Fisher Linear Discriminant Analysis Research Articles

Improved empirical mode decomposition bagging RCSP combined with Fisher discriminant method for EEG feature extraction and classification

BackgroundTraditional Common Spatial Pattern (CSP) algorithms for Electroencephalogram (EEG) signal classification are sensitive to noise and can produce low accuracy in small sample datasets. New methodTo solve the problem, an improved Empirical Mode Decomposition (EMD) Bagging Regularized CSP (RCSP) algorithm is proposed. It filters EEG signals through improved EMD, inhibits high-frequency noise, retains effective information in the characteristic frequency band, and uses Bagging algorithm for data reconstruction. Feature extraction is performed with regularization of spatial patterns and Fisher linear discriminant analysis for feature classification. T-test is used for classification. ResultsThe improved EMD Bagging RCSP algorithm has improved accuracy and robustness compared to CSP and its derivatives. The average classification rate is increased by about 6%, demonstrating the effectiveness and correctness of the proposed algorithm.Comparison with existing methods: The proposed algorithm outperforms CSP and its derivatives by retaining effective information and inhibiting high-frequency noise in small sample EEG datasets. ConclusionsThe proposed EMD Bagging RCSP algorithm provides a reliable and effective method for EEG signal classification and can be used in various applications, including brain-computer interfaces and clinical EEG diagnosis.

Estimation of sex from femoral bone using radiological imaging methods in Turkish population.

Sex estimation is leading to determine the biological profile in forensic medicine. The aim of this study is to research the effectiveness of logistic regression (LogR) and discriminant function analysis (DFA) to create sex estimation models on femur images obtained with Computed Tomography (CT) angiography and to address the differences of femur, which show sexual dimorphism, among populations. All parameters were measured on three planes by adjusting the 300 CT angiography images from 150 women and 150 men that focused on the left femur to the orthogonal plane with standard magnification. The subgroup, which included 30 images randomly generated from these images, was measured twice with an interval of 3 weeks by the first radiologist and once by the second radiologist. According to the Fisher's Linear Discriminant analysis, which was evaluated with ten parameters in the study, it was concluded that the power of discriminating women was 96.7%, the power of discriminating men was 98.7%, and the total discrimination power was 97.7%; these results were 98%, 99.3%, and 98.7%, respectively according to LogR. In this study, DFA and LogR analysis showed that femur provided a very good rate of sexual dimorphism. A database belonging to the Turkish population was created for the femur, allowing for comparison between populations.

Fusion of Coherent and Non-Coherent Pol-SAR Features for Land Cover Classification

Remote Sensing plays a fundamental role in acquiring crucial information about the Earth’s surface from a distance, especially through fully polarimetric data, which offers a rich source of information for diverse applications. However, extracting meaningful insights from this intricate data necessitates sophisticated techniques. In addressing this challenge, one predominant trend that has emerged is known as target decomposition techniques. These techniques can be broadly classified into coherent and non-coherent methods. Each of these methods provides high-quality information using different procedures. In this context, this paper introduces innovative feature fusion techniques, amalgamating coherent and non-coherent information. While coherent techniques excel in detailed exploration and specific feature extraction, non-coherent methods offer a broader perspective. Our feature fusion techniques aim to harness the strengths of both approaches, providing a comprehensive and high-quality fusion of information. In the first approach, features derived from Pauli coherent decomposition, Freeman–Durden non-coherent technique, and the Symmetry criterion from Cameron’s stepwise algorithm are combined to construct a sophisticated feature vector. This fusion is achieved using the well-established Fisher Linear Discriminant Analysis algorithm. In the second approach, the Symmetry criterion serves as the basis for fusing coherent and non-coherent coefficients, resulting in the creation of a new feature vector. Both approaches aim to exploit information simultaneously extracted from coherent and non-coherent methods in feature extraction from Remote Sensing data through fusion at the feature level. To evaluate the effectiveness of the feature generated by the proposed fusion techniques, we employ a land cover classification procedure. This involves utilizing a basic classifier, achieving overall accuracies of approximately 82% and 86% for each of the two proposed techniques. Furthermore, the accuracy in individual classes surpasses 92%. The evaluation aims to gauge the effectiveness of the fusion methods in enhancing feature extraction from fully polarimetric data and opens avenues for further exploration in the integration of coherent and non-coherent features for remote sensing applications.

