Heteroscedastic Discriminant Analysis Research Articles

Scientometric Analysis of COVID-19 Scholars Publication using Machine Learning

The global health crisis that started in December 2019 resulted in an outbreak of coronavirus named COVID-19. Scientists worldwide are working to demystify the transmission and pathogenic mechanisms of the deadly coronavirus. The World Health Organization has declared COVID-19 a pandemic in March 2020, which makes it essential to track and analyse the research state of COVID-19 for guidance on further research. This research was conducted using scientometric analysis, knowledge-mapping analysis, COVID-19 studies and journal classifications. The publications used in this study include over 3000 COVID-19 papers made available to the public from 1 January 2018 to 15 April 2021 in the PubMed databases. In this study, it was discovered that the rapid reaction of researchers worldwide resulted in a fast growth trend between 2019 and 2021 in the number of publications related to COVID-19. It was discovered that the largest number of studies is in the United States of America, which is one of the countries most affected by a pandemic. The method adopted for this study involved the use of documents such as Case Reports (CAT), Journal Article (JAT), letter (LTR), EAT, and Editorial (EDT). This is followed by the classification of COVID-19 related publications that were retrieved from PubMed between 2019 and 2021 using machine learning (ML) models such as Naïve Bayes (NB), Bayesian Generalized Linear Model (BGL), Heteroscedastic Discriminant Analysis (HDA) and Multivariate Adaptive Regression Spline (MAR). Simulation results show that the classification accuracy of MAR is better than that of other ML models used in this study. The sensitivity of the MAR is within the range of 100%. This shows that MAR performs better than NB, BGL and HDA. MAR performs better with an overall accuracy of 89.62%. Our results show a high degree of strong collaboration in coronavirus research and the exchange of knowledge in the global scientific community.

L1 -Norm Heteroscedastic Discriminant Analysis Under Mixture of Gaussian Distributions.

Fisher's criterion is one of the most popular discriminant criteria for feature extraction. It is defined as the generalized Rayleigh quotient of the between-class scatter distance to the within-class scatter distance. Consequently, Fisher's criterion does not take advantage of the discriminant information in the class covariance differences, and hence, its discriminant ability largely depends on the class mean differences. If the class mean distances are relatively large compared with the within-class scatter distance, Fisher's criterion-based discriminant analysis methods may achieve a good discriminant performance. Otherwise, it may not deliver good results. Moreover, we observe that the between-class distance of Fisher's criterion is based on the l2 -norm, which would be disadvantageous to separate the classes with smaller class mean distances. To overcome the drawback of Fisher's criterion, in this paper, we first derive a new discriminant criterion, expressed as a mixture of absolute generalized Rayleigh quotients, based on a Bayes error upper bound estimation, where mixture of Gaussians is adopted to approximate the real distribution of data samples. Then, the criterion is further modified by replacing l2 -norm with l1 one to better describe the between-class scatter distance, such that it would be more effective to separate the different classes. Moreover, we propose a novel l1 -norm heteroscedastic discriminant analysis method based on the new discriminant analysis (L1-HDA/GM) for heteroscedastic feature extraction, in which the optimization problem of L1-HDA/GM can be efficiently solved by using the eigenvalue decomposition approach. Finally, we conduct extensive experiments on four real data sets and demonstrate that the proposed method achieves much competitive results compared with the state-of-the-art methods.

Heteroscedastic discriminant analysis combined with feature selection for credit scoring

Credit granting is a fundamental question and one of the most complex tasks that every credit institution is faced with. Typically, credit scoring databases are often large and characterized by redundant and irrelevant features. An effective classification model will objectively help managers instead of intuitive experience. This study proposes an approach for building a credit scoring model based on the combination of heteroscedastic extension (Loog, Duin, 2002) of classical Fisher Linear Discriminant Analysis (Fisher, 1936, Krzyśko, 1990) and a feature selection algorithm that retains sufficient information for classification purpose. We have tested five feature subset selection algorithms: two filters and three wrappers. To evaluate the accuracy of the proposed credit scoring model and to compare it with the existing approaches we have used the German credit data set from the study (Chen, Li, 2010). The results of our study suggest that the proposed hybrid approach is an effective and promising method for building credit scoring models.

Heteroscedastic Discriminant Analysis Combined with Feature Selection for Credit Scoring

Abstract Credit granting is a fundamental question and one of the most complex tasks that every credit institution is faced with. Typically, credit scoring databases are often large and characterized by redundant and irrelevant features. An effective classification model will objectively help managers instead of intuitive experience. This study proposes an approach for building a credit scoring model based on the combination of heteroscedastic extension (Loog, Duin, 2002) of classical Fisher Linear Discriminant Analysis (Fisher, 1936, Krzyśko, 1990) and a feature selection algorithm that retains sufficient information for classification purpose. We have tested five feature subset selection algorithms: two filters and three wrappers. To evaluate the accuracy of the proposed credit scoring model and to compare it with the existing approaches we have used the German credit data set from the study (Chen, Li, 2010). The results of our study suggest that the proposed hybrid approach is an effective and promising method for building credit scoring models.

