this summary from the Beeb may help people get their heads round the difficult paper
"Imagine the ideal food. One that contains all the nutrients necessary to meet, but not exceed, our daily nutrient demands. If such a food existed, consuming it, without eating any other, would provide the optimal nutritional balance for our body.
Such a food does not exist. But we can do the next best thing.
The key is to eat a balance of highly nutritional foods, that when consumed together, do not contain too much of any one nutrient, to avoid exceeding daily recommended amounts. ...
Scientists studied more than 1,000 foods, assigning each a nutritional score. The higher the score, the more likely each food would meet, but not exceed your daily nutritional needs, when eaten in combination with others"
that is, in combination with others from each of the 4 different main categories (protein-rich, fat-rich (that's where the lard comes in of course), carbohydrate-rich, and low-calorie). The S2 data set focuses on the foods that scored well in this system, organised into the 4 categories (column on the left) while S1 has the whole list.