Runtime Quality Prediction for Web Services via Multivariate Long Short-Term Memory

Algorithm 1

Time series selection and alignment.

	Input: a group of long-term time series data , the maximal size of the subset, and the similarity threshold
	Output: a subset of , in which any time series is highly similar to each other
(1)	Initialize distance matrix .
(2)	For each node in :
(i)	If ,
(a)	First, calculate the time-lag cross-correlation coefficient of any two time series and to get the optimal time delay between them, and align the two time series according to the optimal time delay.
(b)	Then, calculate the values of , where is the optimal warping path between the aligned and .
(ii)	Else, .
(3)	After calculating the distance matrix , calculate the similarity of a time series to the rest of other time series data as .
(4)	Sort the time series according to in ascending order: if and only if .
(5)	Select a subset of according to the following rules. For the sorted time series , choose the first number of time series as the final subset.