scholarly journals Depth-Based Classification for Distributions with Nonconvex Support

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Daniel Hlubinka ◽  
Ondrej Vencalek
Keyword(s):  
Statistical Analysis ◽  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Classification Problem ◽  
Data Depth ◽  
Misclassification Rate ◽  
Skewed Data ◽  
Weighted Version ◽  
Linear Discriminant ◽  
Normal Populations

Halfspace depth became a popular nonparametric tool for statistical analysis of multivariate data during the last two decades. One of applications of data depth considered recently in literature is the classification problem. The data depth approach is used instead of the linear discriminant analysis mostly to avoid the parametric assumptions and to get better classifier for data whose distribution is not elliptically symmetric, for example, skewed data. In our paper, we suggest to use weighted version of halfspace depth rather than the halfspace depth itself in order to obtain lower misclassification rate in the case of “nonconvex” distributions. Simulations show that the results of depth-based classifiers are comparable with linear discriminant analysis for two normal populations, while for nonelliptic distributions the classifier based on weighted halfspace depth outperforms both linear discriminant analysis and classifier based on the usual (nonweighted) halfspace depth.

Appropriateness of Linear Discriminant and Multinomial Classification Analysis in Marketing Research

1978 ◽  
Vol 15 (1) ◽  
pp. 103-112 ◽  
Author(s):  
William R. Dillon ◽  
Matthew Goldstein ◽  
Leon G. Schiffman
Keyword(s):  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Marketing Research ◽  
Classification Problem ◽  
Relative Performance ◽  
New Method ◽  
Classification Methods ◽  
Classification Analysis ◽  
Linear Discriminant ◽  
Usage Behavior

Buyer usage behavior data are used to compare the relative performance of a linear discriminant analysis and several multinomial classification methods. The potential shortcomings of each of the procedures investigated are cited, and a new method for determining the contribution of a variable to discrimination in the context of the multinomial classification problem also is presented.

scholarly journals Asymptotic approximation of misclassification probabilities in linear discriminant analysis with repeated measurements

2021 ◽  
Vol 25 (1) ◽  
pp. 67-85
Author(s):  
Edward K. Ngailo ◽  
Dietrich Von Rosen ◽  
Martin Singull
Keyword(s):  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Asymptotic Approximation ◽  
Repeated Measurements ◽  
Asymptotic Approximations ◽  
Multivariate Normal ◽  
Linear Discriminant ◽  
Normal Populations ◽  
Misclassification Errors ◽  
Observation Vector

We propose asymptotic approximations for the probabilities of misclassification in linear discriminant analysis when the group means follow a growth curve structure. The discriminant function can classify a new observation vector of p repeated measurements into one of several multivariate normal populations with equal covariance matrix. We derive certain relations of the statistics under consideration in order to obtain asymptotic approximation of misclassification errors for the two group case. Finally, we perform Monte Carlo simulations to evaluate the reliability of the proposed results.

scholarly journals Sequential Data Fusion Techniques for the Authentication of the P.G.I. Senise (“Crusco”) Bell Pepper

2021 ◽  
Vol 11 (4) ◽  
pp. 1709
Author(s):  
Alessandra Biancolillo ◽  
Francesca Di Donato ◽  
Francesco Merola ◽  
Federico Marini ◽  
Angelo Antonio D’Archivio
Keyword(s):  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Near Infrared ◽  
External Validation ◽  
Classification Problem ◽  
Sweet Pepper ◽  
Bell Pepper ◽  
Spectroscopic Techniques ◽  
Sequential Data ◽  
Linear Discriminant

