The growing demand for eliciting useful knowledge from data calls for techniques that can discover insights (in the form of patterns) that users need. Methodologies for describing intrinsic and relevant properties of data through the extraction of useful patterns, however, work on fixed input data, and the data representation, therefore, constrains the discovered insights. In this regard, this paper aims at providing foundations to make the descriptive knowledge that is extracted by pattern mining more user-centric by relying on flexible data structures defined on two different perspectives: concepts and data records. In this sense, items in data can be grouped into abstract terms through subjective hierarchies of concepts, whereas data records can also be organized based on the users' subjective perspective. A series of easy-to-follow toy examples are considered for each of the two perspectives to demonstrate the usefulness and necessity of the proposed foundations in pattern mining. Finally, aiming at experimentally testing whether classical pattern mining algorithms can be adapted to such flexible data structures, the experimental analysis comprises different methodologies, including exhaustive search, random search, and evolutionary approaches. All these approaches are based on well-known and widely recognized techniques to demonstrate the usefulness of the provided foundations for future research works and more efficient and specifically designed algorithms. Obtained insights demonstrate the importance of working with subjectivity: an item is a type of soda but belongs to a pack, including two or more soda types.