Linear Discriminant Analysis Method Research Articles

Modified wild Horse Herd Optimization based Bhattacharyya error constraint (BEC) based L2-norm Linear discriminant analysis (LDA) method for the sentiment analysis

People's opinions are analyzed via sentiment analysis in all fields. Reviews and tweets, among other formats, are used to express opinions. Irony, sarcasm, and other difficult-to-discern hidden meanings can occasionally be found in viewpoints. Artificial intelligence must be used to examine the sentiments as a result. We suggest a unique Bhattacharyya error constraint (BEC) based L2-norm linear discriminant analysis (LDA) because some of the earlier efforts lack optimization. There are some overfitting and class disparity issues in this. To address this, we used a brand-new method called Modified Wild Horse Herd Optimization (MHHO). The experiment is run to evaluate the performance of the suggested strategy and to compare it to other approaches already in use. We have used performance measures for comparison, and the results demonstrate that the suggested method successfully assesses the sentiment from the acquired dataset.

Towards robust and sparse linear discriminant analysis for image classification

Linear discriminant analysis (LDA) is a popular dimensionality reduction technique that has been widely used in pattern recognition. However, there exist a large number of redundant features and corrupted noise in real-world applications, which makes the performance of existing LDA methods degrade and thus leads to a decrease in classification accuracy. To address the above issues, we propose a novel robust and sparse LDA formulation dubbed RSLDA+. The key idea is introducing the mixed sparse regularization, i.e., ℓ0-norm plus ℓ2,0-norm, for feature representation and enforce ℓ0-norm for noise reduction. Furthermore, an optimization algorithm based on the alternating direction method of multipliers (ADMM) is developed in combination with hard thresholding operators. Extensive experiments on six common image datasets verify that the proposed RSLDA+ outperforms state-of-the-art LDA variants in classification accuracy. In addition, the ablation, robustness, convergence, stability, and sparsity are analyzed in detail. The results suggest that the proposed RSLDA+ provides an effective and robust method for image classification.

Prediction of technological properties of wheat flour by combination of UV-VIS-NIR spectroscopy and multivariate analysis methods

Over the last decades, optical spectroscopy methods that do not require complex sample preparation have been widely used to identify and control the composition of food products. In the present study, the possibility of using UV-VIS-NIR spectroscopy combined with multivariate analysis for grading wheat flour into groups differing in technological properties was analyzed. UV-VIS-NIR spectra contain information on the combination and intensity of absorption bands assigned to functional groups of the composition components and determining the technological properties of wheat flour. The database of UV-VIS-NIR spectra of wheat flour samples differing by technological properties was formed into three groups: the first group — wheat flour samples with good baking properties, the second group — with reduced baking properties, the third group — with low baking properties. The visible range of UV-VIS-NIR diffuse reflectance spectrum was used to calculate the color coordinates in the CIE colorimetric system L*a*b*. The greatest difference among the groups in the color coordinates of the samples was found for the coordinate b*, which is associated with the different content of coloring pigments. The spectra database was used to build a classification model for grading wheat flour into quality groups using a combination of principal component analysis and linear discriminant analysis (PCA-LDA) methods. The achieved results indicate that the classification model built on the training sample is able to distinguish wheat flour spectra by quality groups with an accuracy of 96.49%. The effective- ness of the model is verified using a test set of spectra of wheat flour samples. The present study confirms that the combina- tion of UV-VIS-NIR spectroscopy in conjunction with the PCA-LDA method has significant potential for determining a quality group of wheat flour based on technological properties.

