Exact Primitives for Time Series Data Mining

Data mining and knowledge discovery algorithms for time series data use primitives such as bursts, periods, motifs, outliers and shapelets as building blocks. For example a model of global temperature considers both bursts (i.e. solar fare) and periods (i.e. sunspot cycle) of the sun. Algorithms for finding these primitives are required to be fast to process large datasets. Because exact algorithms that guarantee the optimum solutions are very slow for their immense computational requirements, existing algorithms find primitives approximately. This thesis presents efficient exact algorithms for two primitives, time series motif and time series shapelet. A time series motif is any repeating segment whose appearances in the time series are too similar to happen at random and thus expected to bear important information about the structure of the data. A time series shapelet is any subsequence that describes a class of time series differentiating from other classes and thus can be used to classify unknown instances. We extend the primitives for different environments. We show exact methods to find motifs in three different types of time series data. They are the in-memory datasets suitable for batched processing, the massive archives of time series stored in hard drives and finally, the streaming time series with limited storage. We also describe an exact algorithm for logical-shapelet discovery that combines multiple shapelets to better describe complex concepts. We use efficient bounds to the goodness measures to increase the efficiency of the exact algorithms. The algorithms are orders of magnitude faster than the trivial solutions and successfully discover motifs/shapelets of real time series from diverse sensors such as EEG, ECG, EPG, EOG, Accelerometers and Motion captures. We show applicability of these algorithms as subroutines in high-level data mining tasks such as summarization, classification and compression.