# How to find modes of multivariate time series dataset [closed]

I have a dataset of different multivariate time series (with features $$x_0, y_0, x_1, y_1$$ that are coordinates of starting and ending point of an event within each time series' observation. The data can be therefore visualised as a set of movements (see the plotted sample below, each color refer to a different time series).

I want to find time series that are modes for my dataset, in the sense that they are representatives of high density regions. How can I do that?

One approach that comes to my mind is DBSCAN clustering (at least for finding dense regions) using DTW distances (DTW distances seems to be really appropriate in case of my data). However, adjusting eps and MinPts parameter seems to be cumbersome in my case as I'm actually not having one, but around 100 datasets that would be supposed to be clustered that way.

Another approach is can imagine is to calculate distance matrix using DTW distance. Then for each observation find the number of neighbours that are within some radius $$\delta$$, count it and choose as a mode those observations that are above some threshold $$m$$. However, this involves choosing 2 parameters arbitrary and I can't really figure out a way that would help to justify the choices. @edit: After some thought, I'm afraid that in this approach I can end up with having few "modes" for one density region...

My question therefore is: what are the ways to find the modes (understood as a local maximum of density) of the dataset in general? And which can work with distances (which I think makes them applicable to my case)?

## closed as unclear what you're asking by mdewey, user158565, mkt, whuber♦Jan 14 at 14:42

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• Could you explain what you mean by "regions"? What do you conceive of as the metric space in which these time series exist? Would it have one dimension, two, four, $4n$ for $n$ observations, or something else? What is the metric (the distance function)? – whuber Jan 14 at 14:41