We present a new method for the understandable description of local temporal relationships in multivariate data, called Time Series Knowledge Mining (TSKM). We define the Time Series Knowledge Representation (TSKR) as a new language for expressing temporal knowledge in time interval data. The patterns have a hierarchical structure, with levels corresponding to the temporal concepts duration, coincidence, and partial order. The patterns are very compact, but offer details for each element on demand. In comparison with related approaches, the TSKR is shown to have advantages in robustness, expressivity, and com-prehensibility. The search for coincidence and partial order in interval data can be formulated as instances of the well known frequent item-set problem. Efficient algorithms for the discovery of the patterns are adapted accordingly. A novel form of search space pruning effectively reduces the size of the mining result to ease interpretation and speed up the algorithms. Human interaction is used during the mining to analyze and validate partial results as early as possible and guide further processing steps. The efficacy of the methods is demonstrated using two real life data sets. In an application to sports medicine the results were recognized as valid and useful by an expert of the field.
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