A hybrid variable selection method combining Fisher's linear discriminant combined population analysis and an improved binary cuckoo search algorithm.

In this paper, a novel hybrid variable selection method for model building by near-infrared (NIR) spectroscopy is proposed for composition measurement in industrial processes. A double-layer structure is designed for variable selection by combining Fisher's linear discriminant combined population analysis (FCPA) and an improved binary cuckoo search algorithm (IBCS). The Fisher classifier combined with model population analysis is used to select the variable interval wherein the useful variables are roughly located even when strong multicollinearity exists among spectral variables. Opposition-based learning (OBL) and jumping genes (JG) are introduced to improve the binary cuckoo search algorithm for the fine selection of key variables, thus avoiding the loss of excellent solutions due to randomness and the local optimum. Different variable selection methods were used to select variables for beer, corn, and diesel fuel datasets, and the partial least squares (PLS) algorithms were used to build calibration models to predict the original extract concentration of beer, the protein and starch content of corn, and the boiling point of diesel fuel, respectively. The results showed that the proposed PLS modeling method based on FCPA-IBCS has higher fitting accuracy and smaller prediction errors.

A research on subclassification of ancient glass based on FLDA and systematic cluster analysis

For the purpose of subclassification of ancient glass, this study first used FLDA (Fisher Linear Discriminant Analysis) to classify the glass, in this study, unknown glasses of known composition were reasonably classified by model analysis with a high accuracy of 92.5%, and the classification pattern of the two types of glass was analysed statistically in conjunction with the data, and the results showed that the high potassium type contained high levels of K and Na chemical components; the lead-barium type, on the other hand, contains a high content of Pb and Ba chemical components. Next, a systematic clustering model was used for cluster analysis, avoiding the disadvantages of the K-means clustering model which is sensitive to outliers, and further analysed by a combination of clustering dendrograms and the law of the elbow in the line graph of aggregation coefficient. The analysis was further Integrated analysed by the law of the Elbow in the clustering dendrograms and the line graphs of aggregation factors. The final subclasses were concluded as follows: high potassium glasses can be divided into two subclasses, K2O-CaO (~10wt%)-SiO2 and K2O-SiO2; lead-barium glasses can be divided into three subclasses, PbO-BaO-SiO2, PbO (~25wt%)-BaO-SiO2 and CaO-PbO (~40wt%)-BaO-SiO2. The study of the subclassification of ancient glass is very helpful and influential for industrial applications. Through the construction of the classification and clustering model in this study, the subclassification division of ancient glass is well carried out, which has an important theoretical basis to support the work of identification and detection, and is of great significance for the study of the origin of ancient glass.

Polymorphism of the coding gene LGALS-3 rs2274273 as an endogenous factor of the predictive effectiveness of the plasma concentration of galectin-3 in relation to the risk of development of chf on the background of eh in women

