Quadratic Discriminant Function Research Articles

Discrimination of quarry blasts from earthquakes in Northern and Central Egypt using linear and quadratic discriminant functions

In this study, seismic events in Northern and Central Egypt are inspected to discriminate quarry blasts from earthquakes. We examine a collection of 639 events in both time and frequency domains with local magnitudes of 1.5 ≤ ML ≤ 3.3 from the Egyptian Seismological Network’s seismic event catalogue between 2009 and 2015. The maximum S-wave to the maximum P-wave amplitude ratio, complexity (C), spectral ratio (Sr), and power of events (Pe) classifiers as well as two statistical approaches, linear discriminant function (LDF) and quadratic discriminant function (QDF), are used to distinguish between earthquakes and quarry blasts. The usage of the LDF and QDF forms did not result in any major differences in the discrimination. The results obtained by the LDF and QDF from (Pe-C) are the best of all approaches. The findings of all approaches were compared to get a final categorization for each event, and a decision was achieved when at least three of the four methods provided the same event category. In Northern Egypt, 243 earthquakes and 308 quarry blasts could be identified as final decisions, with two misclassified events, resulting in an overall success rate of 99.6%. In Central Egypt, 48 earthquakes and 36 quarry blasts were classified as a final decision, with two misclassified events, for an overall success percentage of 97.6%.

Classification of objects within agriculture landscape from high resolution aerial imagery using maximum likelihood discriminant rules

In this study, the performance of object classification based on four discriminant functions, namely linear, quadratic, diagonal linear and diagonal quadratic is investigated and compared. High-resolution aerial imagery captured from a UAV-based remote sensing platform is used for this purpose. Initially, K-means clustering of 9 clusters is used to assist in the selection of training pixels for the subsequent supervised classification implementation. The classification is experimented with using a training set size of 10 through 100 pixels for each of the discriminant functions. The outcome of the classification shows that training set size 40 and 10 are to be the optimal training set sizes for linear and quadratic discriminant function, and diagonal linear and quadratic discriminant function respectively. Overall, the linear discriminant function is found to have the highest overall accuracy of 91% followed by diagonal linear, quadratic, and diagonal quadratic discriminant function with overall accuracies of 82%, 79%, and 73% respectively.

Selecting the number of clusters, clustering models, and algorithms. A unifying approach based on the quadratic discriminant score

Cluster analysis requires fixing the number of clusters and often many hyper-parameters. In practice, one produces several partitions, and a final one is chosen based on validation or selection criteria. There exist an abundance of validation methods that, implicitly or explicitly, assume a certain clustering notion. In this paper, we focus on groups that can be well separated by quadratic or linear boundaries. The reference cluster concept is defined through the quadratic discriminant function and parameters describing clusters’ size, center and scatter. We develop two cluster-quality criteria that are consistent with groups generated from a class of elliptic–symmetric distributions. Using the bootstrap resampling of the proposed criteria, we propose a selection rule that allows choosing among many clustering solutions, eventually obtained from different methods. Extensive experimental analysis shows that the proposed methodology achieves a better overall performance compared to established alternatives from the literature.

Characterization of leaf surface phenotypes based on light interaction

BackgroundLeaf surface phenotypes can indicate plant health and relate to a plant’s adaptations to environmental stresses. Identifying these phenotypes using non-invasive techniques can assist in high-throughput phenotyping and can improve decision making in plant breeding. Identification of these surface phenotypes can also assist in stress identification. Incorporating surface phenotypes into leaf optical modelling can lead to improved biochemical parameter retrieval and species identification.ResultsIn this paper, leaf surface phenotypes are characterized for 349 leaf samples based on polarized light reflectance measured at Brewster’s Angle, and microscopic observation. Four main leaf surface phenotypes (glossy wax, glaucous wax, high trichome density, and glabrous) were identified for the leaf samples. The microscopic and visual observations of the phenotypes were used as ground truth for comparison with the spectral classification. In addition to surface classification, the microscope images were used to assess cell size, shape, and cell cap aspect ratios; these surface attributes were not found to correlate significantly with spectral measurements obtained in this study. Using a quadratic discriminant analysis function, a series of 10,000 classifications were run with the data randomly split between training and testing datasets, with 150 and 199 samples, respectively. The average correct classification rate was 72.9% with a worst-case classification of 60.3%.ConclusionsLeaf surface phenotypes were successfully correlated with spectral measurements that can be obtained remotely. Remote identification of these surface phenotypes will improve leaf optical modelling and biochemical parameter estimations. Phenotyping of leaf surfaces can inform plant breeding decisions and assist with plant health monitoring.