Super-class Discriminant Analysis: A novel solution for heteroscedasticity

The heteroscedasticity problem is a great challenge in pattern recognition, particularly in statistics-based methods. The traditional method that is mainly used to solve this problem is heteroscedastic Discriminant Analysis. In this study, we propose a novel solution to the problem, called Super-class Discriminant Analysis (SCDA). Our method uses the “divide and conquer” methodology to partition the heteroscedastic dataset into super-classes with reduced heteroscedasticity and models them separately. Theoretically, a super-class should contain a set of classes having the same within-class variation. In practice, a heteroscedastic dataset can be coarsely divided into several super-classes based on certain semantic criteria such as gender or race. We evaluate our method with toy data and three real-world datasets, which can be divided into super-classes according to gender and race. Experimental results indicate that the proposed method can effectively resolve the problem of heteroscedasticity.

An optimal image transform for threshold-based cloud detection using heteroscedastic discriminant analysis

We present a simple image transform that optimally combines four image channels into a greyscale image for threshold-based cloud detection. These image channels, namely blue, green, red and near infrared, are present on many low Earth-orbit resource satellites. Applying a single threshold to a greyscale image is a computationally efficient method suitable for onboard implementation. We used heteroscedastic discriminant analysis (HDA), which is a generalization of the popular dimension-reducing linear discriminant analysis, to transform the image. Comparative tests between HDA, existing transforms from the remote-sensing literature (the haze optimized and D transforms), as well as the single red and blue image channels were conducted. Although thin clouds remain challenging for global threshold-based techniques, the HDA transform consistently gave the best average segmentation errors across the test dataset. This dataset consisted of 32 1 megapixel Quickbird and Landsat images. HDA has not previously been applied to remote-sensing data.

Two-Dimensional Heteroscedastic Discriminant Analysis for Facial Gender Classification

In this paper, a novel discriminant analysis named two-dimensional Heteroscedastic Discriminant Analysis (2DHDA) is presented, and used for gender classification. In 2DHDA, equal within-class covariance constraint is removed. Firstly, the criterion of 2DHDA is defined according to that of 2DLDA. Secondly, the criterion of 2DHDA, log and rearranging terms are taken, and then the optimal projection matrix is solved by gradient descent algorithm. Thirdly, face images are projected onto the optimal projection matrix, thus the 2DHDA features are extracted. Finally, Nearest Neighbor classifier is selected to perform gender classification. Experimental results show that higher recognition rate is obtained by way of 2DHDA compared with 2DLDA and HDA .

Linear Discriminant Analysis Using a Generalized Mean of Class Covariances and Its Application to Speech Recognition

To precisely model the time dependency of features is one of the important issues for speech recognition. Segmental unit input HMM with a dimensionality reduction method has been widely used to address this issue. Linear discriminant analysis (LDA) and heteroscedastic extensions, e.g., heteroscedastic linear discriminant analysis (HLDA) or heteroscedastic discriminant analysis (HDA), are popular approaches to reduce dimensionality. However, it is difficult to find one particular criterion suitable for any kind of data set in carrying out dimensionality reduction while preserving discriminative information. In this paper, we propose a new framework which we call power linear discriminant analysis (PLDA). PLDA can be used to describe various criteria including LDA, HLDA, and HDA with one control parameter. In addition, we provide an efficient selection method using a control parameter without training HMMs nor testing recognition performance on a development data set. Experimental results show that the PLDA is more effective than conventional methods for various data sets.

On the relation between discriminant analysis and mutual information for supervised linear feature extraction

This paper provides a unifying view of three discriminant linear feature extraction methods: linear discriminant analysis, heteroscedastic discriminant analysis and maximization of mutual information. We propose a model-independent reformulation of the criteria related to these three methods that stresses their similarities and elucidates their differences. Based on assumptions for the probability distribution of the classification data, we obtain sufficient conditions under which two or more of the above criteria coincide. It is shown that these conditions also suffice for Bayes optimality of the criteria. Our approach results in an information-theoretic derivation of linear discriminant analysis and heteroscedastic discriminant analysis. Finally, regarding linear discriminant analysis, we discuss its relation to multidimensional independent component analysis and derive suboptimality bounds based on information theory.

Heteroscedastic discriminant analysis and reduced rank HMMs for improved speech recognition

We present the theory for heteroscedastic discriminant analysis (HDA), a model-based generalization of linear discriminant analysis (LDA) derived in the maximum-likelihood framework to handle heteroscedastic-unequal variance-classifier models. We show how to estimate the heteroscedastic Gaussian model parameters jointly with the dimensionality reducing transform, using the EM algorithm. In doing so, we alleviate the need for an a priori ad hoc class assignment. We apply the theoretical results to the problem of speech recognition and observe word-error reduction in systems that employed both diagonal and full covariance heteroscedastic Gaussian models tested on the TI-DIGITS database.

Heteroscedastic Discriminant Analysis with Expert Systems and NMR Applications

SYNOPTIC ABSTRACTThe problem of “discriminant analysis,” i.e. of providing a method for classifying new observations into one of k≥2 populations, has been studied by many authors since the area was opened by Fisher in 1936. The probabilities of misclassification are of key interest, and present procedures yield only hopeful approximations to them when population parameters are unknown (as is the case in practice). In this paper we give a new Heteroscedastic Discriminant Analysis Procedure which provides precise estimation of the misclassification probabilities. The results are being incorporated into ESS™, The Expert Statistical System, and are illustrated on NMR data from the human brain.