The problem of feature selection has been an area of considerable research in machine learning. Feature selection is known to be particularly difficult in unsupervised learning because different subgroups of features can yield useful insights into the same dataset. In other words, many theoretically-right answers may exist for the same problem. Furthermore, designing algorithms for unsupervised feature selection is technically harder than designing algorithms for supervised feature selection because unsupervised feature selection algorithms cannot be guided by class labels. As a result, previous work attempts to discover intrinsic structures of data with heavy computation such as matrix decomposition, and require significant time to find even a single solution. This paper proposes a novel algorithm, named Explainability-based Unsupervised Feature Value Selection (EUFVS), which enables a paradigm shift in feature selection, and solves all of these problems. EUFVS requires only a few tens of milliseconds for datasets with thousands of features and instances, allowing the generation of a large number of possible solutions and select the solution with the best fit. Another important advantage of EUFVS is that it selects feature values instead of features, which can better explain phenomena in data than features. EUFVS enables a paradigm shift in feature selection. This paper explains its theoretical advantage, and also shows its applications in real experiments. In our experiments with labeled datasets, EUFVS found feature value sets that explain labels, and also detected useful relationships between feature value sets not detectable from given class labels.