  Starting from a dataset with input/output time series generated by multiple
deterministic linear dynamical systems, this paper tackles the problem of
automatically clustering these time series. We propose an extension to the
so-called Martin cepstral distance, that allows to efficiently cluster these
time series, and apply it to simulated electrical circuits data. Traditionally,
two ways of handling the problem are used. The first class of methods employs a
distance measure on time series (e.g. Euclidean, Dynamic Time Warping) and a
clustering technique (e.g. k-means, k-medoids, hierarchical clustering) to find
natural groups in the dataset. It is, however, often not clear whether these
distance measures effectively take into account the specific temporal
correlations in these time series. The second class of methods uses the
input/output data to identify a dynamic system using an identification scheme,
and then applies a model norm-based distance (e.g. H2, H-infinity) to find out
which systems are similar. This, however, can be very time consuming for large
amounts of long time series data. We show that the new distance measure
presented in this paper performs as good as when every input/output pair is
modelled explicitly, but remains computationally much less complex. The
complexity of calculating this distance between two time series of length N is
O(N logN).
