General methods take advantage of developing frameworks for data mining and machine learning that can be specialized for efficiency according to the problem domain. This paper discusses a declarative modeling method as a form of relational learning. The generic problem is relational data factorization (ReDF): “given a conjunctive query and the input relation, the problem is to compute the extensions of the relations used in the query.”

The solution of an ReDF problem can be only some approximation in general, so constraints and scoring functions belong to the task description. ReDF is general enough to model “a wide range of well-known data analysis problems,” for example, tiling and discriminative k-pattern set mining. This allows one to find commonalities among these domains and the methods applied for them.

The paper translates the ReDF problem to answer set programming (ASP) [1], so runnable prototypes can be described in a declarative way and then the implementation can be refined further. For finding k patterns or tiles, the authors present two algorithms, a greedy one and a sampling one. The maximum k-tiling problem (being not unique) is formalized using an iterative greedy algorithm in ASP.

The authors use Gebser et al. [2] and seven different datasets to compare their implementation to others in the literature. Compared to generic counterparts, their results are good and well suited to make prototypes. Of course, their program is far behind implementations applying specific algorithms.

The paper’s themes are multifold and arborescent. However, its sophisticated structure, clear descriptions, and recurring variants of the example help with understanding. The three authors’ various backgrounds and roles complement each other well.

I recommend this paper for those who are interested in a logic-based treatment of data mining and machine learning methods.