SUPPORTING INFORMATION Embodied greenhouse gas emissions in diets

Analysis and interpretation of large amounts of data has become one of the most important research tasks in earth systems science. Machine learning techniques such as artificial neural networks (ANNs) have several advantages in this regard. They are not only able to replicate the computational power of their biological examples but also are able to represent nonlinear relations, are capable of incorporating new information that is fed in, and are robust in handling noisy data. However, ANNs need large amounts of homogeneous data and the operator has to provide plausible explanations about why they approximate a solution. For the particular food data used in this study, the features of the ANN approach were explicitly wanted, i.e. certain patterns for diets should be derived and an optimal embedding, which allows the assessment of food transition pathways. For our analysis we implemented a neural network approach consisting of: i) a self-organizing map (SOM-) [1] and ii) an algorithm providing a quantitative measure P of topological distortions (TOP) during the mapping of data on the neural network [2]. The employed model approach has been used for several other studies and has shown its effective performance in complex data analysis [3–6]. A SOM in particular can be interpreted as a clustering and non-linear dimensionality reduction technique. The SOM in addition tries to preserve the topological ordering of the input data in the low-dimensional network space. We