# How to consider different samples in functional data clustering?

In the engineering context several data sources like different kinds of measurement signals (for example distances, angles and efficiencies) are very common. If it would be possible to observe these data for instance in unsupervised functional data clustering like [1] it would be a great effort for me.

If I would observe only one parameter the solution might me very clear for me (like the cited paper). But what if we consider several different signals? How would you include these in functional data clustering?

I'm very interested at your ideas.

[1] Jacques, J. & Preda, C.: Functional Data Clustering. A Survey. In: Advances in Data Analysis and Classification 8(3), S. 231-255. DOI:10.1007/s11634-013-0158-y

I think that what you describe is a standard application of multivariate functional data clustering. In the context of multivariate functional data each data unit is treated as the relation of a $d$-dimensional stochastic (often Gaussian) process $X := ( X_1, \dots , X_d )$.
Having said all that, if you look at the Jacques & Preda (2014) you will see that given you project the data to a lower dimensional manifold, multivariate clustering techniques are rather competitive. As a first, easy pass I would suggest you do just that: use an MvFPCA approach of your choice, get the projection scores and try a standard well-understood multivariate clustering approach. I have found mixture-models (like the ones in the CRAN package EMCluster) to work reasonably well but I am sure other techniques can give fruitful results too. Software-wise in R, the CRAN package Funclustering appears to have some MvFPCA out of the box; Happ & Greven (2015) have a package named MFPCA on github, Yang's et al. Singular Decomposition is available in the CRAN packagefdapace.