An Efficient Novel Approach with Multi Class Label Classification through Machine Learning Models for Pancreatic Cancer

Pancreatic cancer is right now the fourth largest cause of cancer-related deaths. Early diagnosis is one good solution for pancreatic cancer patients and reduces the mortality rate. Accurate and earlier diagnosis of the pancreatic tumor is a demanding task due to several factors such as delayed diagnosis and absence of early warning symptoms. The conventional distributed machine learning techniques such as SVM and logistic regression were not efficient to minimize the error rate and improve the classification of pancreatic cancer with higher accuracy. Therefore, a novel technique called Distributed Hybrid Elitism gene Quadratic discriminant Reinforced Learning Classifier System (DHEGQDRLCS) is developed in this paper. First, the number of data samples is collected from the repository dataset. This repository contains all the necessary files for the identification of prognostic biomarkers for pancreatic cancer. After the data collection, the separation of training and testing samples is performed for the accurate classification of pancreatic cancer samples. Then the training samples are considered and applied to Distributed Hybrid Elitism gene Quadratic discriminant Reinforced Learning Classifier System. The proposed hybrid classifier system uses the Kernel Quadratic Discriminant Function to analyze the training samples. After that, the Elitism gradient gene optimization is applied for classifying the samples into multiple classes such as non-cancerous pancreas, benign hepatobiliary disease i.e., pancreatic cancer, and Pancreatic ductal adenocarcinoma. Then the Reinforced Learning technique is applied to minimize the loss function based on target classification results and predicted classification results. Finally, the hybridized approach improves pancreatic cancer diagnosing accuracy. Experimental evaluation is carried out with pancreatic cancer dataset with Hadoop distributed system and different quantitative metrics such as Accuracy, balanced accuracy, F1-score, precision, recall, specificity, TN, TP, FN, FP, ROC_AUC, PRC_AUC, and PRC_APS. The performance analysis results indicate that the DHEGQDRLCS provides better diagnosing accuracy when compared to existing methods.

Refining micro-seismic catalogs around Seydişehir, Turkey

In Turkey, two official seismology centers, Bogazici University Kandilli Observatory and Earthquake Research Institute Regional Earthquake-Tsunami Monitoring Center (KOERI-RETMC) and Republic of Turkey Prime Ministry Disaster Emergency Management Authority (AFAD) announce and share seismic catalogs with the public and international services. According to their seismic network distribution, together with different crustal models and calculation algorithms, obtaining earthquake parameters (location, depth, etc.) could differ between these two centers, especially, affecting source types of the low-magnitude events. Both low-magnitude tectonic events and artificial quakes that originating from open-pit quarry are catalogued by the seismology centers. These two centers announce different source types for the seismic events; therefore, this study focuses on the reliable identification of the micro-seismic events. Magnitude Ml<2.4 177 seismic events commonly identified in KOERI-RETMC and AFAD catalogs are used. Due to the differences between KOERI-RETMC and AFAD seismic catalogs, the “first determination” (FD) was needed to start the discrimination analyses. Then, waveforms of the station SEYD and SEDI are operated by KOERI-RETMC and AFAD were analyzed with four methods (Amplitude Ratio, Complexity, Short Time Fourier Transform and Corner Frequency-Power Spectrum) and two statistical approaches (linear and quadratic discriminant functions) with the use and comparison with FD. Finally, station-based weightings are obtained with all techniques, and the source types of all events are calculated in percent. Generally, the success rates of the methods are calculated over 90%. The reliability increases with the co-usage of many analyses and the application of method-based weighting. Hence, many methods should be used to reliably determine the source types of micro-seismic events. Both centers should make more detailed analyses to identify micro-seismic events and share their reliable and revised catalogs.

