This paper presents FITS, or Feature-value / Instance Transposition Selection, a method for unsupervised clustering. FITS is a tractable, explicable clustering method, which leverages the unsupervised feature value selection algorithm known as UFVS in the literature. FITS combines repeated rounds of UFVS with alternating steps of matrix transposition to produce a set of homogenous clusters that describe data well. By repeatedly swapping the role of feature and instance and applying the same selection process to them, FITS leverages UFVS's speed and can perform clustering in our experiments in tens milliseconds for datasets of thousands of features and thousands of instances.We performed feature selection-based clustering on two real-world data sets. One is aimed at topic extraction from Twitter data, and the other is aimed at gaining awareness of energy conservation from time-series power consumption data. This study also proposes a novel method based on iterative feature extraction and transposition. The effectiveness of this method is shown in an application of Twitter data analysis. On the other hand, a more straightforward use of feature selection is adopted in the application of time series power consumption data analysis.