Analytic continuation of similarity definition in time series
Gang Hua · Computer Engineering and Applications Journal · 2008
The similarity definition of the time series isn't definitely and uniformly represented.That causes great difficulties to the research.The object series are disassembled into multi sub-series whose dimension is equal to the reference series.So this problem can be transformed into the study of the similarity between the object sub-series and the reference series.To reduce the calculable complexity,the sub-series and reference series are transformed by the linear operator of isometrically isomorphism.The similarity relation is macroscopically described by using the sets theory,and the measurement function of series similarity is defined by the norm of vector remainder,which is the remainder between the vector of sub-series and reference series before transformation and the vector of sub-series and reference series after transformation.Then the similarity measurement is unified.The research result provides theory evidence for the similarity research of time series based on Fourier transformation and wavelet transformation.