I have thousands of times series of different length and different time. I want to group them together so that I know the optimal ones to pick as input for a ML algorithm and to document how they are related. Those times series are from stations, some of them inactive and some still active.
My goal would eventually be to use data from active stations in the cluster in order to model the inactive station by assuming that the correlation of the signal will stay the same in time.
I am able to get the euclidean distance and a distance matrix ( used for DTW) for series that overlap but the issue is that most of them will not overlap together. So if I summarize the distance value and put it into a global distance matrix I will have a sparse distance matrix.
I know that hierarchical clustering can deal with data considering only their distance to each other but the distance matrix may contain only finite values (in the scipy version) and adding any sort of fake distance values will greatly affect clustering.
I am aware that DBSCAN might be my only option since I only have sparse distance measure and that any other approach with the raw data will not be possible due to their varying total length and their varying start and end period.
Is DBSCAN the only solution to these types of problems or are there other algorithms or methodology that can cluster using only sparse distance data ?