NetDA: An R Package for Network-Based Discriminant Analysis Subject to Multilabel Classes

In this paper, we introduce the R package NetDA, which aims to deal with multiclassification with network structures in predictors accommodated. To address the natural feature of network structures, we apply Gaussian graphical models to characterize dependence structures of the predictors and directly estimate the precision matrix. After that, the estimated precision matrix is employed to linear discriminant functions and quadratic discriminant functions. The R package NetDA is now available on CRAN, and the demonstration of functions is summarized as a vignette in the online documentation.

Moments of the likelihood-based discriminant function

The likelihood approach used in this paper leads to quadratic discriminant functions. Classification into one of two known multivariate normal populations with a known and unknown covariance matrix are separately considered, where the two cases depend on the sample size and an unknown squared Mahalanobis distance. Their exact distributions are complicated to obtain. Therefore, moments for the likelihood based discriminant functions are established to express the basic characteristics of respective distribution.

Classification of Stateless People through a Robust Nonparametric Kernel Discriminant Function

Statelessness is the absence of any Nationality. These include the Pemba, Shona, Galjeel, people of Burundi and Rwanda descent, and children born in Kenya to British Overseas Citizens after 1983. Frequently, they are not only undocumented but also often overlooked and not included in National Administrative Registers. Accordingly, find it hard to participate in Social and Economic Affairs. There has been a major push by UNHCR and international partners to “map” the size of stateless populations and their demographic profile, as well as causes, potential solutions and human rights situation. One of the requirements by the UNHCR in their push is for countries to find a potential solution to statelessness which starts with classifying/associating a person from these communities to a particular local community that is recognized in Kenya. This paper addresses this problem by adopting a Robust Nonparametric Kernel Discriminant function to correctly classify the stateless communities in Kenya and compare the performance of this method with the existing techniques through their classification rates. This is because Non-parametric functions have proven to be more robust and useful especially when there exists auxiliary information which can be used to increase precision. The findings from this paper indicate that Nonparametric discriminant classifiers provide a good classification method for classifying the stateless communities in Kenya. This is because they exhibit lower classification rates compared to the parametric methods such as Linear and Quadratic discriminant functions. In addition, the finding shows that based on certain similarities in characteristics that exist in these communities that surround the Pemba Community, the Pemba community can be classified as Giriama or Rabai in which they seem to have a strong link. In this regard, the study recommends the use of the Kernel discriminant classifiers in classifying the stateless persons and that the Government of Kenya consider integrating/recognizing the Pemba community into Giriama or Rabai so that they can be issued with the National Identification Cards and be recognized as Kenyans.

Otolith trace elemental analyses and parasites provide useful tools for the stock discrimination of Patagonotothen ramsayi (Regan, 1913) (Nototheniidae) on the southern Patagonian Shelf

The notothenid Patagonotothen ramsayi is one of the most abundant fin fish species on the Patagonian Shelf and it is an important prey species and central to the trophic ecology of the shelf ecosystem of the region. 353 otoliths and the parasites analysed from 80 fishes collected in January 2010, and 2004 and 2006, respectively, from the Falkland Islands Shelf and in an area north of the Falkland Islands on the high seas, were used to gain insights into the stock discrimination using elemental signatures and parasitology. Multivariate analyses (Quadratic Discriminant Function Analysis (QDFA)) of trace elements in the edges of the otolith was extremely well resolved indicating samples taken from the southern (SS), northern Falkland Islands shelf (NS) and the high seas (HS) to the north are clearly separated. Analyses of the otoliths cores were less well resolved, but showed good separation. However, there was overlap with the samples taken on the SS / NS, NS / HS, but no overlap between the samples taken on the SS / HS, indicating some intermixing during larval dispersal. Univariate and multivariate analyses of parasite communities showed a clear separation of samples taken from the SS and HS. In addition, this study has added to the biogeography and knowledge of host specificity of the parasites inhabiting the Patagonian Shelf. Our results demonstrate that the multi-pronged approach of using both otolith trace elemental analyses and parasites can be a powerful tool to resolve stock discrimination in P. ramsayi.

