# Clustering of time series and their transformations

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?