Objective. The purpose of the study is to improve the early diagnosis of the development of left ventricular myocardial hypertrophy (LVH) and the formation of prerequisites for chronic heart failure (CHF) in women with essential hypertension, residents of the Podillya region of Ukraine by determining the plasma concentration of galectin-3 in carriers of different polymorphic variants of the LGALS-3 (rs2274273) gene. Material and methods. 180 women of postmenopausal age, average age of 57.34±0.45, residents of the Podillya region of Ukraine, who lived in this territory in the third generation, were examined. The control group consisted of 67 women, average age of 56.43±0.64 years, without signs of cardiovascular pathology and signs of left ventricular hypertrophy (LVH) for other reasons were detected. The main group included 113 women with essential hypertension, of which 62 had essential hypertension with LVH without heart failure (EH II), 51 had essential hypertension with chronic heart failure stage C according to the ESH/ESC 2023 classification. General clinical examination, enzyme immunoassay method for determining the level of galectin-3 in blood plasma, genotyping of the LGALS3 (rs2274273) gene using polymerase chain reaction, and ultrasound of the heart were performed. The statistical processing of the obtained results was carried out using the package of statistical programs SPSS, STATISTICA v. 10.0. Mathematical methods were used: multiple regression stepwise analysis of proportional risks with 95% CI confidence interval, Fisher's linear discriminant analysis with the creation of a mathematical prognostic model, and cluster analysis. Compliance of the frequency distribution of genotypes in the studied populations to the Hardy-Weinberg equilibrium was checked using the MedCalc Software Ltd. Odds ratio calculator. https://www.medcalc.org/calc/odds_ratio.php and calculated the odds ratio (OR) of developing left ventricular myocardial hypertrophy (LVH) and chronic heart failure (CHF).Results. In patients with EH and CHF, carrying the A allele of the LGALS-3 (rs2274273) gene was associated with a more severe degree of diastolic dysfunction and reduced LVEF compared with carriers of the GG genotype, and higher plasma levels of galectin-3 were also recorded, which were associated with a more significant deterioration structural and functional indicators of the myocardium. With the help of cluster analysis, it was found that carriers of the A allele of the LGALS-3 (rs2274273) gene are more likely to be included in unfavorable cluster 1. In contrast, in cluster 2, with a more favorable course of the disease, carriers of the GG genotype and carriers of the A allele occur with almost the same frequency. Conclusions. In postmenopausal women, residents of the Podillya region of Ukraine, carrying the A allele of the LGALS-3 (rs2274273) gene is associated with a more severe course of EH with the development of LVH, a higher concentration of galectin-3 in the blood plasma, and the formation of CHF with reduced LVEF when compared with carriers of the genotype GG.

Constraint principal components for linear discrimination

In many modern data, the number of variables is much higher than the number of observations and the within-group scatter matrix is singular. Then, the Fisher's linear discriminant analysis (LDA) cannot be applied. The work considers a way to circumvent this problem by doing principal component analysis (PCA) enhanced with additional discriminating features. Two approaches are proposed: the original PCs are rotated to maximize the Fisher's LDA criterion, and second, penalized PCs are produced to achieve simultaneous dimension reduction and maximization of the Fisher's LDA criterion. Both approaches are illustrated and compared to other existing methods on several well known data sets.

Linear discriminant analysis on electrocardiogram achieved classification of cardiac involvement status in amyloid light-chain amyloidosis

ObjectivesCardiac amyloidosis (CA) is the most crucial determinant of amyloid light-chain (AL) amyloidosis patients' prognosis. We attempted cardiac involvement prediction by 12‑lead electrocardiograph (ECG) and echocardiography (UCG) in AL amyloidosis patients. Materials and methodsFifty patients with histologically confirmed AL amyloidosis underwent gadolinium-enhanced magnetic resonance imaging (Gd-MRI), and CA was assessed using late gadolinium enhancement. ECG and UCG parameters were measured on admission. Fisher's linear discriminant analysis was used to create a model for predicting CA using the ECG and UCG parameters. ResultsPrediction by five ECG parameters [QTc(B), QRS-T-angle, III-QRS, aVF-QRS, and V3-R] showed the best performance. Average sensitivity and specificity in the modeling sets, utilizing a linear discriminator based on these five variables, were 99.2 % and 96.8 % and in validation sets, 94.2 % and 90.3 %, respectively. In addition, we tested this model on an additional 26-patient cohort and survival analysis using the Kaplan-Meier method, and significant differences between CA positively predicted and negatively predicted patients were observed. ConclusionHere, we suggest the application of a condensed classical multivariate statistical technique for the diagnosis of CA. It can be used as a guide to invasive endomyocardial biopsy for those in whom Gd-MRI is contraindicated and as a guide for repeat Gd-MRI in follow-up of AL amyloidosis.

