Using Unlabelled Data to Update Classification Rules with Applications in Food Authenticity Studies

Abstract

An authentic food is one that is what it purports to be. Food processors and consumers need to be assured that, when they pay for a specific product or ingredient, they are receiving exactly what they pay for. Classification methods are an important tool in food authenticity studies where they are used to assign food samples of unknown type to known types. A classification method is developed where the classification rule is estimated by using both the labelled and the unlabelled data, in contrast with many classical methods which use only the labelled data for estimation. This methodology models the data as arising from a Gaussian mixture model with parsimonious covariance structure, as is done in model-based clustering. A missing data formulation of the mixture model is used and the models are fitted by using the EM and classification EM algorithms. The methods are applied to the analysis of spectra of food-stuffs recorded over the visible and near infra-red wavelength range in food authenticity studies. A comparison of the performance of model-based discriminant analysis and the method of classification proposed is given. The classification method proposed is shown to yield very good misclassification rates. The correct classification rate was observed to be as much as 15% higher than the correct classification rate for model-based discriminant analysis. Copyright 2006 Royal Statistical Society.

Butter and butter oil classification by PTR-MS

“…An authentic food is one, which conforms to the description that is provided by the producer. The description may relate to the process history of a product, its geographic origin or the species or variety of ingredients [1]. Product labelling is one of the issues that helps the consumer and the authorities to undertake legal action, because an infringement of the label could result in a charge in the court of justice.…”

“…Traditional analytical strategies to guarantee quality and to uncover adulteration have relied on determination of the amount of marker compound(s) in a suspect material and a subsequent comparison of the value(s) obtained with those established for equivalent material of known provenance [1].…”

Bayesian kernel projections for classification of high dimensional data

“…The data come from a food authenticity study [Dean et al, 2006]: analysis of spectra of raw homogenized meat samples recorded over the visible and near infra- Note that these wavelengths differentiate the colour of the samples so the segregation is between the red and white meat groups.…”

Generalized mixture models, semi-supervised learning, and unknown class inference

“…Semi-supervised learning methods based on mixture models seek to improve classification results for known classes by using both labeled and unlabeled data (see for instance Dean et al 2006). Although the resulting known-class inference is improved, it does not provide a solution for detecting unknown classes.…”

“…Here, the summation over the labeled data only contributes to the overall log-likelihood when the labeled data point originates from the appropriate generating component or class (see Dean et al 2006;Miller and Uyar 1997). This is an extension of the standard mixture model and the parameter space consists of = {α, {θ k } M k=1 }.…”