How to cluster a set of objects each with its' own set of data?

I have a problem where I have a set of objects (say smartphones for ease of explanation). For each phone, we collected several characteristic features (such as duration of calls, how many calls made, received etc) over a period of 3 months (say). Now based on these collected datasets, we need to group the phones into clusters. The situation is kind of like in the following figure:

My first thought was to follow what we do during working with images. Make a vector out of the image matrix and then do the clustering. In my case, we make the vector by maintaining the temporal sequence. So for each phone, if the size of the dataset be m x p and there are n such phones, we build a dataset with size n x (m x p). However, I cannot decide if there is any problem with this approach or whether it will achieve what we want.

I am looking for some ideas.Any suggestions would be greatly appreciated.

Thanks and regards.