The nearest-neighbor chain algorithm is an efficient method for performing agglomerative hierarchical clustering. It optimizes the standard agglomerative clustering process, reducing the naive implementation's runtime complexity from $O(n^3)$ to $O(n^2)$.

Algorithm Steps:

1. Initialize each data point as its own single-element cluster.
2. Initialize an empty stack $S$.
3. While there is more than one cluster remaining: a. If $S$ is empty, push an arbitrary remaining cluster onto $S$. b. Let $C_{top}$ be the cluster at the top of $S$. Find its nearest neighbor cluster, $C_{next}$. c. If $C_{next}$ is already in $S$, it must be the cluster immediately below $C_{top}$ on the stack (meaning they are mutual nearest neighbors). Pop both $C_{top}$ and $C_{next}$ from $S$, merge them into a new cluster, and update the pairwise distances. d. If $C_{next}$ is not in $S$, push $C_{next}$ onto $S$.

Note: Refer to "Modern hierarchical, agglomerative clustering methods" (Müllner, 2011) for detailed analysis and correctness proofs.