Reducing the time complexity of the fuzzy c-means algorithm

In this paper, we present an efficient implementation of the fuzzy c-means clustering algorithm. The original algorithm alternates between estimating centers of the clusters and the fuzzy membership of the data points. The size of the membership matrix is on the order of the original data set, a prohibitive size if this technique is to be applied to very large data sets with many clusters. Our implementation eliminates the storage of this data structure by combining the two updates into a single update of the cluster centers. This change significantly affects the asymptotic runtime as the new algorithm is linear with respect to the number of clusters, while the original is quadratic. Elimination of the membership matrix also reduces the overhead associated with repeatedly accessing a large data structure. Empirical evidence is presented to quantify the savings achieved by this new method.