Application of Skew-normal in Classification of Satellite Image

The aim of this paper is to investigate the flexibility of the skewnormal distribution to classify the pixels of a remotely sensed satellite image. In the most of remote sensing packages, for example ENVI and ERDAS, it is assumed that populations are distributed as a multivariate normal. Then linear discriminant function (LDF) or quadratic discriminant function (QDF) is used to classify the pixels, when the covariance matrix of populations are assumed equal or unequal, respectively. However, the data was obtained from the satellite or airplane images suffer from non-normality. In this case, skew-normal discriminant function (SDF) is one of techniques to obtain more accurate image. In this study, we compare the SDF with LDF and QDF using simulation for different scenarios. The results show that ignoring the skewness of the data increases the misclassification probability and consequently we get wrong image. An application is provided to identify the effect of wrong assumptions on the image accuracy.

Analysis of Wrist Pulse Signal: Emotions and Physical Pain

BackgroundPulse diagnosis (wrist pulse signal) is a well-known traditional technique used for a health examination. It has the potential to detect cardiac and non-cardiac diseases. ObjectiveA study was conducted to investigate human emotions using wrist pulse signal assessment. The aim was to categorize anxiety, boredom, physical pain, and reference state by processing and analysis of acquired signals. MethodA protocol was designed to induce emotions. Data were acquired from 24 healthy volunteers. Signals were processed and further analyzed using paired t-test and Analysis of Variance (ANOVA). Machine learning algorithms, Linear Discriminant Function (LDF), Quadratic Discriminant Function (QDF), and Support Vector Machine using kernel Gaussian radial basis function (RBF-SVM) were used to evaluate significant features and classify the emotions. ResultsComputing significant plus ranked features performed better over randomly selected features for pairwise emotion classification. Here, the QDF classifier outperforms LDF. Additionally, ANOVA validated the effectiveness of statistically prominent features to classify emotional states. Ratio_Pulse_Strength, total_power, Spectral Entropy, and meancd5 came out as the four most significant features to classify the emotion “Anxiety”, “Boredom”, “Pain”, and “Reference” with positive prediction rate of 100%, 73%, 100%, and 86% respectively using RBF-SVM in the user-independent model. ConclusionPreviously, WPS has been used mainly to detect physical abnormality in the human body. The results endorse the potential of user-independent human emotion detection using a wrist pulse signal. The present work was focusing on a few emotional states. Results are encouraging and may be well applied to many more states.

Discrimination of Seismic Events (2006–2020) in North Korea UsingP/LgAmplitude Ratios from Regional Stations and a Bivariate Discriminant Function

AbstractTwo events of magnitude (mb) 3.6–3.8 occurred in southern North Korea (NK) on 27 June 2019 and 11 May 2020. Although these events were located ∼330–400 km from the known nuclear test site, the fact that they occurred within the territory of NK, a country with a recent history of underground nuclear tests, made them events of interest for the monitoring community. We used P/Lg ratios from regional stations to categorize seismic events that occurred in NK from 2006 to May 2020, including these two recent events, the six declared NK nuclear tests, and the cavity collapse and triggered earthquakes that followed the 3 September 2017 nuclear explosion. We were able to separate the cavity collapse from the population of nuclear explosions. However, based on P/Lg ratios, the distinction between the earthquakes and the cavity collapse is ambiguous. The performed discriminant analyses suggest that combining Pg/Lg and Pn/Lg ratios results in improved discriminant power compared with any of the ratio types alone. We used the two ratio types jointly in a quadratic discriminant function and successfully classified the six declared nuclear tests and the triggered earthquakes that followed the September 2017 explosion. Our analyses also confirm that the recent southern events of June 2019 and May 2020 are both tectonic earthquakes that occurred naturally.

Computable error bounds for asymptotic approximations of the quadratic discriminant function

This paper is concerned with computable error bounds for asymptotic approximations of the expected probabilities of misclassification (EPMC) of the quadratic discriminant function $Q$. A location and scale mixture expression for $Q$ is given as a special case of a general discriminant function including the linear and quadratic discriminant functions. Using the result, we provide computable error bounds for asymptotic approximations of the EPMC of $Q$ when both the sample size and the dimensionality are large. The bounds are numerically explored. Similar results are given for a quadratic discriminant function $Q_0$ when the covariance matrix is known.

