I'm trying to implement the algorithm described in Natarajan (1995, p .3) but I have a regrettably poor grasp of how to read the notation involved. I've managed to tease out most of it (I think) but I'm stumped on this bit:
choose $k \in \{1,2,...,n\} - \tau$ such that $a_k^{(r)}$ of $\mathbf{A}^{(r)}$ is closest to $b^{(r)}$
Before that point, it establishes the initial state $\tau \leftarrow \phi$, and I've gathered that capital Phi is either the reciprocal of the golden ratio or the CDF of the standard normal distribution. Looking forward, I see $\tau \leftarrow \tau \cup \{k\}$, which I believe would indicate the latter.
Unfortunately, neither case really makes sense to me because my intuition says $k \in \{1,2,...,n\}$ is going to be a scalar integer; a column index of A (because we're really choosing a column $a_k^{(r)}$ to project).
I'm clearly missing something, so I'd appreciate the help.