Bell pepper is the common name of the berry obtained from some varieties of the Capsicum annuum species. This agro-food is appreciated all over the world and represents one of the key ingredients of several traditional dishes. It is used as a fresh product, or dried and ground as a seasoning (e.g., paprika). Specific varieties of sweet pepper present organoleptic peculiarities and they have been awarded by quality marks as a further confirmation of their unicity (e.g., Piment d’Espelette, Pimiento de Herbón, Peperone di Senise). Due to the market value of this aliment, it can be subjected to frauds, such as adulterations and sophistication. The present study lays on these considerations and aims at developing a spectroscopy-based approach for authenticating Senise bell pepper and for detecting its adulteration with common paprika. In order to achieve this goal, 60 pure samples of bell pepper from Senise were analyzed by mid- and near-infrared spectroscopies. Then, in order to mimic the adulteration, 40 mixtures of Senise bell pepper and paprika were prepared and analyzed (by the same spectroscopic techniques). Eventually, two different multi-block classification approaches (sequential and orthogonalized partial least squares linear discriminant analysis and sequential and orthogonalized covariance selection linear discriminant analysis) were used to discriminate between pure and adulterated Senise bell pepper samples. Both proposed procedures achieved extremely successful results in external validation, correctly classifying all the (thirty-five) test samples, indicating that both approaches represent a winning solution for the investigated classification problem.

scholarly journals Performance of Linear Discriminant Analysis Using Different Robust Methods

2018 ◽  
Vol 11 (1) ◽  
pp. 284 ◽  
Author(s):  
Mufda Jameel Alrawashdeh ◽  
Taha Radwan Radwan ◽  
Kalid Abunawas Abunawas
Keyword(s):  
Statistical Analysis ◽  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Multivariate Statistical Analysis ◽  
Robust Methods ◽  
Minimum Covariance Determinant ◽  
Multivariate Statistical ◽  
Linear Discriminant ◽  
Misclassification Probability ◽  
Conventional Banks

This study aims to combine the new deterministic minimum covariance determinant (DetMCD) algorithm with linear discriminant analysis (LDA) and compare it with the fast minimum covariance determinant (FastMCD), fast consistent high breakdown (FCH), and robust FCH (RFCH) algorithms. LDA classifies new observations into one of the unknown groups and it is widely used in multivariate statistical analysis. The LDA mean and covariance matrix parameters are highly influenced by outliers. The DetMCD algorithm is highly robust and resistant to outliers and it is constructed to overcome the outlier problem. Moreover, the DetMCD algorithm is used to estimate location and scatter matrices. The DetMCD, FastMCD, FCH, and RFCH algorithms are applied to estimate misclassification probability using robust LDA. All the algorithms are expected to improve the LDA model for classification purposes in banks, such as bankruptcy and failures, and to distinguish between Islamic and conventional banks. The performances of the estimators are investigated through simulation and actual data.

Classification of Diesel Engine Health Using Sparse Linear Discriminant Analysis (SLDA)

2009 ◽  
Author(s):  
Neha Chandrachud ◽  
Ravindra Kakade ◽  
Peter H. Meckl ◽  
Galen B. King ◽  
Kristofer Jennings
Keyword(s):  
Steady State ◽  
Diesel Engine ◽  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Optimal Number ◽  
Classification Model ◽  
Misclassification Rate ◽  
Linear Discriminant ◽  
State Data ◽  
Input Variables

With requirements for on-board diagnostics on diesel engines becoming more stringent for the coming model years, diesel engine manufacturers must improve their ability to identify fault conditions that lead to increased exhaust emissions. This paper proposes a statistical classifier model to identify the state of the engine, i.e. healthy or faulty, using an optimal number of sensors based on the data acquired from the engine. The classification model proposed in this paper is based on Sparse Linear Discriminant Analysis. This technique performs Linear Discriminant Analysis with a sparseness criterion imposed such that classification, dimension reduction and feature selection are merged into one step. It was concluded that the analysis technique could produce 0% misclassification rate for the steady-state data acquired from the diesel engine using five input variables. The classifier model was also extended to transient operation of the engine. The misclassification rate in the case of transient data was reduced from 31% to 26% by using the steady-state data trained classifier using thirteen variables.

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