The use of a logarithmic term when computing TF and IDF values is motivated by Zipf’s law about the frequency of word occurrences in English texts.

The IDF monotonicity assumption states that terms that appear in only a few documents of the corpus are more important than terms that appear in many documents.

Lemmatization or stemming is used to identify different parts-of-speech in texts when creating a VSM for item representation.

Casefolding as a text preprocessing technique to create a TF-IDF item representation may introduce semantic ambiguities of terms, i.e., terms with different meanings are mapped to the same term.

When dealing with short texts (e.g., status messages or microblogs), the logarithmic variant of the TF formulation typically outperforms using a binary TF formulation for item representation.

Content-based filtering is well-suited to recommend “long tail” items because content features are less affected by popularity biases than user ratings, and are therefore more objective.

The vector space model (VSM) represents each document as a fixed-dimensional vector of term weights.

The regularization term in the optimization function of an SGD-trained MF model is used to avoid unbound values in the w_u and h_i vectors.

The algorithm for user-based CF can be adopted to integrate relational information between users. For this purpose, the similarity term sim(i,j) between users i and j can be computed using Katz centrality or K-path centrality.

CF approaches are prone to a community bias which refers to the fact that the preferences of the user base are not representative of the population at large.