Quality evaluation of compounds in leaves of six Taxus species based on UPLC-MS/MS and chemometrics.

Introduction: Taxus species are used as medicinal plants all over the world. The leaves of Taxus species are sustainable medicinal resources that are rich in taxoids and flavonoids. However, traditional identification methods cannot effectively identify Taxus species on the basis of leaces used as raw medicinal materials, because their appearance and morphological characteristics are almost the same, and the probability of error identification increases in accordance with the subjective consciousness of the experimenter. Moreover, although the leaves of different Taxus species have been widely used, their chemical components are similar and lack systematic comparative research. Such a situation is challenging for quality assessment. Materials and methods: In this study, ultra-high-performance liquid chromatography coupled with triple quadrupole mass spectrometry combined with chemometrics was applied for the simultaneous determination of eight taxoids, four flavanols, five flavonols, two dihydroflavones, and five biflavones in the leaves of six Taxus species, namely, T. mairei, T. chinensis, T. yunnanensis, T. wallichiana, T. cuspidata, and T. media. Chemometric methods, including hierarchical cluster analysis, principal component analysis, orthogonal partial least squares-discriminate analysis, random forest iterative modeling, and fisher linear discriminant analysis, were utilized to differentiate and evaluate the six Taxus species. Results: This proposed method exhibited good linearity (R 2 = 0.9999-0.9972) with a lower quantification limits of 0.94-3.05ng/mL for all analytes. The intra- and inter-day precisions were within 6.83%. Six compounds, namely, 7-xylosyl-10-deacetyltaxol, ginkgetin, rutin, aromadendrin, 10-deacetyl baccatin III, and epigallocatechin, were identified through chemometrics for the first time. These compounds can be used as important chemical markers to distinguish the above six Taxus species rapidly. Conclusion: This study established a method for determination of the leaves of six Taxus species, and revealing the differences in the chemical components of these six Taxus species.

Fisher Linear Discriminant and Systematic Cluster Analysis based on analysis and identification of the composition of ancient glass products

The Silk Road was a channel of cultural exchange between China and the West in ancient times, of which glass was a valuable physical evidence of early trade exchanges. Therefore, it is important to analyze the ancient glass products for the research related to ancient times. In this paper, in order to get the classification law of high potassium and lead-barium glass, firstly, the discriminant relationship function was obtained by using Fisher Linear Discriminant Analysis. Secondly, the data were downscaled by Principal Component Analysis to get five principal components, and then Fisher Linear Discriminant Analysis was used to get the discriminant function, and the results all passed the cross-check, and the model accuracy was 95.29% and 91.43%, respectively. The subclasses were classified by Systematic Clustering Model and Elbow Method, and it was concluded that the high potassium glass was mainly divided into two subclasses based on whether the silica content was greater than 80%; the lead-barium glass was mainly divided into four subclasses based on the content of three different chemical components: silica, barium oxide and phosphorus pentoxide. And through the reasonableness and sensitivity analysis, this paper got that different chemical compositions have different size influence on the classification of glass.

A branch and bound method solving the max–min linear discriminant analysis problem

Fisher linear discriminant analysis (FLDA or LDA) is a well-known technique for dimension reduction and classification. The method was first formulated in 1936 by Fisher in the one-dimensional setting. In this paper, we will examine the LDA problem using a different objective function. Instead of maximizing the sum of all distances between all classes, we will define an objective function that will maximize the minimum separation among all distances between all classes. This leads to a difficult nonconvex optimization problem. We present a branch and bound method for the problem in the case where the reduction is to the one-dimensional space.

