scholarly journals Annotations on the Relationship Among Discriminant Functions

2020 ◽  
pp. 161-165
Author(s):  
Awogbemi Clement Adeyeye
Keyword(s):  
Linear Relationship ◽  
Discriminant Function ◽  
Dimensional Space ◽  
Discriminant Functions ◽  
Classification Problems ◽  
Linear Discriminant ◽  
Equal Variance ◽  
Quadratic Discriminant Function ◽  
Higher Dimensional ◽  
The Relationship

Different forms of discriminant functions and the essence of their appearances were considered in this study. Various forms of classification problems were also considered, and in each of the cases mentioned, classification from simple functions of the observational vector rather than complicated regions in the higher-dimensional space of the original vector were made. Violation of condition of equal variance covariance matrix for Linear Discriminant Function (LDF) results to Quadratic Discriminant Function (QDF). The relationships among the classification statistics examined were established: The Anderson’s (W) and Rao’s (R) statistics are equivalent when the two sample sizes are equal, and when a constant is equal to 1, W, R and John-Kudo’s (Z) classification statistics are asymptotically comparable. A linear relationship is also established between W and Z classification statistics.

scholarly journals On the Error Rate Comparison of the Quadratic Discriminant Function, Euclidean Distance Classifier, Fisher’s Linear Discriminant Function and the Vine Copulas

2018 ◽  
Vol 8 (1) ◽  
pp. 113
Author(s):  
A. Nanthakumar
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Euclidean Distance ◽  
Error Rates ◽  
Linear Discriminant Function ◽  
Misclassification Error ◽  
Classification Problems ◽  
Linear Discriminant ◽  
Quadratic Discriminant Function ◽  
Vine Copulas

The estimation of the error rates is of vital importance in classification problems as this is used as a basis to choose the best discriminant function; that is, the one with a minimum misclassification error. The quadratic discriminant function (QDF), Euclidean Distance Classifier (EDC), and Fisher’s Linear Discriminant Function (FLDC) have been in use for a long time for the purpose of classification. In this paper, we compare the misclassification error rate of the QDF, EDC, and FLDC with the Vine Copulas based on Gaussian and Clayton models. The results were obtained for the general case where the means are unequal and the covariance matrices are unequal.

The performance of delta check methods.

1979 ◽  
Vol 25 (12) ◽  
pp. 2034-2037 ◽  
Author(s):  
L B Sheiner ◽  
L A Wheeler ◽  
J K Moore
Keyword(s):  
False Positive ◽  
False Positive Rate ◽  
True Positive Rate ◽  
True Positive ◽  
Discriminant Functions ◽  
Linear Discriminant ◽  
Operating Rate ◽  
Positive Rate ◽  
The Relationship

Abstract The percentage of mislabeled specimens detected (true-positive rate) and the percentage of correctly labeled specimens misidentified (false-positive rate) were computed for three previously proposed delta check methods and two linear discriminant functions. The true-positive rate was computed from a set of pairs of specimens, each having one member replaced by a member from another pair chosen at random. The relationship between true-positive and false-positive rates was similar among the delta check methods tested, indicating equal performance for all of them over the range of false-positive rate of interest. At a practical false-positive operating rate of about 5%, delta check methods detect only about 50% of mislabeled specimens; even if the actual mislabeling rate is moderate (e.g., 1%), only abot 10% of specimens flagged a by a delta check will actually have been mislabeled.

Complex Behavioral Indices Weighted by Linear Discriminant Functions for the Prediction of Cerebral Damage

1964 ◽  
Vol 19 (3) ◽  
pp. 907-923 ◽  
Author(s):  
Lawrence Wheeler
Keyword(s):  
Discriminant Function ◽  
Correct Prediction ◽  
Trail Making Test ◽  
Cerebral Damage ◽  
Discriminant Functions ◽  
Criterion Group ◽  
Linear Discriminant ◽  
Trail Making ◽  
Weighted Score ◽  
Prediction Control

