Time-series data subspaces that can be considered equivalent are called equivalence structures. Extraction of equivalence structures can be applied for various purposes, such as feature extraction, the analysis of neural network behavior, and dimension matching of different datasets. However, the extraction requires comparisons of all possible subspaces of the whole space of a multidimensional time series dataset, and the comparisons cause combinatorial explosion with the number of the dimensions of subspaces. In this paper, we analyze the characteristics of equivalence structures for the development of fast equivalence structure extraction.