Analysis and identification of glass products based on fisher linear discriminant analysis and logistic regression for dichotomous classification

This paper focuses on establishing multiple linear regression models, correlation analysis, fisher linear discriminant analysis, logistic regression to deal with dichotomous classification, sensitivity analysis, systematic clustering and gray correlation analysis to solve the problem of compositional analysis and identification of ancient glass products. The subclasses of each category of glass are divided, and the division results are derived, so that the rationality and sensitivity of the classification results can be analyzed, and finally the classification laws of high potassium glass and lead-barium glass are derived. Analysis The chemical composition of unknown glass artifacts, predict their glass types, and perform sensitivity analysis on the predicted results.

Fisher's linear discriminant analysis model for inscribing the effect of chemical composition on cultural heritage

In this study, the relationship between weathering and glass type, decoration and colour was first analysed using Goodman and Kruskal's tau-y coefficients, and a chi-squared test was performed, which showed that weathering was most influenced by glass type, and was influenced by glass decoration but very little by glass colour. A Fisher linear discriminant analysis model was then established, and the eight chemical components with the greatest correlation to artefact type were calculated using SPSS software under the conditions of the two glass types respectively, and optimised using a grey correlation algorithm with specified thresholds for screening components, resulting in four final elements affecting high potassium glass as potassium oxide, magnesium oxide, iron oxide and copper oxide, and affecting lead and barium types as calcium oxide, aluminium oxide, lead oxide and barium oxide, aluminium oxide, lead oxide, barium oxide and strontium oxide.

Research on Glass Classification and Recognition Based on Fisher's Linear Discriminant and Hierarchical Clustering

Buried in the ground, the glass cultural relics weathered, and a large number of internal elements were exchanged. In order to classify the types of glass, this paper first uses Fisher linear discriminant analysis to obtain a binary classification model of glass types, and finds that the prediction accuracy of the model has reached 90%. Considering the possible overfitting of the model, this paper also uses the principal component analysis method to reduce the dimension of the data, thus obtaining the model and determining that its accuracy rate is maintained above 90%. In order to identify the types of unknown glass cultural relics, the multi-category Fisher’s Linear Discriminant method based on principal component analysis was used to identify the subcategories they belonged to.

오류 라벨을 포함한 분류모형의 강건성 모의실험연구

In order to increase the accuracy and performance of classification models, the quality of data must be guaranteed. There are various factors that affect the quality of these data, such as measurement accuracy, missing value, and sampling biases. This study focuses on the robustness of the classification model for mislabeled data. The reason we are interested in mislabeled data is that it significantly degrades the performance of the model more than other common measurement errors. In this study, the efficiency of various classification methods for data with mislabels is reviewed. Fisher's linear discriminant analysis model (LDA), quadratic discriminant analysis model (QDA), and logistic regression model were considered in the statistical model-based method, and SVM (support vector machine) and boosting are compared in the algorithm-based method. As a result of simulation study, it is found that the statistical model based approaches show better results in terms of robustness in the data assuming various situations of mislabels.

Identification of the Authenticity and Geographical Origin of Bear Bile Powder by Using High Performance Liquid Chromatography - Charged Aerosol Detector Fingerprints Combined with Chemometrics.

Bear bile powder (BBP) is a rare animal-derived traditional Chinese medicine, and it has been widely used to treat visual disorders and hepatobiliary diseases in East Asia. However, there is still a lack of reliable quality control methods for BBP. This study was designed to establish a comprehensive quality map of BBP based on bile acids. High-performance liquid chromatography coupled with charged aerosol detector (HPLC-CAD) was used for fingerprint establishment and quantitative analysis of BBP. The similarities of HPLC-CAD chromatograms for 50 batches of BBP were more than 0.95, while the similarities of reference chromatograms between 6 other animal bile and BBP were low than 0.7. Additionally, five bile acids in BBP, including tauroursodeoxycholic acid, taurocholic acid, taurochenodeoxycholic acid, ursodesoxycholic acid, and chenodeoxycholic acid, were simultaneously quantified. This method has been validated with good regression as well as satisfactory precision, sensitivity, stability, repeatability, and accuracy. Using this method, the contents of five bile acids in BBP samples from five producing areas were determined and compared. Furthermore, Fisher linear discriminant analysis was performed to discriminate the geographic origins of BBP. The result demonstrated that HPLC-CAD fingerprint combined with multi-components quantification is an effective and reliable method for quality control of BBP, it could be a meaningful reference for the quality evaluation of medicinal bile.

