Quadratic Discriminant Analysis Methods Research Articles

Comparison of discriminant methods and deep learning analysis in plant taxonomy: a case study of Elatine

Elatine is a genus in which, flower and seed characteristics are the most important diagnostic features; i.e. seed shape and the structure of its cover found to be the most reliable identification character. We used a combination of classic discriminant methods by combining with deep learning techniques to analyze seed morphometric data within 28 populations of six Elatine species from 11 countries throughout the Northern Hemisphere to compare the obtained results and then check their taxonomic classification. Our findings indicate that among the discriminant methods, Quadratic Discriminant Analysis (QDA) had the highest percentage of correct matching (mean fit—91.23%); only the deep machine learning method based on Convolutional Neural Network (CNN) was characterized by a higher match (mean fit—93.40%). The QDA method recognized the seeds of E. brochonii and E. orthosperma with 99% accuracy, and the CNN method with 100%. Other taxa, such as E. alsinastrum, E. trianda, E. californica and E. hungarica were matched with an accuracy of at least 95% (CNN). Our results indicate that the CNN obtains remarkably more accurate classifications than classic discriminant methods, and better recognizes the entire taxa pool analyzed. The least recognized species are E. macropoda and E. hexandra (88% and 78% match).

Stable isotope ratio analysis for the authentication of sea urchin (Mesocentrotus nudus) from different culture areas in the North Yellow Sea, China

Reliable methods of tracing the geographical origin of sea urchin are urgently needed for food safety and consumer health. To the best of our knowledge, the present study was the first attempt to trace the geographic origins of sea urchin by using stable isotope techniques. The δ13C, δ15N and δ18O values from the gonad and spine of sea urchins collected from five locations were analyzed. From the gonad samples, the δ13C values ranged from −22.07‰ to −18.37‰, the δ15N values ranged from 6.59‰ to 9.99‰, and the δ18O values ranged from 17.64‰ to 27.19‰. From the spine samples, the δ13C values ranged from −5.43‰ to −3.57‰, the δ15N values ranged from 7.95‰ to 13.66‰, and the δ18O values ranged from 33.99‰ to 40.15‰. The δ13C and δ15N values from the gonads differed significantly among samples from different geographic origins, but the δ18O values did not differ. The δ15N and δ18O values from the spines differed significantly among samples from different geographic origins, but the δ13C values did not differ. Both quadratic discriminant analysis (QDA) and the k-nearest neighbor (KNN) methods yielded low recognition of the δ13C, δ15N, and δ18O values from the gonad samples. However, higher accuracy was obtained using the stable isotope values from the spine samples combined with QDA or KNN methods. Moreover, the KNN methods gave more satisfactory accuracy, the initial, cross-validated, and predictive classification rates were 97.1%, 97.1%, and 93.3%, respectively. The C, N, and O stable isotope analysis of spine samples may be used to verify the geographic origin of sea urchins.

How likely is septic shock to develop in a patient with Fournier's gangrene? A risk prediction model based on a 7-year retrospective study.

BackgroundFournier’s gangrene (FG) is a rare life-threatening form of necrotizing fasciitis. The risk factors for septic shock in patients with FG are unclear. This study aimed to identify potential risk factors and develop a prediction model for septic shock in patients with FG.MethodsThis retrospective cohort study included patients who were treated for FG between May 2013 and May 2020 at the Sixth Affiliated Hospital, Sun Yat-sen University (Guangzhou, China). The patients were divided into a septic shock group and a non-septic shock group. An L1-penalized logistic regression model was used to detect the main effect of important factors and a penalized Quadratic Discriminant Analysis method was used to identify possible interaction effects between different factors. The selected main factors and interactions were used to obtain a logistic regression model based on the Bayesian information criterion.ResultsA total of 113 patients with FG were enrolled and allocated to the septic shock group (n = 24) or non-septic shock group (n = 89). The best model selected identified by backward logistic regression based on Bayesian information criterion selected temperature, platelets, total bilirubin (TBIL) level, and pneumatosis on pelvic computed tomography/magnetic resonance images as the main linear effect and Na+ × TBIL as the interaction effect. The area under the ROC curve of the probability of FG with septic shock by our model was 0.84 (95% confidence interval, 0.78–0.95). The Harrell's concordance index for the nomogram was 0.864 (95% confidence interval, 0.78–0.95).ConclusionWe have developed a prediction model for evaluation of the risk of septic shock in patients with FG that could assist clinicians in identifying critically ill patients with FG and prevent them from reaching a crisis state.

