Bayesian Discriminant Analysis Research Articles

Characterization of Unplasticized Polyvinyl Chloride Windows by Confocal Raman Microspectroscopy and Chemometrics

In order to nondestructively and accurately identify unplasticized polyvinyl chloride windows, a classification method based on multi-feature algorithm selection modeling was developed. Confocal Raman microspectroscopy was used to obtain the spectral profiles of 150 samples from five brands. The differences in model recognition accuracy were compared among three preprocessing methods: Savitzky-Golay filtering, Hilbert transform, and wavelet transform. The best preprocessing method was selected, and the competitive adaptive reweighted sampling was used to extract feature wavelengths. Furthermore, a Bayesian classification model was constructed to classify and differentiate each sample. The results showed that confocal Raman microspectroscopy can reflect the differences in physicochemical information among different samples. Preprocessing can improve the model’s recognition accuracy, with wavelet transform (96%) > Hilbert transform (90%) > Savitzky-Golay filtering (76%) > untreated (72%). Wavelet transform can remove noise from spectral data without changing the peak region and its absorbance. Based on wavelet transform processing and competitive adaptive reweighted sampling (CARS) combined with Bayesian discriminant analysis, a 100% accurate classification of 150 samples was successfully achieved.

Classification of cancer cells and gene selection based on microarray data using MOPSO algorithm.

Microarray information is crucial for the identification and categorisation of malignant tissues. The very limited sample size in the microarray has always been a challenge for classification design in cancer research. As a result, by pre-processing gene selection approaches and genes lacking their information, the microarray data are deleted prior to categorisation. In essence, an appropriate gene selection technique can significantly increase the accuracy of illness (cancer) classification. For the classification of high-dimensional microarray data, a novel approach based on the hybrid model of multi-objective particle swarm optimisation (MOPSO) is proposed in this research. First, a binary vector representing each particle's position is presented at random. A gene is represented by each bit. Bit 0 denotes the absence of selection of the characteristic (gene) corresponding to it, while bit 1 denotes the selection of the gene. Therefore, the position of each particle represents a set of genes, and the linear Bayesian discriminant analysis classification algorithm calculates each particle's degree of fitness to assess the quality of the gene set that particle has chosen. The suggested methodology is applied to four different cancer database sets, and the results are contrasted with those of other approaches currently in use. The proposed algorithm has been applied on four sets of cancer database and its results have been compared with other existing methods. The results of the implementation show that the improvement of classification accuracy in the proposed algorithm compared to other methods for four sets of databases is 25.84% on average. So that it has improved by 18.63% in the blood cancer database, 24.25% in the lung cancer database, 27.73% in the breast cancer database, and 32.80% in the prostate cancer database. Therefore, the proposed algorithm is able to identify a small set of genes containing information in a way choose to increase the classification accuracy. Our proposed solution is used for data classification, which also improves classification accuracy. This is possible because the MOPSO model removes redundancy and reduces the number of redundant and redundant genes by considering how genes are correlated with each other.

Northward Shifts of the Sahara Desert in Response to Twenty-First-Century Climate Change

Abstract The spatial extent of the Sahara (the largest nonpolar desert) has significant impacts on the livelihood of people residing in its surrounding areas. Despite the fact that climate change would foreseeably impact the location and size of the desert, its future responses (i.e., advance or retreat) are rarely explored in previous studies. Here, through the development of an ensemble Bayesian discriminant analysis approach, we use 10 of the latest high-resolution GCM (global climate model) simulations to document robust annual and seasonal responses of the Sahara Desert to twenty-first-century climate change, with the consideration of modeling uncertainties. We find northward shifts of the Sahara/Sahel and eastern expansion of the nondesert zone under both SSP2–4.5 and SSP5–8.5 scenarios, the former more pronounced in the wet season and the latter in the dry season. Countries located near the Mediterranean may thus experience higher risks of drought, while the projected retreat of the Saharan southern boundary will be beneficial to the local water availability of proximal countries. Significance Statement Given that sub-Saharan Africa is one of the most vulnerable regions to climate change, the Sahara’s expansion would bring unexpected health risks to billions of people. It is thus vital to understand its robust response to global warming. However, previous studies are merely focused on using a simple precipitation threshold as the definition criterion to estimate the varying size of the Sahara Desert. In addition, significant uncertainty in precipitation projections also limits relevant investigations of the Sahara’s future responses. Here, by developing an ensemble Bayesian discriminant analysis approach, we could provide an objective basis for desert identification under large intermodel uncertainty. Further, we find significant northward shifts of both the Sahara and the Sahel, which may induce higher risks of drought over the northwest of North Africa.

