In this paper, we propose a class of algorithms for detecting the change-points in time-series data based on subspace identification, which is originaly a geometric approach for estimating linear state-space models generating time-series data. Our algorithms are derived from the principle that the subspace spanned by the columns of an observability matrix and the one spanned by the subsequences of time-series data are approximately equivalent. In this paper, we derive a batch-type algorithm applicable to ordinary time-series data, i.e., consisting of only output series, and then introduce the online version of the algorithm and the extension to be available with input-output time-series data. We illustrate the superior performance of our algorithms with comparative experiments using artificial and real datasets.