Linear discriminant functions were applied to seven dichotomized measures from each of 224 patients who were divided into control, left cerebral damage, right cerebral damage, and diffuse or bilateral damage groups. The measures were: Wechsler Verbal Weighted Score, Wechsler Performance Weighted Score, Halstead Impairment Index, Trail Making Test A, Trail Making Test B, Aphasia 4-rule Prediction, and age of patient. Four comparisons were made, one for each criterion group vs all remaining groups. The discriminant function in each comparison produced a single weighted score per S, and an optimum, least-squares type of separation between the two sets of scores. The resulting distributions of summed, weighted scores in each comparison were inspected for the point of minimum overlap, and an individual's weighted score, falling above or below this point, categorized him as belonging either in the single criterion group or in any one of the remaining three groups. These assignments, when compared with the actual criterion classes of the patients, were expressed as percentages of correct prediction: control vs non-control, 83.0%; left damage vs non-left, 87.5%; right damage vs non-right, 85.7%; diffuse (or bilateral) damage vs non-diffuse, 84.4%. Each measure was examined individually for percentages of correct prediction, but the discriminant function was superior in all instances, being approached only by the Halstead Impairment Index (one comparison) and by the Aphasia 4-rule Prediction (two comparisons). The seven-variable discriminant function was approximately as efficient as either of two previous functions that included more than 20 variables each.

An Application of the Linear Discriminant Function to Insect Taxonomy

1954 ◽  
Vol 86 (2) ◽  
pp. 69-73 ◽  
Author(s):  
R. S. Bigelow ◽  
C. Reimer
Keyword(s):  
Discriminant Function ◽  
Related Species ◽  
Linear Discriminant Function ◽  
Discriminant Functions ◽  
Reliable Criterion ◽  
Closely Related Species ◽  
Linear Discriminant ◽  
Insect Taxonomy

This paper is a report an the applicability of the linear discriminant function to insect taxonomy. Mather and Dobzhansky (1939) and Cox (1953) applied this technique to problems in insect taxonomy, but the former study was concerned with detecting a difference between samples, and the latter used the function only secondarily. In this paper, discriminant functions were calculated from several combinations of linear characters in males of two closely related species of grasshopper, Arphia pseadonietana (Thomas) and A. conspersa Scudder, to determine: (a) whether a reliable criterion could be found for relatively inexperienced workers to determine individual specimens with a predictable degree of precision; and (b) which characters, or combination of characters, would provide the most reliable criteria.

scholarly journals Opening the Black Box: the Relationship between Neural Networks and Linear Discriminant Functions

1997 ◽  
Vol 14 (1) ◽  
pp. 19-30 ◽  
Author(s):  
Roger A. Kemp ◽  
Calum MacAulay ◽  
Branko Palcic
Keyword(s):  
Neural Networks ◽  
Decision Making ◽  
Classification Problem ◽  
Black Box ◽  
Discriminant Functions ◽  
Classification Problems ◽  
Statistical Decision ◽  
Feed Forward ◽  
Linear Discriminant ◽  
Feed Forward Neural Networks

Over the last ten years feed‐forward neural networks have become a popular tool for statistical decision making. During this time, they have been applied in many fields, including cytological classification. Neural networks are often treated as a black box, whose inner workings are concealed from the researcher. This is unfortunate, since the inner workings of a neural network can be understood in a manner similar to that of a linear discriminant function, which is the standard tool that researchers use for decision making.This paper discusses feed‐forward neural networks and some methods to improve their performance for classification problems. Their relationship to discriminant functions will be examined for a simple two‐dimensional classification problem.

scholarly journals Classification of all-rounders in limited over cricket - a machine learning approach

2021 ◽  
Vol 6 (4) ◽  
pp. 295-306
Author(s):  
Ananda B. W. Manage ◽  
Ram C. Kafle ◽  
Danush K. Wijekularathna
Keyword(s):  
Machine Learning ◽  
Support Vector Machine ◽  
Logistic Regression ◽  
Discriminant Function ◽  
Linear Discriminant Function ◽  
Classification Rule ◽  
Support Vector ◽  
Classification Methods ◽  
Linear Discriminant ◽  
Quadratic Discriminant Function