Feature Selection Based on IoT Aware QDA Node Authentication in 5G Networks

The coming generation in mobile networks is the fifth generation (5G), which appears to be the promoter of the upcoming digital world. 5G is defined by a single piece of cellular access technology or a combination of advanced access technologies. Rather, 5G is a true network assembler that provides consistent support for a slew of novel network topologies. Prior generations provide as a suitable starting point and give support for the security architecture for 5G security. Through authentication and cryptography techniques, many works have tackled the security issues in 3G and 4G networks in an effective manner. However, security of 5G networks while data transmission was not improved. The IoT aware Quadratic Discriminant Analysis (QDA) Node Authentication Method is proposed in order to achieve safe data communication in the 5G network. The suggested method performs feature selection using Quadratic Discriminant Analysis to identify relevant properties of mobile nodes such as trust value, residual energy level, and node cooperativeness. Simulation can be used to test the data packets, the number of mobile nodes in a security level, the computation overhead, and the authentication accuracy. The observed output clearly demonstrates that the Quadratic Discriminant Analysis Method significantly enhances the authentication accuracy of each node and the security level with less overhead than state-of-the-art-methods.

Improvement decoding performance based on GQDA during a high engagement demanding paradigm

This research concentrates on the study of dexterous brain-computer interaction, combining a new paradigm and method for the decoding of electroencephalography (EEG) motor intention. An EEG evoking paradigm by implementing margin energy constraint in complex coupling objects is used for inducing strong intention and providing high recognition accuracy. Motor intention decoding from task-dependent EEG was given by a generalized quadratic discriminant analysis, which is proposed based on discriminant analysis. The generalization method is flexible and adaptive to any given data. Furthermore, we conduct a systematic comparison relative to extracted features in different dimensions and to find the optimal feature dimension. Cross-validation is used to make the generalized quadratic discriminant analysis method adaptive individually for each volunteer. The discriminant performance of state recognition given by area under the receiver operating characteristics curve is ∼ 0.96 from ten volunteers, this performance has been found to compare very favorably with some well-known powerful classifiers. It has been demonstrated that the proposed method generalized quadratic discriminant analysis has excellent decoding performance in manipulating complex objects. Together, this work can provide a guarantee for improving the accuracy of intention recognition on data level with the high engagement demanding task, and may inspire better EEG acquisition contexts.

A family of divergence-based classifiers for Polarimetric Synthetic Aperture Radar (PolSAR) imagery vector and matrix features

ABSTRACT Polarimetric Synthetic Aperture Radar (PolSAR) is one of the most important remote sensing tools. However, PolSAR images are strongly contaminated by a multidimensional interference (called speckle noise), making their processing (e.g. in the classification context) difficult. In terms of structure, multilook PolSAR data follow a definite positive hermitian behaviour and, therefore, require tailored classifiers for their features. Some classic classifiers – such as Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), K-Nearest Neighbours (KNN), and Support Vector Machine (SVM) – have been yielding unacceptable performance to these data, when applied directly. One justification is because they do not often take into account neither the speckle presence nor properties which are inherent to under-study relieves. This paper addresses a collection of PolSAR divergence-based classifiers, deduced from the normal, skew-normal, t-Student, and skew-t vector models as well as the scaled complex Wishart (SCW) distribution. The last model is a standard supposition to describe multilook PolSAR data, having two parameters: covariance matrix (which is directed to data nature) and number of looks (which controls the speckle noise effect). The considered remainder laws aim to model the main diagonal of these data, known as multivariate intensities. The performance of proposed methods is quantified and compared with those due to the Kullback-Leibler (KL) distance for multivariate normal distribution and to LDA, QDA, KNN, and SVM methods. Experiments with both artificial and real PolSAR data are considered. Results favour optimal Rényi classifiers for an Airborne Synthetic Aperture Radar (AIRSAR) image of San Francisco and the t-Student KL classifier for an SAR image system of the Electromagnetics Institute (EMISAR) image of Foulum.