Support vector machine with discriminative low‐rank embedding

AbstractSupport vector machine (SVM) is a binary classifier widely used in machine learning. However, neglecting the latent data structure in previous SVM can limit the performance of SVM and its extensions. To address this issue, the authors propose a novel SVM with discriminative low‐rank embedding (LRSVM) that finds a discriminative latent low‐rank subspace more suitable for SVM classification. The extension models of LRSVM are introduced by imposing different orthogonality constraints to prevent computational inaccuracies. A detailed derivation of the authors’ iterative algorithms are given that is essentially for solving the SVM on the low‐rank subspace. Additionally, some theorems and properties of the proposed models are presented by the authors. It is worth mentioning that the subproblems of the proposed algorithms are equivalent to the standard or the weighted linear discriminant analysis (LDA) problems. This indicates that the projection subspaces obtained by the authors’ algorithms are more suitable for SVM classification compared to those from the LDA method. The convergence analysis for the authors proposed algorithms are also provided. Furthermore, the authors conduct experiments on various machine learning data sets to evaluate the algorithms. The experiment results show that the authors’ algorithms perform significantly better than other algorithms, which indicates their superior abilities on classification tasks.

On the Equivalence of Linear Discriminant Analysis and Least Squares Regression.

Studying the relationship between linear discriminant analysis (LDA) and least squares regression (LSR) is of great theoretical and practical significance. It is well-known that the two-class LDA is equivalent to an LSR problem, and directly casting multiclass LDA as an LSR problem, however, becomes more challenging. Recent study reveals that the equivalence between multiclass LDA and LSR can be established based on a special class indicator matrix, but under a mild condition which may not hold under the scenarios with low-dimensional or oversampled data. In this article, we show that the equivalence between multiclass LDA and LSR can be established based on arbitrary linearly independent class indicator vectors and without any condition. In addition, we show that LDA is also equivalent to a constrained LSR based on the data-dependent indicator vectors. It can be concluded that under exactly the same mild condition, such two regressions are both equivalent to the null space LDA method. Illuminated by the equivalence of LDA and LSR, we propose a direct LDA classifier to replace the conventional framework of LDA plus extra classifier. Extensive experiments well validate the above theoretic analysis.

"Susceptibility MRI in Brain Nuclei Improves Early Diagnosis of Parkinson’s Disease Using Linear Discriminant Analysis Method"

"Susceptibility MRI in Brain Nuclei Improves Early Diagnosis of Parkinson’s Disease Using Linear Discriminant Analysis Method"

Soil microbial diversity and composition response to degradation of the alpine meadow in the southeastern Qinghai-Tibet Plateau.

With the interaction between global climate change and unreasonable human utilization, the alpine meadows on the Qinghai-Tibet Plateau have suffered various weathering degrees. Uncovering the degradation mechanism and restoration strategies can be facilitated by gaining insights into the diversity of soil microflora during meadow degradation. Therefore, we used Illumina sequencing technology to investigate the patterns of soil microbial diversity, microbial community composition, and the driving factors of microbial change in all non-degraded (ND), lightly degraded (LD), moderately degraded (MD), and severely degraded (SD) alpine meadows in the southeastern Qinghai-Tibet Plateau. Our results pointed out that with the intensification of degradation, vegetation characteristics were significantly reduced, and soil parameters significantly varied among all degraded meadows. The contents of soil organic carbon (SOC), total nitrogen (TN), available phosphorus (AN), and total phosphorous (AK) in soils decreased with the increase of degradation. The dominant bacterial phyla were the same regardless of the meadow degradation level with Actinobacteria (37.67%) and Proteobacteria (20.62%) having the highest relative abundance. Meanwhile, the dominant fungi were Ascomycota (49.9%). Based on the linear discriminant analysis (LDA) and effect size (LEfSe) method, 38 bacterial and 49 fungal species were found to be affected in the degraded alpine meadow, most of which belonged to Actinobacteria and Ascomycota, respectively. Mantel test analysis illustrated that the bacterial community was mainly significantly dependent on below-ground biomass, pH, soil organic carbon, and total nitrogen, while the fungal community was significantly dependent on soil organic carbon, total nitrogen, available nitrogen, and available potassium. These results suggest that the degeneration of alpine meadows contributes to the variability of the diversity and composition of microflora on the Tibetan plateau. Yet this effect is mainly dependent on soil factors.

