Notice that the 3 instances in figure 1 are not exactly equal. Rather, they are similar. Finding exactly equal patterns is trivial and meaningless.
Our algorithm implements this notion of tightness of similarity boundaries by using the iSAX time series approximation technique .
The different similarity boundaries are iSAX resolutions.
iSAX divides a time series into w (word length) frames, calculate each frame's average and then convert the list of averages to a sequence of symbols. The number of symbols a is the alphabet size or resolution. This process is depicted in figure 3 with a word size of 8 and two different resolutions 4 and 16.
Figure 3: iSAX conversion process for time series X using w=8 and a) a=4; b) a=16 (code provided by SAX authors).
The series smoothing caused by the frame averaging process and the resolution create similarity boundaries. The higher the resolution, the tighter the similarity boundaries are. Also, the closer two time series need to be in order to be considered as similar.