I'm learning about spline regression right now and there's this notation of basis function.
$$f(X)=\sum^M_{m=1}B_mh_m(X)$$
This is the notation using is The Elements of Statistical Learning - Data Mining, Inference and Prediction. $B_m$ seems to be the function that's defined in that interval and they write basis functions are $h_1(X)=I(X<\epsilon_1)$ where $\epsilon_1$ is a knot. I'm having trouble understanding what a basis function is and what $f(X)$ is.