Classification of colorectal primer carcinoma from normal colon with mid‐infrared spectra

AbstractIn this project, we used formalin‐fixed paraffin‐embedded (FFPE) tissue samples to measure thousands of spectra per tissue core with Fourier transform mid‐infrared spectroscopy using an FT‐IR imaging system. These cores varied between normal colon (NC) and colorectal primer carcinoma (CRC) tissues. We created a database to manage all the multivariate data obtained from the measurements. Then, we applied classifier algorithms to identify the tissue based on its yielded spectra. For classification, we used the random forest, a support vector machine, XGBoost, and linear discriminant analysis methods, as well as three deep neural networks. We compared two data manipulation techniques using these models and then applied filtering. In the end, we compared model performances via the sum of ranking differences (SRD).

Chitin‐Based Functional Films for the Colorimetric Detection of Ethylene Glycol

A new method is developed for producing large‐area color thin films for the colorimetric detection of ethylene glycol. This method is based on thermal evaporation of chitin. This process enables easy manipulation of the thickness and color patterns of the film by using shadow masks and repeated evaporation. This film is used to demonstrate a colorimetric sensor for the detection of ethylene glycol gas. The use of chitin allows the manufacture of inexpensive and environment‐friendly gas detectors. When the film is exposed to target gas, the film reacts with ethylene glycol and hydroxyl group on the chitin‐film by etherification. Then the films undergo both chemical and structural changes, resulting in color changes at low ppm concentrations. It is able to compare the sensor reaction to gases with and without the hydroxyl group. The selectivity of the sensor is confirmed by analyzing the gas containing the hydroxyl group through the linear discriminant analysis (LDA) method. It is expected that the results will be utilized to provide low‐cost and low‐power systems for gas monitoring.

Adaptive and fuzzy locality discriminant analysis for dimensionality reduction

Linear discriminant analysis (LDA) uses labeled samples for acquiring a discriminant projection direction, by which data of different categories are separated into distinct groups in a lower-dimensional subspace. In response to the issue that LDA lacks robustness to non-Gaussian data with rich local information, improvements on LDA explore the subspace manifold structure by building a fully connected similarity graph. However, these methods are vulnerable to the interference of noisy and redundant information. In this paper, we propose a new local LDA method, named adaptive and fuzzy locality discriminant analysis (AFLDA), which aims at extracting precise and compact features. Firstly, an adaptive and fuzzy k-means strategy is adopted, where the membership between data and corresponding subclass centers for each class is learned to establish a hybrid bipartite graph and capture local information. Secondly, we design a discrete and probability constraint imposed on the membership matrix to explore the intricate structure of multimodal data. Moreover, the subblock partition for each class makes data accommodate to multimodal subclasses. Thirdly, the maximum total scatter regularization term is introduced, which amply disperses the data to enhance the recognition of local structure and avoid trivial solutions. Finally, to eliminate the interference of noisy and redundant information, AFLDA learns an optimized subspace, where cluster centers and the membership matrix are updated alternately. Promising results in experiments illustrate the efficacy of the model.

A High-Performance Method Based on Features Fusion of EEG Brain Signal and MRI-Imaging Data for Epilepsy Classification

Abstract A 1-dimensional (1D) and 2-dimensional (2D) biomedical signal analysis based on the Discrete Cosine Transform (DCT) feature extraction method was performed to diagnose epilepsy disorders with high accuracy. For this purpose, Electroencephalogram (EEG) data were used for 1D signal analysis and Magnetic Resonance Imaging (MRI) data were used for 2D signal analysis. The feature vectors were obtained by applying 1D DCT together with statistical methods such as mean, variance, standard deviation, kurtosis, and skewness for EEG data and by applying 2D DCT together with the statistical method of mean for MRI data. The most useful features were selected by applying Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Forward Selection and Backward Selection methods to the obtained feature vectors. Using EEG stand-alone features, MRI stand-alone features and EEG-MRI fused features, the classification of healthy and epileptic subjects was performed in the form of two clusters. The result of epilepsy classification in this work is 96% success of 1D EEG data by using the features selected by the PCA method, 94% success of 2D MRI data using the selected features by applying the Forward Method, 100% classification accuracy of 1D EEG and 2D MRI datasets by LDA method using the obtained fused features . The article shows that the fused features of EEG-MRI can be used very effectively for the diagnosis of epilepsy.