Comparison and optimization of rapid and nondestructive qualitative analysis models based on fourier transform infrared spectroscopy information of drugs

It is a key issue in the field of drug prevention and control to realize the rapid and nondestructive qualitative analysis of drugs. In this study, spectral data of 196 pieces of drug samples based on actual cases which are three types in total, were sorted out. The Bayesian discriminant analysis (BDA) models were constructed based on full spectral, fingerprint spectral and functional group spectral data sets were extracted by principal component analysis (PCA). The classification results for different types of data sets were compared, and the optimal spectral region were selected. In the BDA, the model based on the data of the fingerprint spectra the highest classification accuracy, and the classification accuracy of the sample training set based on three types of drugs was 0.837. The identification models based on data sets of fingerprint spectra were established by multilayer perceptron (MLP) and support vector machines (SVM), as well as compare the model parameters of SVM models based on different kernel functions. According to the results, it shows that in the three types of drugs recognition and classification process, the SVM model based on linear kernel functions has achieved the best classification effect, with the overall classification accuracy of the sample training set reaches 0.849, and the model can fully classify drugs of the same type. The classification results were ideal for the SVM model based on linear kernel functions for fingerprint spectral data set. The results of this study demonstrate the potential of Fourier transform infrared spectroscopy in combination with the chemometrics methods of SVM as a new method for the identification of different types and different kinds of drugs of the same type.

Neglected Spatiotemporal Variations of Model Biases in Ensemble‐Based Climate Projections

AbstractThe Bayesian model averaging (BMA) method has been widely used for generating probabilistic climate projections. However, the averaging weights used in BMA can only reflect the spatially‐ and temporally‐averaged performance of each ensemble member, without the ability to address the spatiotemporal variations of model biases. This can lead to inevitable exaggeration or understatement of the contributions of individual members to the ensemble mean, thus reducing the robustness of the resulting probabilistic projections. Here we propose a new method to help address the neglected spatiotemporal variations of model biases. Through the proposed method, the BMA weights are used as prior distributions to drive the Bayesian discriminant analysis in order to generate refined weights for individual ensemble models according to their spatially‐ and temporally‐clustered performance. Through applying the proposed method to Canada, we demonstrate its effectiveness in generating robust probabilistic climate projections (e.g., the average R2 increases from 0.82 to 0.89).

Application of Machine Learning in Developing Decision-Making Support Models for Decompressed Vertebroplasty.

Background: The common treatment methods for vertebral compression fractures with osteoporosis are vertebroplasty and kyphoplasty, and the result of the operation may be related to the value of various measurement data during the operation. Material and Method: This study mainly uses machine learning algorithms, including Bayesian networks, neural networks, and discriminant analysis, to predict the effects of different decompression vertebroplasty methods on preoperative symptoms and changes in vital signs and oxygen saturation in intraoperative measurement data. Result: The neural network shows better analysis results, and the area under the curve is >0.7. In general, important determinants of surgery include numbness and immobility of the lower limbs before surgery. Conclusion: In the future, this association model can be used to assist in decision making regarding surgical methods. The results show that different surgical methods are related to abnormal vital signs and may affect the length of hospital stay.

Penalizing ordered and multinomial likelihood functions with prior information for discrete choice modeling of consumer demand

This research note extends Bayesian discriminant analysis procedures to the ordered and multinomial logistic likelihood functions. Use of the procedure is warranted when the researcher desires to identify the membership of individuals randomly drawn from distinct groups or locations in a population, rather than from a random sample of undifferentiated individuals from a population. An empirical application analyzes consumers’ reasons why they choose to support a beef product produced with enhanced pasture management practices.

Comparison of Whiskbroom and Pushbroom darkfield elastic light scattering spectroscopic imaging for head and neck cancer identification in a mouse model