Student’s Health Exercise Recognition Tool for E-Learning Education

Due to the recently increased requirements of e-learning systems, multiple educational institutes such as kindergarten have transformed their learning towards virtual education. Automated student health exercise is a difficult task but an important one due to the physical education needs especially in young learners. The proposed system focuses on the necessary implementation of student health exercise recognition (SHER) using a modified Quaternion-based filter for inertial data refining and data fusion as the pre-processing steps. Further, cleansed data has been segmented using an overlapping windowing approach followed by patterns identification in the form of static and kinematic signal patterns. Furthermore, these patterns have been utilized to extract cues for both patterned signals, which are further optimized using Fisher’s linear discriminant analysis (FLDA) technique. Finally, the physical exercise activities have been categorized using extended Kalman filter (EKF)-based neural networks. This system can be implemented in multiple educational establishments including intelligent training systems, virtual mentors, smart simulations, and interactive learning management methods.

Fisher's Linear Discriminant Analysis With Space-Folding Operations.

Fisher's linear discriminant analysis (LDA) is an easy-to-use supervised dimensionality reduction method. However, LDA may be ineffective against complicated class distributions. It is well-known that deep feedforward neural networks with rectified linear units as activation functions can map many input neighborhoods to similar outputs by a succession of space-folding operations. This short paper shows that the space-folding operation can reveal to LDA classification information in the subspace where LDA cannot find any. A composition of LDA with the space-folding operation can find classification information more than LDA can do. End-to-end fine-tuning can improve that composition further. Experimental results on artificial and open data sets have shown the feasibility of the proposed approach.

Analysis of different glass compositions based on Spearman's correlation coefficient

Glass is a valuable physical evidence of our early trade exchanges, and the analysis and identification of the composition of ancient glass products is of great significance to the study of our ancient history. However, ancient glass is highly susceptible to weathering by the burial environment, and during the weathering process, the internal elements of the glass and the environmental elements inevitably exchange in large quantities, resulting in changes in its composition ratio and color, thus affecting the correct judgment of its category. In this paper, Fisher's linear discriminant analysis is established to predict, analyze and identify the composition of ancient glass using mathematical and statistical methods. The study of this problem is important for the research and identification of ancient historical relics in China.

Bearing Fault Diagnosis Based on Randomized Fisher Discriminant Analysis.

In this paper, a novel randomized Fisher discriminant analysis (RFDA) based bearing fault diagnosis method is proposed. First, several representative time-domain features are extracted from the raw vibration signals. Second, linear Fisher discriminant analysis (FDA) is extended to nonlinear FDA named RFDA by introducing the random feature map to deal with the non-linearity issue. Specifically, the extracted time-domain features data are mapped onto a high-dimensional space using the random feature map function rather than kernel functions. Third, the time-domain features are fed into the built RFDA model to extract the discriminant features for diagnosis. Moreover, a Bayesian inference is employed to identify the class of the collected vibration signals to diagnose the bearing status. The proposed method uses random Fourier features to approximate the kernel matrix in the kernel Fisher discriminant analysis. Through employing randomized Fisher discriminant analysis, the nonlinearity issue is dealt with, and the computational burden is remarkably reduced compared to the kernel Fisher discriminant analysis (KFDA). To illustrate the superior performance of the proposed RFDA-based bearing fault diagnosis method, comparative experiments are conducted on two widely used datasets, the Case Western Reserve University (CWRU) bearing dataset and the Paderborn University (PU) bearing dataset. For the CWRU dataset, the computation time of RFDA is much shorter than KFDA, while the accuracy rate reaches the same level of KFDA. For the PU dataset, the accuracy rate of RFDA is slightly higher than KFDA, and the computation time is only 44.14% of KFDA.