Real-time discriminant analysis in the presence of label and measurement noise

Quadratic discriminant analysis (QDA) is a widely used classification technique. Based on a training dataset, each class in the data is characterized by an estimate of its center and shape, which can then be used to assign unseen observations to one of the classes. The traditional QDA rule relies on the empirical mean and covariance matrix. Unfortunately, these estimators are sensitive to label and measurement noise which often impairs the model’s predictive ability. Robust estimators of location and scatter are resistant to this type of contamination. However, they have a prohibitive computational cost for large scale industrial experiments. We present a novel QDA method based on a recent real-time robust algorithm. We additionally integrate an anomaly detection step to classify the most atypical observations into a separate class of outliers. Finally, we introduce the label bias plot, a graphical display to identify label and measurement noise in the training data. The performance of the proposed approach is illustrated in a simulation study with huge datasets, and on real datasets about diabetes and fruit.

Comparison of chemometrics and AOCS official methods for predicting the shelf life of edible oil

The present study addressed the determination of the shelf life of edible oil using the non-destructive method of electronic nose (E-Nose) and compared it with the AOCS official ​method. The studied oils included two samples: newly-produced oils (a) and those produced 6 months before (b). These samples were assessed for 150 days. Data collection was conducted using an electronic nose equipped with 8 metal oxide semiconductor (MOS) sensors. Data analysis was also achieved by various methods including cluster analysis (CA), linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA), support vector machine (SVM), and AOCS official method. According to the results, the classification accuracy of SVM, QDA, and LDA methods was 96.25, 95.8, and 94.4%, respectively. All the methods were in line with the results obtained by AOCS.

Various and multilevel of coiflet discrete wavelet transform and quadratic discriminant analysis for classification misalignment on three phase induction motor

For a long time ago, induction motor has been used in various industry due to strong construction, high efficiency, and cheap maintenance. Induction motor needs to be maintained regularly so that it can operate for a long time. Based on studied, bearing faults result in failure of 42% -50% of all motor failures. One of the causes of bearing failure is misalignment when installing induction motor. This research proposes classification misalignment in induction using coiflet discrete wavelet transform and Quadratic Discriminant Analysis. Simulation of motor condition is introduced in this research as normal operation and two misalignment variations. And then, various type of coiflet discrete wavelet transform in first level until third level is used to extract motor vibration signal into high frequency signal. Then, three types of signal extraction, namely sum, range and energy level, will be used for input to Linear and Quadratic Discriminant Analysis. Linear and Quadratic Discriminant Analysis will analysis signal extraction and classify them into normal operation and two misalignment condition. The results show that first level of coiflet discrete wavelet transform is the best level for classification misalignment on induction motor, both using the Linear Discriminant Analysis and Quadratic Discriminant Analysis methods. The accuracy obtained from the two methods is the same or almost the same.

