Mathematical Programming Approaches for the Classification Problem in Two-Group Discriminant Analysis

1990 ◽  
Vol 25 (4) ◽  
pp. 427-454 ◽  
Author(s):  
Erich A. Joachimsthaler ◽  
Antonie Stam
Keyword(s):  
Discriminant Analysis ◽  
Mathematical Programming ◽  
Classification Problem

scholarly journals On the binary classification problem in discriminant analysis using linear programming methods

2020 ◽  
Vol 30 (1) ◽  
Author(s):  
Michael O. Olusola ◽  
Sydney I. Onyeagu
Keyword(s):  
Linear Programming ◽  
Discriminant Analysis ◽  
Binary Classification ◽  
Classification Problem ◽  
Solution Technique ◽  
Phase Method ◽  
Bound Constraints ◽  
Two Phase ◽  
Linear Discriminant ◽  
Binary Classification Problem

This paper is centred on a binary classification problem in which it is desired to assign a new object with multivariate features to one of two distinct populations as based on historical sets of samples from two populations. A linear discriminant analysis framework has been proposed, called the minimised sum of deviations by proportion (MSDP) to model the binary classification problem. In the MSDP formulation, the sum of the proportion of exterior deviations is minimised subject to the group separation constraints, the normalisation constraint, the upper bound constraints on proportions of exterior deviations and the sign unrestriction vis-à-vis the non-negativity constraints. The two-phase method in linear programming is adopted as a solution technique to generate the discriminant function. The decision rule on group-membership prediction is constructed using the apparent error rate. The performance of the MSDP has been compared with some existing linear discriminant models using a previously published dataset on road casualties. The MSDP model was more promising and well suited for the imbalanced dataset on road casualties.

Motor Oil Classification Using Color Histograms and Pattern Recognition Techniques

2018 ◽  
Vol 101 (6) ◽  
pp. 1967-1976 ◽  
Author(s):  
Shiva Ahmadi ◽  
Ahmad Mani-Varnosfaderani ◽  
Biuck Habibi
Keyword(s):  
Pattern Recognition ◽  
Discriminant Analysis ◽  
Classification Problem ◽  
Classification Model ◽  
Motor Oil ◽  
Pattern Recognition Techniques ◽  
Color Histograms ◽  
Different Types ◽  
Motor Oils

Abstract Motor oil classification is important for quality control and the identification of oil adulteration. In this work, we propose a simple, rapid, inexpensive and nondestructive approach based on image analysis and pattern recognition techniques for the classification of nine different types of motor oils according to their corresponding color histograms. For this, we applied color histogram in different color spaces such as red green blue (RGB), grayscale, and hue saturation intensity (HSI) in order to extract features that can help with the classification procedure. These color histograms and their combinations were used as input for model development and then were statistically evaluated by using linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), and support vector machine (SVM) techniques. Here, two common solutions for solving a multiclass classification problem were applied: (1) transformation to binary classification problem using a one-against-all (OAA) approach and (2) extension from binary classifiers to a single globally optimized multilabel classification model. In the OAA strategy, LDA, QDA, and SVM reached up to 97% in terms of accuracy, sensitivity, and specificity for both the training and test sets. In extension from binary case, despite good performances by the SVM classification model, QDA and LDA provided better results up to 92% for RGB-grayscale-HSI color histograms and up to 93% for the HSI color map, respectively. In order to reduce the numbers of independent variables for modeling, a principle component analysis algorithm was used. Our results suggest that the proposed method is promising for the identification and classification of different types of motor oils.

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.

Gaussian Discriminant Analysis for Optimal Delineation of Mild Cognitive Impairment in Alzheimer’s Disease

2018 ◽  
Vol 28 (08) ◽  
pp. 1850017 ◽  
Author(s):  
Chen Fang ◽  
Chunfei Li ◽  
Mercedes Cabrerizo ◽  
Armando Barreto ◽  
Jean Andrian ◽  
...  
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Cognitive Impairment ◽  
Mild Cognitive Impairment ◽  
Discriminant Analysis ◽  
Classification Problem ◽  
Classification Performance ◽  
High Dimensional ◽  
Support Vector ◽  
Brain Hemispheres

Over the past few years, several approaches have been proposed to assist in the early diagnosis of Alzheimer’s disease (AD) and its prodromal stage of mild cognitive impairment (MCI). Using multimodal biomarkers for this high-dimensional classification problem, the widely used algorithms include Support Vector Machines (SVM), Sparse Representation-based classification (SRC), Deep Belief Networks (DBN) and Random Forest (RF). These widely used algorithms continue to yield unsatisfactory performance for delineating the MCI participants from the cognitively normal control (CN) group. A novel Gaussian discriminant analysis-based algorithm is thus introduced to achieve a more effective and accurate classification performance than the aforementioned state-of-the-art algorithms. This study makes use of magnetic resonance imaging (MRI) data uniquely as input to two separate high-dimensional decision spaces that reflect the structural measures of the two brain hemispheres. The data used include 190 CN, 305 MCI and 133 AD subjects as part of the AD Big Data DREAM Challenge #1. Using 80% data for a 10-fold cross-validation, the proposed algorithm achieved an average F1 score of 95.89% and an accuracy of 96.54% for discriminating AD from CN; and more importantly, an average F1 score of 92.08% and an accuracy of 90.26% for discriminating MCI from CN. Then, a true test was implemented on the remaining 20% held-out test data. For discriminating MCI from CN, an accuracy of 80.61%, a sensitivity of 81.97% and a specificity of 78.38% were obtained. These results show significant improvement over existing algorithms for discriminating the subtle differences between MCI participants and the CN group.

Discriminant analysis via mathematical programming: Certain problems and their causes

1989 ◽  
Vol 16 (4) ◽  
pp. 353-362 ◽  
Author(s):  
Tom M. Cavalier ◽  
James P. Ignizio ◽  
Allen L. Soyster
Keyword(s):  
Discriminant Analysis ◽  
Mathematical Programming
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