The early detection of head and neck cancer is a prolonged challenging task. It requires a precise and accurate identification of tissue alterations as well as a distinct discrimination of cancerous from healthy tissue areas. A novel approach for this purpose uses microspectroscopic techniques with special focus on hyperspectral imaging (HSI) methods. Our proof-of-principle study presents the implementation and application of darkfield elastic light scattering spectroscopy (DF ELSS) as a non-destructive, high-resolution, and fast imaging modality to distinguish lingual healthy from altered tissue regions in a mouse model. The main aspect of our study deals with the comparison of two varying HSI detection principles, which are a point-by-point and line scanning imaging, and whether one might be more appropriate in differentiating several tissue types. Statistical models are formed by deploying a principal component analysis (PCA) with the Bayesian discriminant analysis (DA) on the elastic light scattering (ELS) spectra. Overall accuracy, sensitivity, and precision values of 98% are achieved for both models whereas the overall specificity results in 99%. An additional classification of model-unknown ELS spectra is performed. The predictions are verified with histopathological evaluations of identical HE-stained tissue areas to prove the model’s capability of tissue distinction. In the context of our proof-of-principle study, we assess the Pushbroom PCA-DA model to be more suitable for tissue type differentiations and thus tissue classification. In addition to the HE-examination in head and neck cancer diagnosis, the usage of HSI-based statistical models might be conceivable in a daily clinical routine.Graphical abstract

Bayesian discriminant function analysis based forecasting of crop yield in Kanpur district of Uttar Pradesh


 Discriminant function analysis technique using Bayesian approach has been attempted for wheat forecasting in Kanpur district of Uttar Pradesh, India both qualitatively and quantitatively. Crop yield data and weekly weather data on temperature (maximum and minimum), relative humidity (maximum and minimum), rainfall for 16 weeks of the crop cultivation have been used in the study. These data have been utilized for model fitting and validation. Crop years were divided into two and three groups based on the de-trended yield. Crop yield forecast models have been developed using posterior probabilities calculated through Bayesian approach in stepwise discriminant function analysis along with year as regressors for different weeks. Suitable strategy has been used to solve the problem of number of variables more than number of data points. Performance of the models obtained at different weeks was compared using Adjusted R2, PRESS (Predicted error sum of square), number of misclassifications. Forecasts were evaluated using RMSE (Root Mean Square Error) and MAPE (Mean absolute percentage error) of forecast. The result shows that the model based on three groups case perform better. The performance of the proposed Bayesian discriminant function analysis technique approach was better as compared to existing discriminant function analysis score based approach both qualitatively and quantitatively.

Research on eigenvalue selection method of power market credit evaluation based on non parametric Bayesian discriminant analysis and cluster analysis

This paper presents a set of nonparametric methods for selecting credit evaluation indicators under the condition of unknown index distribution, and applies the data of four power companies as samples for application analysis. The results show that through the first round of credit feature screening based on nonparametric Bayes discrimination and the second round of nonparametric clustering, this paper finally constructs a credit feature screening model based on non parametric Bayesian discriminant and clustering analysis, and carries out application analysis. Finally, 18 credit characteristics which can be used in power market credit evaluation are screened out, and the evaluation accuracy has been significantly improved from 73.64% to 77.02%.

Simultaneous Determination of D-amino Acids in Rat Urine by Highperformance Liquid Chromatography-tandem Mass Spectrometry Method: Application to Investigate the Clinical Value of D-amino Acids in the Early Diagnosis of Alzheimer’s Disease

Background: D-amino acids are closely related to the development and progression of Alzheimer's disease (AD) and are expected as the novel biomarkers for AD diagnosis. Objective:The aim was to investigate the potential clinical value of D-amino acids for Alzheimer's disease. Methods:A simple and sensitive HPLC/MS-MS method was developed for the simultaneous determination of D-alanine, D-glutamine, D-proline and D-serine in rat urine. The samples were firstly pretreated by methanol, then derivatized by 7-chloro-4-nitrobenzoxadiazole with Fudosteine as internal standard, enantioseparated on Sumichiral OA-2500S column, using a mobile phase composed of acetonitrile- methanol (50:50, v/v) containing 0.5% formic acid, and detected with 4000 Qtrap MS/MS in electrospray-ionization source by negative ion mode. Results:The established method was successfully applied to determine the D-amino acid levels in rat urine from 20 Alzheimer's disease rats and 20 age-matched normal controls. The mean levels of Damino acids in the urine of Alzheimer's disease rats were all significantly lower than those in normal controls. Based on the contents of D-amino acids, the distinction model between Alzheimer's disease rats and normal controls was established by the Bayesian discriminant analysis. Conclusion: The relationship between Alzheimer's disease and D-amino acids revealed that D-amino acids would be potential biomarkers for Alzheimer’s disease.