In cricket, all-rounders play an important role. A good all-rounder should be able to contribute to the team by both bat and ball as needed. However, these players still have their dominant role by which we categorize them as batting all-rounders or bowling all-rounders. Current practice is to do so by mostly subjective methods. In this study, the authors have explored different machine learning techniques to classify all-rounders into bowling all-rounders or batting all-rounders based on their observed performance statistics. In particular, logistic regression, linear discriminant function, quadratic discriminant function, naïve Bayes, support vector machine, and random forest classification methods were explored. Evaluation of the performance of the classification methods was done using the metrics accuracy and area under the ROC curve. While all the six methods performed well, logistic regression, linear discriminant function, quadratic discriminant function, and support vector machine showed outstanding performance suggesting that these methods can be used to develop an automated classification rule to classify all-rounders in cricket. Given the rising popularity of cricket, and the increasing revenue generated by the sport, the use of such a prediction tool could be of tremendous benefit to decision-makers in cricket.

A Comparison Of Regularized Linear Discriminant Functions For Poorly-Posed Classification Problems

2021 ◽  
pp. 1-36
Author(s):  
L. A. Thompson ◽  
Wade Davis ◽  
Phil D. Young ◽  
Dean M. Young ◽  
Jeannie S. Hill
Keyword(s):  
Discriminant Functions ◽  
Classification Problems ◽  
Linear Discriminant

Quadratic Discriminant Analysis with Covariance for Stock Delineation and Population Differentiation: A Study of Beaked Redfishes (Sebastes mentella and S. fasciatus)

1985 ◽  
Vol 42 (10) ◽  
pp. 1672-1676 ◽  
Author(s):  
R. K. Misra
Keyword(s):  
Discriminant Analysis ◽  
Fisheries Management ◽  
Discriminant Function ◽  
Population Differentiation ◽  
Quadratic Discriminant Analysis ◽  
Morphometric Data ◽  
Linear Discriminant ◽  
Vital Importance ◽  
Quadratic Discriminant Function ◽  
Sebastes Mentella

Stock delineation is of vital importance in fisheries management programs. Linear discriminant function (LDF) has been employed extensively in population differentiation studies but is of severely restricted usefulness when populations differ in their dispersion matrices. Quadratic discriminant function (QDF) is the appropriate analysis to employ in these situations. Here, I analyzed morphometric data of beaked redfishes (Sebastes mentella and S. fasciatus) by a recently developed conditional QDF.

scholarly journals ANALISIS DISKRIMINAN PADA KLASIFIKASI DESA DI KABUPATEN TABANAN MENGGUNAKAN METODE K-FOLD CROSS VALIDATION

2017 ◽  
Vol 6 (2) ◽  
pp. 106 ◽  
Author(s):  
IDA AYU MADE SUPARTINI ◽  
I KOMANG GDE SUKARSA ◽  
I GUSTI AYU MADE SRINADI
Keyword(s):  
Discriminant Analysis ◽  
Covariance Matrix ◽  
Discriminant Function ◽  
Rural Areas ◽  
Urban Areas ◽  
Cross Validation ◽  
Quadratic Discriminant Analysis ◽  
Linear Discriminant ◽  
Quadratic Discriminant Function ◽  
Fold Cross Validation

Tabanan Regency is one of the eight regencies and one municipality in Bali Province. Administratively, it is divided into 10 districs and  villages. There are rural areas and urban areas in the regions. Discriminant analysis is a technique related to the separation of objects into different groups that have been set previously. The purpose of this research is to classify villlages in Tabanan Regency into urban or rural groups with discriminant analysis. Linear discriminant analysis assumes that the covariance matrix of the two groups are equals, if the assumption of equality of covariance matrix is violated, quadratic discriminant analysis can be used for classification. This research uses k-fold crosss validation method for calculating the accuracy of quadratic discriminant function where . Quadratic discriminant function is obtained by  with the smallest APER value (). All of classification results are stable and consistence.

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