A representation of time series based on implicit polynomial curve

Implicit polynomial (IP) curve is applied to represent data set boundary in image processing and computer vision. In this work, we employed it to reduce dimensionality of time series and produce similarity measure for time series mining. To use IP curve, time series was transformed to star coordination series. Then the star coordination series was fitted by implicit polynomial curve. That is, IP curve approximated (IPA) time series. Lastly, similarity measure of the time series was produced from the fitting implicit polynomial curve. To guarantee no false negatives, the lower bounding lemma for the similarity measure based on IP curve (IPD) was proved. We extensively compared IPA with other similarity measure and dimension reduction techniques in classification frameworks. Experimental results from the tests on various datasets indicate that IPA is more efficient than other methods.

► Time series was transformed to star coordination series for representation.
► Fitting star coordination series with implicit polynomial curve.
► The coefficients of fitting implicit polynomial curve represents the time series.
► Implicit polynomial curve is efficient representation method for time series.