A Mine Water Source Prediction Model Based on LIF Technology and BWO-ELM.

The traditional methods for identifying water sources in coal mines lack the ability to quickly detect water sources and are prone to causing secondary pollution of samples. In contrast, laser induced fluorescence (LIF) technology has been introduced for the identification of coal mine water sources due to its high sensitivity and real-time performance. However, extreme learning machine (ELM) have shortcomings in randomly selecting weights and biases. The Beluga Whale Optimization (BWO) algorithm has efficient optimization capability, global search capability, adaptability and parallelism, and can find the optimal weights and biases in a short time. The combination of LIF technology and BWO-ELM model can be applied to quickly identify the welling water source in coal mine. Select sandstone water and old goaf water from the Huainan mining area as experimental samples, and mix them in different proportions to prepare 7 mixed water samples for testing. Utilize LIF technology to obtain spectral curve images, preprocess them with polynomial smoothing algorithm (SG) and spectral multiple scattering correction (MSC), and perform dimensionality reduction using factor analysis (FA) and linear discriminant analysis (LDA) methods. Finally, construct ELM models, Long Short Term Memory (LSTM) models, BWO-ELM models, and Particle Swarm Optimization Extreme Learning Machine(PSO-ELM) models for the dimensionality reduced data. In order to improve the reliability and accuracy of the results, the experimental results were kept to 5 decimal places. From the experimental results, it can be seen that SG-LDA-BWO-ELM has the best fitting effect, with a fitting coefficient of 0.99990, a root mean square error of 0.00041, a mean square error approaching 0, and an average absolute error of 0.00021. It has the best convergence and the smallest absolute error among all models, making it the most suitable for identifying mine water inrush. It is of great significance for preventing and controlling mine water disasters and ensuring coal mine production safety.

Innovative Tools for Nitrogen Fertilization Traceability in Organic Farming Products: A Cauliflower Case Study

Different research works have been carried out over the years to investigate new and reliable systems to test the authenticity of products obtained using organic cultivation methods. Based on a previously proposed integrated approach for discriminating organic from conventional products through the acquisition of isotopic data and other chemical and biochemical parameters, we herein report the results of an open-field cultivation case study for cauliflower crop. Experiments were carried out on soil, leaves, and corymb samples of cauliflowers grown using six different nitrogen fertilization treatments (organic, conventional, and mixed at different % of mineral fertilizers). The results of this study have shown that a multivariate analysis of isotopic data (13C/12C; 15N/14N, 34S/32S, 2H/1H, and 18O/16O isotopic ratios) combined with other parameters (fresh weight, total soluble solids, total acidity, cut resistance, CIE L*, a*, b* color indices, head height, head diameter, ascorbic acid content, total polyphenols, and ORAC units) performed using the linear discriminant analysis method gives researchers the possibility to discriminate organic products from conventional ones. Our study highlighted that the different isotopic signatures impressed on the cauliflowers by the different nitrogenous sources combined with the qualitative pattern of the crop, significantly affected by the different treatments, could effectively be jointly used to trace the organic origin of the crop.

Systemic Lupus Erythematosus: How Machine Learning Can Help Distinguish between Infections and Flares.

Systemic Lupus Erythematosus (SLE) is a multifaceted autoimmune ailment that impacts multiple bodily systems and manifests with varied clinical manifestations. Early detection is considered the most effective way to save patients' lives, but detecting severe SLE activity in its early stages is proving to be a formidable challenge. Consequently, this work advocates the use of Machine Learning (ML) algorithms for the diagnosis of SLE flares in the context of infections. In the pursuit of this research, the Random Forest (RF) method has been employed due to its performance attributes. With RF, our objective is to uncover patterns within the patient data. Multiple ML techniques have been scrutinized within this investigation. The proposed system exhibited around a 7.49% enhancement in accuracy when compared to k-Nearest Neighbors (KNN) algorithm. In contrast, the Support Vector Machine (SVM), Binary Linear Discriminant Analysis (BLDA), Decision Trees (DT) and Linear Regression (LR) methods demonstrated inferior performance, with respective values around 81%, 78%, 84% and 69%. It is noteworthy that the proposed method displayed a superior area under the curve (AUC) and balanced accuracy (both around 94%) in comparison to other ML approaches. These outcomes underscore the feasibility of crafting an automated diagnostic support method for SLE patients grounded in ML systems.

