Adaptive segmentation-based symbolic representations of time series for better modeling and lower bounding distance measures

Time series data-mining algorithms usually scale poorly with regard to dimensionality. Symbolic representations have proven to be a very effective way to reduce the dimensionality of time series even using simple aggregations over episodes of the same length and a fixed set of symbols. However, computing adaptive symbolic representations would enable more accurate representations of the dataset without compromising the dimensionality reduction. Therefore we propose a new generic framework to compute adaptive Segmentation Based Symbolic Representations (SBSR) of time series. SBSR can be applied to any model but we focus on piecewise constant models (SBSRLO) which are the most commonly used. SBSR are built by computing both the episode boundaries and the symbolic alphabet in order to minimize information loss of the resulting symbolic representation. We also propose a new distance measure for SBSRLO tightly lower bounding the euclidean distance measure.