On the Lattice of Conceptual Measurements

Beyond that, almost every data set is further scaled prior to (data)processing to meet the requirements of the employed data analysis method, such as the introduction of artificial metrics, the numerical representation of nominal features, etc. This scaling is usually accompanied by a grade of detail, which in turn is becoming more and more of a problem for data science tasks as the availability of features increases and their human explainability decreases. Often used methods to deal with this problem from the field of machine learning, such as principal component analysis, do enforce particular, possible inapt, levels of measurement, e.g., food tastes represented by real numbers, and amplify the problem for explainability. Therefore, understanding the set of possible scaling maps, identifying its (algebraic) properties, and deriving to some extent human explainable control over it, is a pressing problem. This is especially important since found patterns and dependencies may be artifacts of some scaling map and may therefore corrupt any subsequent task,e.g., classification tasks.