An Efficient Greedy Search Algorithm for High-dimensional Linear Discriminant Analysis.

High-dimensional classification is an important statistical problem that has applications in many areas. One widely used classifier is the Linear Discriminant Analysis (LDA). In recent years, many regularized LDA classifiers have been proposed to solve the problem of high-dimensional classification. However, these methods rely on inverting a large matrix or solving large-scale optimization problems to render classification rules-methods that are computationally prohibitive when the dimension is ultra-high. With the emergence of big data, it is increasingly important to develop more efficient algorithms to solve the high-dimensional LDA problem. In this paper, we propose an efficient greedy search algorithm that depends solely on closed-form formulae to learn a high-dimensional LDA rule. We establish theoretical guarantee of its statistical properties in terms of variable selection and error rate consistency; in addition, we provide an explicit interpretation of the extra information brought by an additional feature in a LDA problem under some mild distributional assumptions. We demonstrate that this new algorithm drastically improves computational speed compared with other high-dimensional LDA methods, while maintaining comparable or even better classification performance.

Latent Linear Discriminant Analysis for feature extraction via Isometric Structural Learning

Linear discriminant analysis (LDA) is one of the most successful feature extraction methods, which projects high-dimensional data to a low-dimensional space with discriminative features. However, there are problems in the existing LDAs: (1) the effect of hidden data is not exploited in LDA, (2) the LDAs cannot preserve the local isometric structure, (3) there is no consideration for structural consistency that unifies the supervised global and unsupervised local information. In this paper, we propose a brand-new LDA method, namely, Latent Linear Discriminant Analysis with Isometric Structural Learning (L2DA-ISL). We formulate LDA to a latent representation framework that considers both the discriminability from observed data and hidden data. Then, we propose isometric structural learning to capture the intrinsic local structural information. Lastly, we establish the concept of structural consistency in LDA framework. Extensive experiments and comparisons show that L2DA-ISL achieves a promising performance with structural consistency and stronger robustness in feature extraction.

Convolutional Neural Network-Based Classification of Steady-State Visually Evoked Potentials with Limited Training Data

One approach employed in brain–computer interfaces (BCIs) involves the use of steady-state visual evoked potentials (SSVEPs). This article examines the capability of artificial intelligence, specifically convolutional neural networks (CNNs), to improve SSVEP detection in BCIs. Implementing CNNs for this task does not require specialized knowledge. The subsequent layers of the CNN extract valuable features and perform classification. Nevertheless, a significant number of training examples are typically required, which can pose challenges in the practical application of BCI. This article examines the possibility of using a CNN in combination with data augmentation to address the issue of a limited training dataset. The data augmentation method that we applied is based on the spectral analysis of the electroencephalographic signals (EEG). Initially, we constructed the spectral representation of the EEG signals. Subsequently, we generated new signals by applying random amplitude and phase variations, along with the addition of noise characterized by specific parameters. The method was tested on a set of real EEG signals containing SSVEPs, which were recorded during stimulation by light-emitting diodes (LEDs) at frequencies of 5, 6, 7, and 8 Hz. We compared the classification accuracy and information transfer rate (ITR) across various machine learning approaches using both real training data and data generated with our augmentation method. Our proposed augmentation method combined with a convolutional neural network achieved a high classification accuracy of 0.72. In contrast, the linear discriminant analysis (LDA) method resulted in an accuracy of 0.59, while the canonical correlation analysis (CCA) method yielded 0.57. Additionally, the proposed approach facilitates the training of CNNs to perform more effectively in the presence of various EEG artifacts.