Annotations on the Relationship Among Discriminant Functions

Different forms of discriminant functions and the essence of their appearances were considered in this study. Various forms of classification problems were also considered, and in each of the cases mentioned, classification from simple functions of the observational vector rather than complicated regions in the higher-dimensional space of the original vector were made. Violation of condition of equal variance covariance matrix for Linear Discriminant Function (LDF) results to Quadratic Discriminant Function (QDF). The relationships among the classification statistics examined were established: The Anderson’s (W) and Rao’s (R) statistics are equivalent when the two sample sizes are equal, and when a constant is equal to 1, W, R and John-Kudo’s (Z) classification statistics are asymptotically comparable. A linear relationship is also established between W and Z classification statistics.

Discrimination of the natural and artificial quakes in the Eastern Marmara Region, Turkey

The aim of this study is to determine the source of seismic quakes is whether natural or artificial in the Eastern Marmara Region which is also included two branches of western part of the North Anatolian Fault Zone. It is known as one of the most seismically hazardous region in Turkey and 1999 Izmit and Duzce Earthquakes were occurred inside this area. In addition, it has geothermal springs, lots of mining areas, tunnel, bridge and road construction points. Under these conditions, it is seismologically important to make a study about the discrimination of the natural and artificial events. 611 seismic events with Ml ≤ 2.5 which has occurred between 2017 and 2019, recorded by 11 seismic stations that are being operated by Republic of Turkey Prime Ministry Disaster and Emergency Management Authority Presidential of Earthquake Department were analyzed. Amplitude ratio, complexity and continuous wavelet transform (CWT) methods were performed; linear and quadratic discriminant functions (LDF, QDF) were used for statistical processes to all waveforms and their results. All waveforms were identified by significant manual investigation that P wave first motion polarity, no or low amplitude S wave recording, the vision of coda wave decay and Rg phase detection and it called as a first determination. The results were compared to first determination and the final decisions were gained with the combination of their all. Besides with the all methods, CWT analyze could give more reliable results than the others and amplitude ratio method can serve better results than complexity. Otherwise, LDF could classify the events better than QDF. Through the final decision, 395 earthquake and 182 blast recordings were clearly discriminated with the accuracy of 94.44% and the source types of 34 seismic events could not be identified. The obtained discriminant functions for each station are useful to determine the source types of the events and they could clarify the contaminated earthquake catalogues. Increasing the reliability of the final results would be related with using these methods together.

Sensitivity Analysis of the Quadratic Discriminant Function for Predicting Pregnancy Outcomes

The prevalence rate of stillbirth is ten times higher in developing countries relative to developed countries with a 2016 rate of 18 percent in Ghana. This study employed the Quadratic Discriminant Function for discriminating and classifying of pregnancy outcomes based on some predictors. The study further examined the sensitivity of the Quadratic Discriminant Function in predicting pregnancy outcomes with variations in the training and test samples of deliveries recorded in a hospital in Accra, Ghana. The study considered the scenarios; 50:50, 60:40, 70:30 and 75:25 ratios of training sets to testing sets. Predictor variables on both maternal factors (maternal age, parity and gravida) and fetus variables (weight at birth and gestational period) were all statistically significant (P < .01) in discriminating between live birth and stillbirth. Results showed that maternal age had a negative effect on the live birth outcomes, while parity, gravida, gestational period and fetus weight recorded positive effects on live birth outcomes. The 75:25 ratio outperformed the other ratios in discriminating between live and stillbirth based on the Actual Error Rate of 7.28% compared to 7.81%, 12.14% and 13.79% for the 50:50, 70:30 and 60:40 ratios respectively whereas, the receiver operating characteristic curve shows the 70:30 (AUC= 0.9233) ratio outperformed the others. The study recommend the use of either the 70:30 or 75:25 training to test ratios for classification and discrimination related problems. Moreover, further research to establish the power of the respective training to test sample ratios with other statistical classification tools and more socio-economic variables can be considered.

