This algorithm is claimed to manage with the weakness of the
simple and fast-kmedoids (fastkmed). The origin of the
algorithm is a centroid-based algorithm by applying the Euclidean distance.
Then, Bbecause the function is a medoid-based algorithm, the object mean
(centroid) and variance are redefined into medoid and deviation, respectively.
The alpha argument is a stretch factor, i.e. a constant defined by
the user. It is applied to determine a set of medoid candidates. The medoid
candidates are calculated by
\(O_c = \){\(X_i\)| \(\sigma_i \leq \alpha \sigma,
i = 1, 2, \ldots, n\) },
where \(\sigma_i\) is the average deviation of object i, and
\(\sigma\) is the average deviation of the data set. They are computed by
$$\sigma = \sqrt{\frac{1}{n-1} \sum_{i=1}^n d(O_i, v_1)}$$
$$\sigma_i = \sqrt{\frac{1}{n-1} \sum_{i=1}^n d(O_i, O_j)}$$
where n is the number of objects, \(O_i\) is the object i,
and \(v_1\) is the most centrally located object.