Beyond one billion time series: indexing and mining very large time series collections with $$i$$ SAX2+

Hexadecimal Aggregate Approximation Representation and Classification of Time Series Data

Time series data are widely found in finance, health, environmental, social, mobile and other fields. A large amount of time series data has been produced due to the general use of smartphones, various sensors, RFID and other internet devices. How a time series is represented is key to the efficient and effective storage and management of time series data, as well as being very important to time series classification. Two new time series representation methods, Hexadecimal Aggregate approXimation (HAX) and Point Aggregate approXimation (PAX), are proposed in this paper. The two methods represent each segment of a time series as a transformable interval object (TIO). Then, each TIO is mapped to a spatial point located on a two-dimensional plane. Finally, the HAX maps each point to a hexadecimal digit so that a time series is converted into a hex string. The experimental results show that HAX has higher classification accuracy than Symbolic Aggregate approXimation (SAX) but a lower one than some SAX variants (SAX-TD, SAX-BD). The HAX has the same space cost as SAX but is lower than these variants. The PAX has higher classification accuracy than HAX and is extremely close to the Euclidean distance (ED) measurement; however, the space cost of PAX is generally much lower than the space cost of ED. HAX and PAX are general representation methods that can also support geoscience time series clustering, indexing and query except for classification.