Application of infrared thermal imaging technique and discriminant analysis methods for non-destructive identification of fungal infection of potato tubers

A reliable, nondestructive and fast method based on active thermography has been evaluated in the present research to detect Fusarium solani fungus in potato tubers. This fungus causes the main disease in potato as dry rot. Healthy potato tubers and fungal contaminated ones at different stages (1 to 7 day after infection) have been provided to be classified. Different heating/cooling treatments including two heating temperature levels (60 and 90 °C) and four cooling time levels (10, 25, 40 and 70 s) were considered to find optimum thermography condition. The thermal images were acquired using a thermography camera and a heating box. The treatments were analyzed in a factorial experiment based on completely randomized design and heating temperature of 90 °C and cooling time of 40 s were selected as optimum thermography condition. Some statistical features were extracted and classified by linear and quadratic discriminant analysis methods. The classification results demonstrated that quadratic discriminant analysis can classify the healthy and contaminated tubers at different stages with high accuracy (98.5%).

Tea types classification with data fusion of UV-Vis, synchronous fluorescence and NIR spectroscopies and chemometric analysis.

The potential of selected spectroscopic methods - UV-Vis, synchronous fluorescence and NIR as well a data fusion of the measurements by these methods - for the classification of tea samples with respect to the production process was examined. Four classification methods - Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), Regularized Discriminant Analysis (RDA) and Support Vector Machine (SVM) - were used to analyze spectroscopic data. PCA analysis was applied prior to classification methods to reduce multidimensionality of the data. Classification error rates were used to evaluate the performance of these methods in the classification of tea samples. The results indicate that black, green, white, yellow, dark, and oolong teas, which are produced by different methods, are characterized by different UV-Vis, fluorescence, and NIR spectra. The lowest error rates in the calibration and validation data sets for individual spectroscopies and data fusion models were obtained with the use of the QDA and SVM methods, and did not exceed 3.3% and 0.0%, respectively. The lowest classification error rates in the validation data sets for individual spectroscopies were obtained with the use of RDA (12,8%), SVM (6,7%), and QDA (2,7%), for the UV-Vis, SF, and NIR spectroscopies, respectively. NIR spectroscopy combined with QDA outperformed other individual spectroscopic methods. Very low classification errors in the validation data sets - below 3% - were obtained for all the data fusion data sets (SF + UV-Vis, SF + NIR, NIR + UV-Vis combined with the SVM method). The results show that UV-Vis, fluorescence and near infrared spectroscopies may complement each other, giving lower errors for the classification of tea types.

THE AKARI FIS CATALOGUE OF YSOS AND EXTRAGALACTIC OBJECTS

The point sources in the Bright Source Catalogue of the AKARI Far-Infrared Surveyor (FIS) were classified based on their FIR and mid-IR fluxes and colours into young stellar object (YSO) and extragalactic source types using a Quadratic Discriminant Analysis method (QDA) and Support Vector Machines (SVM). The reliability of the selection of YSO candidates is high, and the number of known YSO candidates were increased significantly, that we demonstrate in the case of the nearby open cluster IC348. Our results show that we can separate galactic and extragalactic AKARI point sources in the multidimensioal space of FIR fluxes and colours with high reliability, however, differentiating among the extragalactic sub-types needs further information.

Predicting Antimicrobial Peptides by Using Increment of Diversity with Quadratic Discriminant Analysis Method.

Antimicrobial peptides are crucial components of the innate host defense system of most living organisms and promising candidates for antimicrobial agents. Accurate classification of antimicrobial peptides will be helpful to the discovery of new therapeutic targets. In this work, the Increment of Diversity with Quadratic Discriminant analysis (IDQD) was presented to classify antifungal and antibacterial peptides based on primary sequence information. In the jackknife test, the proposed IDQD model yields an accuracy of 86.02 percent with the sensitivity of 74.31 percent and specificity of 92.79 percent for identifying antimicrobial peptides, which is superior to other state-of-the-art methods. This result suggests that the proposed IDQD model can be efficiently used to antimicrobial peptide classification.

