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.
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.