Nom document digitalization by deep convolution neural networks

Nom is an ancient script used in Vietnam until the current Latin-based Vietnamese alphabet became common, and a large number of ancient Nom documents are in existence. Due to the gradual degradation of Nom documents and a decrease in the number of scholars who can understand them, a system to digitalize Nom documents is urgently necessary. This paper presents a segmentation-based method for digitalizing Nom documents using deep convolution neural networks. Nom pages are preprocessed, segmented into isolated characters, and then recognized by a single-character OCR. The structure of the U-Net is applied to create segmentation maps and extract character regions from them. Subsequently, we propose coarse and fine combined classifiers to recognize each character pattern. The results by the best classifier are revised by a decoder using a langue model. The decoder is the same as the connectionist temporal classification decoder used in end-to-end text recognition systems. Compared with the traditional segmentation method using projection profiles and the Voronoi diagram (IoU = 81.23%), the segmentation method using the deep convolution neural network produces a better result (IoU = 92.08%) for detecting character regions. The proposed CNN models for recognizing segmented character patterns outperforms the traditional models using the modified quadratic discriminant function and the learning vector quantization with the recognition rate of 85.07%. The combination of coarse and fine classifiers, the training dataset with salt and pepper noises, and the attention layer are the key factors in the recognition rate improvement.

Endocrine disrupting chemicals associated with dry eye syndrome

BackgroundDry eye syndrome (DES) is a multifactorial disease that causes changes in the tear film and occurs more frequently in women. Sex hormones (SHs) influence tear production, and SHs imbalance is associated with DES. Endocrine-disrupting chemicals (EDCs) are compounds that can bind to SHs receptors, changing the SHs action in several organs and tissues. MethodsThe levels of 21 EDCs were measured in the urine of DES patients and healthy controls. All individuals were submitted to eye exams for DES and responded to the questionnaire “Ocular Surface Disease Index (OSDI)”. DES was considered present when the OSDI score was >20 and one of the DES tests surpassed the established thresholds. ResultsMethyl-protocatechuic acid (OHMeP), had higher urine levels in DES individuals than in control individuals (p = 0.0189). On the other hand, triclocarban (TCC) exhibited lower urine levels in DES individuals than in control individuals (p = 0.0081). Statistically significant positive associations were found between Methyl Paraben (MeP), EtP (ethyl paraben) and OHMeP with fluorescein staining test; between TCC and Tear breakup time test and between OHMeP and OSDI score. Significant negative associations were found between EtP and OHMeP and schirmer test; between OHMeP and Tear breakup time test; between TCC and the OSDI score and fluorescein and lissamine staining test.The quadratic discriminant function classified 94.4% of individuals in their groups based on the urine levels of EDCs. ConclusionThe following EDCs, MeP, EtP, and OHMeP, were associated with signs and symptoms of DES. TCC had a paradoxical protective effect against DES. These findings suggest that EDCs are associated with DES and the exposure should be included in the investigation of causes and risk factors for DES.

Classification of all-rounders in limited over cricket - a machine learning approach

In cricket, all-rounders play an important role. A good all-rounder should be able to contribute to the team by both bat and ball as needed. However, these players still have their dominant role by which we categorize them as batting all-rounders or bowling all-rounders. Current practice is to do so by mostly subjective methods. In this study, the authors have explored different machine learning techniques to classify all-rounders into bowling all-rounders or batting all-rounders based on their observed performance statistics. In particular, logistic regression, linear discriminant function, quadratic discriminant function, naïve Bayes, support vector machine, and random forest classification methods were explored. Evaluation of the performance of the classification methods was done using the metrics accuracy and area under the ROC curve. While all the six methods performed well, logistic regression, linear discriminant function, quadratic discriminant function, and support vector machine showed outstanding performance suggesting that these methods can be used to develop an automated classification rule to classify all-rounders in cricket. Given the rising popularity of cricket, and the increasing revenue generated by the sport, the use of such a prediction tool could be of tremendous benefit to decision-makers in cricket.