1H NMR- based metabolomics approaches as non- invasive tools for diagnosis of endometriosis

So far, non-invasive diagnostic approaches such as ultrasound, magnetic resonance imaging, or blood tests do not have sufficient diagnostic power for endometriosis disease. Lack of a non-invasive diagnostic test contributes to the long delay between onset of symptoms and diagnosis of endometriosis. The present study focuses on the identification of predictive biomarkers in serum by pattern recognition techniques and uses partial least square discriminant analysis, multi-layer feed forward artificial neural networks (ANNs) and quadratic discriminant analysis (QDA) modeling tools for the early diagnosis of endometriosis in a minimally invasive manner by (1)H- NMR based metabolomics. This prospective cohort study was done in Pasteur Institute, Iran in June 2013. Serum samples of 31 infertile women with endometriosis (stage II and III) who confirmed by diagnostic laparoscopy and 15 normal women were collected and analyzed by nuclear magnetic resonance spectroscopy. The model was built by using partial least square discriminant analysis, QDA, and ANNs to determine classifier metabolites for early prediction risk of disease. The levels of 2- methoxyestron, 2-methoxy estradiol, dehydroepiandrostion androstendione, aldosterone, and deoxy corticosterone were enhanced significantly in infertile group. While cholesterol and primary bile acids levels were decreased. QDA model showed significant difference between two study groups. Positive and negative predict value levels obtained about 71% and 78%, respectively. ANNs provided also criteria for detection of endometriosis. The QDA and ANNs modeling can be used as computational tools in noninvasive diagnose of endometriosis. However, the model designed by QDA methods is more efficient compared to ANNs in diagnosis of endometriosis patients.

Supervised and Unsupervised Classification Using Mixture Models

This chapter is dedicated to model-based supervised and unsupervised classification. Probability distributions are defined over possible labels as well as over the observations given the labels. To this end, the basic tools are the mixture models. This methodology yields a posterior distribution over the labels given the observations which allows to quantify the uncertainty of the classification. The role of Gaussian mixture models is emphasized leading to Linear Discriminant Analysis and Quadratic Discriminant Analysis methods. Some links with Fisher Discriminant Analysis and logistic regression are also established. The Expectation-Maximization algorithm is introduced and compared to the $K$-means clustering method. The methods are illustrated both on simulated datasets as well as on real datasets using the R software.

A selection of AKARI FIS BSC extragalactic objects

AbstractThe point sources in the Bright Source Catalogue (BSC) of the AKARI Far–Infrared Surveyor (FIS) were classified based on their far–IR and mid–IR fluxes and colours using Quadratic Discriminant Analysis method (QDA) and Support Vector Machines (SVM). The reliability of our results show that we can successfully separate galactic and extragalactic AKARI point sources in the multidimensional space of fluxes and colours. However, differentiating among the extragalactic sub–types needs further information.

Identify five kinds of simple super-secondary structures with quadratic discriminant algorithm based on the chemical shifts

The biological function of protein is largely determined by its spatial structure. The research on the relationship between structure and function is the basis of protein structure prediction. However, the prediction of super secondary structure is an important step in the prediction of protein spatial structure. Many algorithms have been proposed for the prediction of protein super secondary structure. However, the parameters used by these methods were primarily based on amino acid sequences. In this paper, we proposed a novel model for predicting five kinds of protein super secondary structures based on the chemical shifts (CSs). Firstly, we analyzed the statistical distribution of chemical shifts of six nuclei in five kinds of protein super secondary structures by using the analysis of variance (ANOVA). Secondly, we used chemical shifts of six nuclei as features, and combined with quadratic discriminant analysis (QDA) to predict five kinds of protein super secondary structures. Finally, we achieved the averaged sensitivity, specificity and the overall accuracy of 81.8%, 95.19%, 82.91%, respectively in seven-fold cross-validation. Moreover, we have performed the prediction by combining the five different chemical shifts as features, the maximum overall accuracy up to 89.87% by using the C,Cα,Cβ,N,Hα of Hα chemical shifts, which are clearly superior to that of the quadratic discriminant analysis (QDA) algorithm by using 20 amino acid compositions (AAC) as feature in the seven-fold cross-validation. These results demonstrated that chemical shifts (CSs) are indeed an outstanding parameter for the prediction of five kinds of super secondary structures. In addition, we compared the prediction of the quadratic discriminant analysis (QDA) with that of support vector machine (SVM) by using the same six CSs as features. The result suggested that the quadratic discriminant analysis method by using chemical shifts as features is a good predictor for protein super secondary structures.

