Automated systems for producing product recommendations to users is a relatively new area within the field of machine learning. Matrix factorization techniques have been studied to a large extent on data consisting of explicit feedback such as ratings, but to a lesser extent on implicit feedback data consisting of for example purchases.The aim of this study is to investigate how well matrix factorization techniques perform compared to other techniques when used for producing recommendations based on purchase data. We conducted experiments on data from an online bookstore as well as an online fashion store, by running algorithms processing the data and using evaluation metrics to compare the results. We present results proving that for many types of implicit feedback data, matrix factorization techniques are inferior to various neighborhood- and association rules techniques for producing product recommendations. We also present a variant of a user-based neighborhood recommender system algorithm \textit{(UserNN)}, which in all tests we ran outperformed both the matrix factorization algorithms and the k-nearest neighbors algorithm regarding both accuracy and speed. Depending on what dataset was used, the UserNN achieved a precision approximately 2-22 percentage points higher than those of the matrix factorization algorithms, and 2 percentage points higher than the k-nearest neighbors algorithm. The UserNN also outperformed the other algorithms regarding speed, with time consumptions 3.5-5 less than those of the k-nearest neighbors algorithm, and several orders of magnitude less than those of the matrix factorization algorithms.