Collaborative filtering is a technique used to predict whether a particular user will like a particular item. User-based or item-based collaborative techniques have been used extensively in many commercial recommender systems. In this paper, a hybrid collaborative filtering method that combines user-based and item-based methods using a low-dimensional linear model is proposed. The proposed method solves the problems of sparsity and a large database by using NMF among the low-dimensional linear models. In collaborative filtering systems the methods using the NMF are useful in expressing users as semantic relations. However, they are model-based methods and the process of computation is complex, so they can not recommend items dynamically. In order to complement the shortcomings, the proposed method clusters users into groups by using NMF and selects features of groups by using TF-IDF. Mutual information is then used to compute similarities between items. The proposed method clusters users into groups and extracts features of groups on offline and determines the most suitable group for an active user using the features of groups on online. Finally, the proposed method reduces the time required to classify an active user into a group and outperforms previous methods by combining user-based and item-based collaborative filtering methods.