We denote this mapping by c u = closest(v i , C), where closest returns the centroid in C with the minimum distance to v i .
finally, the BoC k representation for each document where c corresponds to each of the k centroids and n = |{v BoC k (d j ) corresponds to a histogram of centroid frequencies, where each pair (c , n ) represents a centroid (meta-word) and its corresponding frequency in the document.