The simple algorithm is to build a correlation matrix between of purchases between all items in the store. Then, when given an item to generate recommendations

The simple algorithm is to build a correlation matrix between of purchases between all items in the store. Then, when given an item to generate recommendations for, you provide the other items with the highest scores, with a "top sellers" correction for the items that are correlated with everything. I used to work for a company that implemented similar recommendation services. We approached this problem by modelling whether or not a category was likely to have recurring purchases.