A Bibliography of Discriminant Analysis

Cacoullos, T.; Styan, George P. H.

doi:10.1016/b978-0-12-154050-0.50025-3

Cited by 18 publications

(8 citation statements)

References 334 publications

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“…LDA ( − ) assumes that conditional probabilities are normally distributed with the same variance−covariance matrix for each group, and because probabilities are positive, taking the natural logarithm of posterior probabilities gives for each group a classification function that is linear in the original variables, hence, the name of this method. In this case, the above-mentioned Bayes' rule becomes “a sample should be assigned to the class whose classification function is largest”.…”

Section: Methodsmentioning

confidence: 99%

Chemical Authentication of Extra Virgin Olive Oil Varieties by Supervised Chemometric Procedures

Bucci

Magrì

Magrı̀

et al. 2002

J. Agric. Food Chem.

125

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This work has focused on discriminating extra virgin olive oils from Sabina (Lazio, Italy) by olive fruit variety (cultivar). A set of oils from five of the most widespread cultivars (Carboncella, Frantoio, Leccino, Moraiolo, and Pendolino) in this geographical area was analyzed for chemical composition using only the Official Analytical Methods, recognized for the quality control and commercial classification of this product. The obtained data set was converted into a computer-compatible format, and principal component analysis (PCA) and a method based on the Fisher F ratio were used to reduce the number of variables without a significant loss of chemical information. Then, to differentiate these samples, two supervised chemometric procedures were applied to process the experimental data: linear discriminant analysis (LDA) and artificial neural network (ANN) using the back-propagation algorithm. It was found that both of these techniques were able to generalize and correctly predict all of the samples in the test set. However, these results were obtained using 10 variables for LDA and 6 (the major fatty acid percentages, determined by a single gas chromatogram) for ANN, which, in this case, appears to provide a better prediction ability and a simpler chemical analysis. Finally, it is pointed out that, to achieve the correct authentication of all samples, the selected training set must be representative of the whole data set.

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Section: Methodsmentioning

confidence: 99%

Chemical Authentication of Extra Virgin Olive Oil Varieties by Supervised Chemometric Procedures

Bucci

Magrì

Magrı̀

et al. 2002

J. Agric. Food Chem.

125

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“…The discriminant analysis is a multivariate statistical technique, which attempts to determine the best linear combination of explanatory variables (called "predictors") to differentiate between groups of cases into which the dependent variable is subdivided. An advantage of the discriminant analysis technique, compared to e.g., regression analysis, is that makes it possible to reveal some common characteristics of the cases forming subgroups into which the values of the dependent variable are split (Cacoullos, 1973;Huberty and Olejnik, 2006).…”

Section: Discussionmentioning

confidence: 99%

Does Zipf’s law hold for primate cities? Some evidence from a discriminant analysis of world countries

Portnov

2011

Jahrb Reg wiss

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may

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“…. , m. In order to overcome the hypothesis of the linear discriminant analysis concerned with the covariance matrix, quadratic analysis is used [11]. It considers the covariance matrix of each class and therefore diVers from the calculation in equation (10), becoming fk: ‰…z i ¡ · z k † 0 ¢ S ¡1 k ¢ …z i ¡ · z k †Šˆming … 11 † Quadratic discriminant analysis makes it possible to judge whether or not the considered samples of n w tiles have been properly extracted from one of the m class of marble.…”

Section: The Software Algorithmmentioning

confidence: 99%

“…Discriminant analysis is carried out to set those limits. Linear discriminant analysis uses the distance of Mahalanobis to classify tile i in compliance with class k [11]:…”

Section: The Software Algorithmmentioning

confidence: 99%

An automatic visual system for marble tile classification

Carrino

Polini

Turchetta

2002

Proceedings of the Institution of Mechanical Engineers, Part B:

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The international market of ornamental stone has seen the use of materials quarrying from East Europe, Africa, Asia and South America, characterized by a low cost of labour. This event has embittered the competition in this ®eld. Hence, it becomes fundamental to produce machined products of high quality in a more e cient way. This work aims to design and ful®l a prototype to automatically classify the Royal Perlato tiles of Coreno. It is based on arti®cial vision. The implemented hardware visual system is cheap because it is made up of components readily available and is easily obtainable by small and medium ornamental stone businesses. The developed software algorithm is based on a multifactor analysis of variance and a quadratic discriminant analysis. The experimental results show that the developed hardware and software system permits all the tiles of Royal Perlato of Coreno to be classi®ed properly. Moreover, the developed system not only improves the e ciency of the selection but also reduces the controversies between the manufacturer and buyer, making tile classi®cation more selective and increasing the number of qualitative classes taken into consideration. Finally, it allows the duplication on the selection line without altering data dispersion.

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A Bibliography of Discriminant Analysis

Cited by 18 publications

References 334 publications

Chemical Authentication of Extra Virgin Olive Oil Varieties by Supervised Chemometric Procedures

Chemical Authentication of Extra Virgin Olive Oil Varieties by Supervised Chemometric Procedures

Does Zipf’s law hold for primate cities? Some evidence from a discriminant analysis of world countries

An automatic visual system for marble tile classification

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