We Have Seen the Future, and It Is Symbolic

Many high level representations of time series have been proposed for data mining. One representation that the data mining community has not considered in detail is the discretization of the original data into symbolic strings. At first glance this seems a surprising oversight. There is an enormous wealth of existing algorithms and data structures that allow the efficient manipulations of strings. Such algorithms have received decades of attention in the text retrieval community, and more recent attention from the bioinformatics community. Some simple examples of tools that are not defined for real-valued sequences but are defined for symbolic approaches include hashing, Markov models, suffix trees, decision trees etc. There is, however, a simple explanation for the data mining communitys lack of interest in string manipulation as a supporting technique for mining time series. If the data are transformed into virtually any of the other popular data mining representations, then it is possible to measure the similarity of two time series in that representation space, such that the distance is guaranteed to lower bound the true distance between the time series in the original space. This simple fact is at the core of almost all algorithms in time series data mining and indexing. However, in spite of the fact that there are dozens of techniques for producing different variants of the symbolic representation, there is no known method for calculating the distance in the symbolic space, while providing the lower bounding guarantee.