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**Variable selection and updating in model-based discriminant analysis for high dimensional data with food authenticity applications.**
*(English)*
Zbl 1189.62105

Summary: Food authenticity studies are concerned with determining if food samples have been correctly labeled or not. Discriminant analysis methods are an integral part of the methodology for food authentication. Motivated by food authenticity applications, a model-based discriminant analysis method that includes variable selection is presented. The discriminant analysis model is fitted in a semi-supervised manner using both labeled and unlabeled data. The method is shown to give excellent classification performance on several high-dimensional multiclass food authenticity data sets with more variables than observations. The variables selected by the proposed method provide information about which variables are meaningful for classification purposes. A headlong search strategy for variable selection is shown to be efficient in terms of computation and achieves excellent classification performance. In applications to several food authenticity data sets, our proposed method outperformed default implementations of Random Forests, AdaBoost, transductive SVMs and Bayesian Multinomial Regression by substantial margins.

### MSC:

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62P99 | Applications of statistics |

65C60 | Computational problems in statistics (MSC2010) |

### Keywords:

food authenticity studies; headlong search; model-based discriminant analysis; normal mixture models; semi-supervised learning; updating classification rules; variable selection
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\textit{T. B. Murphy} et al., Ann. Appl. Stat. 4, No. 1, 396--421 (2010; Zbl 1189.62105)

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