-α and IL-6 signified a group of fertile women with endometriosis; however only IL-6 presented a discriminating value in multifunctional analysis of examined subgroups. The analysed range of factors had a greater tendency to discriminate between infertility status rather than endometriosis.

A post-processing/region of interest (ROI) method for discriminating patterns of activity in statistical maps of fMRI data

To combine functional neuroimaging studies across subjects, anatomical and functional data are typically either transformed to a common space or averaged across regions of interest (ROIs). However, if there are (1) anatomical variations within the subject pool (as in clinical or aging populations), (2) non-Gaussian distributions of task-related activity within a typical ROI or, (3) more ROIs than subjects, neither spatial transformation of the data to a common space nor averaging across all subjects’ ROIs is suitable for standard discriminant analysis. To solve these problems, we describe a post-processing method that uses voxel-based statistics representing task-related activity (pooled within ROIs) to establish combinations of ROIs that maximally differentiate tasks across all subjects. The method involves randomized resampling from multiple ROIs within each subject, multivariate linear discriminant analysis across all subjects and validation with bootstrapping techniques. When applied to experimental data from healthy subjects performing two motor tasks, the method detected some brain regions, including the supplementary motor area (SMA), that participated in a distributed network differentially active between tasks. However there was not a significant difference in SMA activity when this region was examined in isolation. We suggest this method is a practical means to combine voxel-based statistics within anatomically defined ROIs across subjects.