Application of Dimension Reduction Methods for Stress Detection

Effective detection of stress situations plays an important role in combating it. This is the main source of motivation for research to identify and evaluate different psychological conditions. Different monitor signals are used to identify individuals' stress situations in daily life. Electroencephalogram (EEG) signals are the main component used to detect stress and depression. The long-term acquisition of this signals partially interrupts daily life and negatively affects it. Researchers are trying to develop wearable technologies that can eliminate this disadvantage. In this study, stress situations are detected utilizing different sensors without EEG signals. The achievements of three different classification methods for different dimensional feature spaces have been compared. The effects of the feature selection and dimension reduction methods on the system performance have been analyzed. During the dimension reduction process, Minimum Redundancy Maximum Relevance (MRMR), Anova, Chi-2, Relieff, Kruskal Wallis (KW) and Principal Component Analysis (PCA) methods are implemented. Support Vector Machines (SVM), Linear Discriminant Analysis (LDA) and k-Nearest Neighbor (k-NN) methods are used as classifiers. The best performance is achieved with 96.2 % accuracy in 15-dimensional by using LDA and PCA methods together.

A novel approach for determining coconut drink adulteration by means of laser light backscattering imaging

AbstractIn this work, the simulated adulteration of coconut drink by dilution with water was investigated using laser-light backscattering (LLB) imaging. The laser vision system consisted of six low power laser modules, emitting 1 mm diameter beams at wavelengths of 532, 635, 780, 808, 850 and 1,064 nm. The backscattering images were acquired by a grey scale camera with 12 bit resolution. Eight parameters were extracted to describe the backscattering profile. The methods of linear discriminant analysis (LDA) and partial least squares (PLS) regression were performed on LLB parameters for classifying and predicting dilution level of adulterated coconut drink samples. Based on the results, LLB signals responded sensitively to adulteration. LDA results showed that adulterated samples were correctly recognized with accuracies between 60 and 100%. PLS models were able to estimate the adulteration level of samples with coefficients of determination of 0.57–0.97 in validation. This result demonstrated the potential of laser-light backscattering imaging as a rapid and non-destructive optical technique for evaluation of coconut drink adulteration.

Discrimination of artificial strawberry aroma by electronic nose based on nanocomposites

AbstractAn electronic nose containing an array of gas sensors with interdigitated electrodes coated with nanocomposites based on polyaniline (Pani) combined with carboxylated multiwalled carbon nanotubes doped with different acids was used to discriminate artificial strawberry aromas. Principal component analysis (PCA) and linear discriminant analysis (LDA) were used to investigate if the electronic nose was able to distinguish between different strawberry aromas. In addition, a nonlinear projection of the interactive document map technique (IDMAP) was applied to evaluate the distinction ability of the gas sensor array. The sensing layers showed tubular characteristics for Pani/MWCNT_COOH morphology and the group's representative doped state. The main and most common compound identified by gas chromatography in strawberry aromas was ethyl butyrate. The gas sensors showed high sensitivity (>6.55 mV/ppm), low limit of detection (LD <0.31 ppm), limit of quantification (LQ <5.43 ppm), short response time (<63 s) and recovery time (<10.15 s) for different artificial strawberry aromas. The results demonstrate that the electronic nose could differentiate among the artificial strawberry aromas. The volatile profile of strawberry aromas was distinguished into distinct groups using both LDA and PCA analysis. The use of IDMAP permitted the identification of the major contributors to the distinguishing ability of gas sensors with a high silhouette coefficient (0.91). The sensor array was efficient at aroma discrimination, demonstrating excellent potential for food analysis in industrial applications.Practical applicationsThe distinction between natural and artificial flavors has significantly shrunk as volatile chemical technology has advanced. Historically, it was difficult to industrially replicate natural aromas. Identification and analysis of aromas are challenging tasks. Targeted aroma compounds are frequently present in low concentrations (parts per million), which makes it very challenging to identify them. The electronic nose system is a promising new analytical method that can quickly and accurately, without pre‐treating the sample, detect and identify the full information of aroma compounds in real time. It is generally accepted as a nondestructive, affordable, and portable method with high feasibility, speed, and ease of use. For qualitative differentiation and distinguishing, PCA, LDA, and IDMAP methods were also used.