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If we have a column vector of timeseries ($n$ instances $\times$ $k$ observations in time) and $p$ number of transformations (e.g., derivative transformations) that can be applied to each of the time series. This can be represented as

  1. a multivariate time series for each $n$ instances (an $n \times k \times p$ array), or
  2. $p$ separate matrices ($n \times k$) which describe different characteristics of the time series.

Is there an advantage to taking a multivariate time series clustering approach (in the form of 1) vs. clustering each time series transformation separately (in the form of 2) and arriving at $p$ cluster categories for each instance?

Are there good techniques for handling such cases?

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A clear cut answer would depend on the time series, actual transformations and clustering algorithm you have in mind.
Reason is most clustering algorithms are based on different similarity function and this metric is based on the transformations themselves.
For example transformations that change scale(log) and clustering that based on euclidean distance are "losing" information.
Or a transformation that use binning(SAX) of the time series and a cosine-similarity based clustering might be a bad mix too.

Practice wise I would go with option number 2.
In my experience there exists a little number of transformations which extract the most relevant characteristics out of your time-series. These transformations would be most apparent when looking at each clustering result separately.

If I find any realted atricles on this, will add to my answer.
Hope this helps,

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