Calculation of the Roadside Clear Zone Width along Highways Based on the Safe Slope

International crash data indicate that roadside characteristics contribute to more than half of all roadside accidents involving serious injury or death. Therefore, research on roadside safety is urgently needed. Based on the vehicle departure speed, pavement height (i.e., the difference between pavement elevation and ground elevation), slope gradient, and horizontal curve radius, this study uses PC-Crash simulation software to carry out tests of trucks and cars exiting a road. A chi-squared automatic interaction detection (CHAID) decision tree is used to explore the causative mechanism of vehicle rollover, and the concept of a “safe slope” to ensure that vehicles do not roll over is proposed. Aiming at straight and curved sections, discriminant functions of vehicle rollover and nonrollover are fitted through Bayesian discriminant analysis, and safe slope calculation models for trucks and cars are then constructed. Based on the obtained safe slope models, calculation methods for the safe slope and the roadside clear zone width involving different traffic compositions are proposed by calibrating the lateral distance from the final position of nonrollover vehicles to the road edge. The results show that the factors affecting vehicle rollover are, in descending order of importance, the slope gradient, pavement height, vehicle type, departure speed, and horizontal curve radius. For a section with a large proportion of cars, the slope gradient should not be steeper than 1:3.5. The horizontal curve radius should not be less than 600 m for a section with a large proportion of trucks and a slope gradient steeper than 1:3.5 or shallower than 1:2.5. Additionally, for a section with a pavement higher than 0.5 m and a slope gradient steeper than 1:2.5, the operating speed limit should be lower than 60 km/h. These research results have theoretical value and practical significance to improve the driving safety level and reducing the risk of roadside accidents.

Solvent-controlled synthesis of full-color carbon dots and its application as a fluorescent food-tasting sensor for specific recognition of jujube species

Full-color luminescent carbon dots (CDs) possess enormous feasible applications in fluorescence sensing. However, the modulation of luminescent emission requires proper synthesis strategies with distinctive precursors to regulate the surface chemistry of the CDs. In this work, the full-color CDs were prepared with the same reactants by adjusting the reaction solvent to cover the entire spectral range. The factors that determined their luminescence caused by solvents were discussed. We found that CDs had a rapid sensing ability to Fe3+ with a wide detection range and high accuracy. Moreover, the discriminant model of jujube species depending on internal Fe3+ content was established successfully using principal component analysis and Bayesian discriminant analysis. This study provides a novel perspective for the preparation of full-color CDs by the same reactants and provides strong application potential in the identification of jujube species by a fluorescent sensor.

A Novel Model Using Virtual State Variables and Bayesian Discriminant Analysis to Classify Surrounding Rock Stability

To accurately classify the stability of surrounding rock masses, a novel method (VSV-BDA) based on virtual state variables (VSVs) and Bayesian discriminant analysis (BDA) is proposed. The factors influencing stability are mapped by an artificial neural network (ANN) capable of recognizing the model of rock mass classification, and the obtained output vector is treated as VSVs, which are verified as obeying a multinormal distribution with equal covariance matrixes by normal distribution testing and constructed statistics. The prediction variance ratio test method is introduced to determine the optimal dimension of the VSVs. The VSV-BDA model is constructed through the use of VSVs and the optimal dimension on the basis of the training samples, which are divided from the collected samples into three situations having different numbers. ANN and BDA models are also constructed based on the same training samples. The predictions by the three models for the testing samples are compared; the results show that the proposed VSV-BDA model has high prediction accuracy and can be applied in practical engineering.

Forensic Classification of Pigments by Attenuated Total Reflectance – Fourier Transform Infrared Spectroscopy and Chemometrics

The rapid, nondestructive, and accurate classification of pigments in forensic science is important and indispensable. Here, a method for distinguishing different brands and types of pigments was developed by attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) with chemometrics. A total of 48 pigment samples were collected, and the corresponding infrared spectra were obtained. Baseline correction, multivariate scatter correction, standard normal variable analysis and Savitzky-Golay smoothing were used to preprocess the infrared spectra. Principal component analysis (PCA), factor analysis (FA), Laplacian eigenmaps (LE) and linear discriminant analysis (LDA) were used to extract the characteristic variables of the spectra for the samples. The results were classified by Bayesian discriminant analysis (BDA) and the K-nearest neighbor (KNN) method. The results show that BDA provided a more efficient and accurate model than KNN and the overall classification accuracy was almost 100.0%. Additionally, the classification model was more accurate after extracting the characteristic variables than with the direct use of BDA or KNN. The classification accuracy of gouache and acrylic pigments was 100.0% based on BDA and characteristic variables. The classification accuracy of the BDA and PCA model was 97.2% for two types of gouache pigments and two brands of Picasso gouache pigments. The results indicate that the combination of ATR-FTIR and BDA with a dimensionality reduction method is a potential tool for the classification of different brands and types of pigments.

