I have a time-series data set with ~20 observations with one variable of interest measured everyday for several months for each observation. If I plot the variable on a timeline for each observation separately, each observation will have its own unique pattern. My goal is to categorize these patterns into several groups. I can roughly do so by just looking at the plots themselves and compare them, but I do not know how to approach this problem from the statistical standpoint. Is there any tool / technique that will identify the patterns and categorize the observations based on that?
The most simple approach would be to:
compute statistical descriptors for each timeseries (such as mean, max, min, standard deviation or more sophicticated ones after fourier transformation in the frequency domain) and
then cluster the time-series in the feature space using algorithms such as DBSCAN (you could as well use k-means, yet you would have to define the target number of clusters k).
Yet the resulting clusters depend on the features/descriptors you chose. The choice of features is therefore critical and must be done using domain knowledge.