The underlying objective of food authentication studies is to determine whether unknown food samples have been correctly labeled. In this paper, we study three near-infrared (NIR) spectroscopic datasets from food samples of different types: meat samples (labeled by species), olive oil samples (labeled by their geographic origin) and honey samples (labeled as pure or adulterated by different adulterants). We apply and compare a large number of classification, dimension reduction and variable selection approaches to these datasets. NIR data pose specific challenges to classification and variable selection: the datasets are high - dimensional where the number of cases (n) << number of features (p) and the recorded features are highly serially correlated. In this paper, we carry out a comparative analysis of different approaches and find that partial least squares, a classic tool employed for these types of data, outperforms all the other approaches considered.