Bayesian Discriminant Analysis of Yogurt Products Based on Raman Spectroscopy.

The quality discrimination of dairy products is an important basis on which to achieve quality assurance. Taking the discriminant analysis of brand yogurt products as an example, a new rapid discriminant method can be constructed. The first three principal components were selected as the pattern vectors of the samples. Then, at random, 75% of the samples were collected as a training set, and their mean values and covariance matrices were calculated to construct a Gauss Bayesian discriminant model. The remaining 25% of samples were employed as a test set, and the pattern vectors of each sample were input into the above model. Next, the posterior probability of each sample in relation to each category could be obtained. Results: The category corresponding to the maximum posterior probability as the brand classification of each sample was defined. We constructed a Gauss Bayesian discriminant model to discriminate these different yogurt products after the principal component feature extraction of Raman properties. The results indicate the rationality and wide application prospects of this approach. A fast dairy product discriminant method based on Gauss Bayesian model and Raman spectroscopy was established.

A Bayesian discriminant analysis method under semiparametric density ratio models

We propose a semiparametric Bayesian discriminant analysis method. Statistical simulation shows that when the hypothesis of normal distribution is satisfied, our method is comparable to and even slightly better than the traditional method; when the hypothesis of normal distribution is not satisfied, our method is obviously better than the traditional one. We also apply our method to analyze a real data set and find that our method is better than the traditional one. Finally, we point out that implementation of our method is easy since the usual polytomous logistic regression procedures in many statistical softwares can be employed.

Combination of an E-Nose and an E-Tongue for Adulteration Detection of Minced Mutton Mixed with Pork

An E-panel, comprising an electronic nose (E-nose) and an electronic tongue (E-tongue), was used to distinguish the organoleptic characteristics of minced mutton adulterated with different proportions of pork. Meanwhile, the normalization, stepwise linear discriminant analysis (step-LDA), and principle component analysis were employed to merge the data matrix of E-nose and E-tongue. The discrimination results were evaluated and compared by canonical discriminant analysis (CDA) and Bayesian discriminant analysis (BAD). It was shown that the capability of discrimination of the combined system (classification error 0%∼1.67%) was superior or equable to that obtained with the two instruments separately, and E-tongue system (classification error for E-tongue 0∼2.5%) obtained higher accuracy than E-nose (classification error 0.83%∼10.83% for E-nose). For the combined system, the combination of extracted data of 6 PCs of E-nose and 5 PCs of E-tongue was proved to be the most effective method. In order to predict the pork proportion in adulterated mutton, multiple linear regression (MLR), partial least square analysis (PLS), and backpropagation neural network (BPNN) regression models were used, and the results were compared, aiming at building effective predictive models. Good correlations were found between the signals obtained from E-tongue, E-nose, and fusion data of E-nose and E-tongue and proportions of pork in minced mutton with correlation coefficients higher than 0.90 in the calibration and validation data sets. And BPNN was proved to be the most effective method for the prediction of pork proportions with R2 higher than 0.97 both for the calibration and validation data set. These results indicated that integration of E-nose and E-tongue could be a useful tool for the detection of mutton adulteration.

Accurate Bayesian Data Classification Without Hyperparameter Cross-Validation

We extend the standard Bayesian multivariate Gaussian generative data classifier by considering a generalization of the conjugate, normal-Wishart prior distribution and by deriving the hyperparameters analytically via evidence maximization. The behaviour of the optimal hyperparameters is explored in the high-dimensional data regime. The classification accuracy of the resulting generalized model is competitive with state-of-the art Bayesian discriminant analysis methods, but without the usual computational burden of cross-validation.

Study on health management decision support system

To adapt to market informatization, the introduction of health management decision support system can help the management decision of health administration and medical affairs. A database was established according to the requirements of the business layer and data mining technology. Information data which were related to method, model and knowledge in the database were extracted and used for establishing knowledge base, model base and method base; the knowledge base, model base, method base and database were integrated together to form the decision support layer. Finally the decision support layer and presentation layer formed the overall framework of health management decision support system. According to the database characteristics and after comparison of different models, Bayesian discriminant analysis model was determined to be used in the discriminant analysis module, and trend extropolation predictive model was used in the prediction module. The developed system was used to predicting the category of serious diseases, which initially proved the function of health management decision support of the system.