K-means clustering of proportional data using L1 distance

We present a new L1-distance-based k-means clustering algorithm to address the challenge of clustering high-dimensional proportional vectors. The new algorithm explicitly incorporates proportionality constraints in the computation of the cluster centroids, resulting in reduced L1 error rates. We compare the new method to two competing methods, an approximate L1-distance k-means algorithm, where the centroid is estimated using cluster means, and a median L1 k-means algorithm, where the centroid is estimated using cluster medians, with proportionality constraints imposed by normalization in a second step. Application to clustering of projects based on distribution of labor hours by skill illustrates the advantages of the new algorithm.