Order, duration and gap - take them all

Based on a formal characterization of time-series and state-sequences, a new distance measurement dealing with both non-temporal and temporal distances for state-sequence matching is proposed in this paper. In addition to formulating the temporal order over state-sequences, it also takes into account of temporal distances in terms of both the temporal duration of each state and the temporal gaps between adjacent pairs of states, which are neglected in most existing approaches to time-series and state-sequence matching. In particular, when specialized as a real-penalty-style measurement by means of reifying the cost functions, it is more flexible with regards to real-life applications than binary-value-style distance measurements. In addition, it is more robust than those existing real-penalty-style distance measurements since it can filter out noise during the matching procedure. Experimental results on reconstructed time-series data from UCI KDD Archive demonstrate that it can tackle the most general problems in matching time-series data with rich temporal information.