The shadow value of each data point is defined as twice the distance to
the closest centroid divided by the sum of distances to closest and
second-closest centroid. If the shadow values of a point is close to 0, then the
point is close to its cluster centroid. If the shadow value is close to 1, it
is almost equidistant to the two centroids. Thus, a cluster that is
well separated from all other clusters should have many points with
small shadow values.
The silhouette value of a data point is defined as the scaled difference
between the average dissimilarity of a point to all points in its own
cluster to the smallest average dissimilarity to the points of a
different cluster. Large silhouette values indicate good separation.
The main difference between silhouette values and shadow values is that
we replace average dissimilarities to points in a cluster by
dissimilarities to point averages (=centroids). See Leisch (2009) for
details.