Objective based geochemical anomaly detection—Application of discriminant function analysis in anomaly delineation in the Kuh Panj porphyry Cu mineralization (Iran)

A common objective method for anomaly detection in geochemical exploration is target delineation by discriminant function analysis. Discriminant analysis (DA) is a multivariate statistical technique that classifies each observation into a specific group based on observed predictor variables and predefined groups. In the present study a new approach is considered for geochemical anomaly identification employing DA and “real” pre-defined “anomaly” and “background” data set. The anomalous and background samples are identified based on presence or absence of mineralization in depth; so, this method is introduced as “objective approach”. In order to classify surface geochemical samples into anomaly and background, assays of core drillings in the Kuh Panj porphyry Cu mineralization are used. They are classed as anomaly if the presence of mineralization is proven and are labeled as background if the absence of mineralization is confirmed in cores. Stepwise Linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA) are utilized to achieve discrimination functions. For the test data used to generate the models, both LDA and QDA methods have led to perfect classification however cross validation has shown 84% and 74% total correct classification for LDA and QDA respectively. Outcomes of this research have demonstrated that LDA can effectively be employed as an objective method for geochemical anomaly identification if available information from geology and geochemistry of target area are employed and utilized. It is also shown that the definition of anomalism in geochemical exploration can be improved remarkably by this approach.

Kernel quadratic discriminant analysis for small sample size problem

It is generally believed that quadratic discriminant analysis (QDA) can better fit the data in practical pattern recognition applications compared to linear discriminant analysis (LDA) method. This is due to the fact that QDA relaxes the assumption made by LDA-based methods that the covariance matrix for each class is identical. However, it still assumes that the class conditional distribution is Gaussian which is usually not the case in many real-world applications. In this paper, a novel kernel-based QDA method is proposed to further relax the Gaussian assumption by using the kernel machine technique. The proposed method solves the complex pattern recognition problem by combining the QDA solution and the kernel machine technique, and at the same time, tackles the so-called small sample size problem through a regularized estimation of the covariance matrix. Extensive experimental results indicate that the proposed method is a more sophisticated solution outperforming many traditional kernel-based learning algorithms.

Design and development of a metal oxide based electronic nose for spoilage classification of beef

A metal oxide sensor-based electronic nose system consisting of nine sensors was designed and used to analyze the volatile compounds emanating from beef strip loins (M. Longisimmus lumborum) stored at 4 °C and 10 °C. Two statistical techniques, i.e., linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA) were used to develop classification models from the collected sensor signals. The performances of the developed models were validated by two different methods, i.e., leave-1-out cross validation and bootstrapping. Also, each classification model was developed using 6 and 10 features. The classification models classified meat samples based on the microbial population into “unspoiled” (microbial counts < 6 log 10 cfu/g) and “spoiled” (microbial counts ≥ 6 log 10 cfu/g). For the meat samples stored at 10 °C, the highest classification accuracies obtained by LDA method with leave-1-out and bootstrapping validations were 83.8% and 89.1%, respectively. On the other hand, classification by QDA and subsequent validation by leave-1-out and bootstrapping provided highest accuracies of 81.5% and 93.2%, respectively. For samples stored at 4 °C, the LDA method provided highest classification accuracies of 80% and 86.6% using leave-1-out and bootstrapping validation, respectively. The highest classification accuracies obtained for the samples stored at 4 °C were 85% and 96% by using QDA method with leave-1-out and bootstrapping validations, respectively.