# Clustering of functional data

What are the commonly use techniques to cluster function ? In my case it is time series data from different subject. My time is discrete (1, 2 till 24) and my response is continuous.

• Do you have continuous or discrete time? What is the range? Reals or integer? – Karel Macek Nov 3 '17 at 6:06
• @KarelMacek i have updated my question to answer your comments thank you – Wis Nov 3 '17 at 6:08
• Is it fair to say that loosely "functional data" is time-series data? – Vladislavs Dovgalecs Nov 3 '17 at 16:23

For clustering, we need to measure the distance of the functions. There are some standard metrics in functional analysis based on some norms, e.g. P norms like $$\int_X ||f(x)-g(x)||dx$$ check this https://en.wikipedia.org/wiki/Lp_space#The_p-norm_in_finite_dimensions . The trick is that P norms for discrete cases (and your data belong to that) correpond to standard Manhatan/Eucliean etc metrics that are commonly used in clustering of all arts such as k-means or hierarchical.