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In this paper, we first propose a new iterative algorithm, called the K-sets+algorithm for clustering data points in a semi-metric space, where the distancemeasure does not necessarily satisfy the triangular inequality. We show thatthe K-sets+ algorithm converges in a finite number of iterations and it retainsthe same performance guarantee as the K-sets algorithm for clustering datapoints in a metric space. We then extend the applicability of the K-sets+algorithm from data points in a semi-metric space to data points that only havea symmetric similarity measure. Such an extension leads to great reduction ofcomputational complexity. In particular, for an n * n similarity matrix with mnonzero elements in the matrix, the computational complexity of the K-sets+algorithm is O((Kn + m)I), where I is the number of iterations. The memorycomplexity to achieve that computational complexity is O(Kn + m). As such, boththe computational complexity and the memory complexity are linear in n when then * n similarity matrix is sparse, i.e., m = O(n). We also conduct variousexperiments to show the effectiveness of the K-sets+ algorithm by using asynthetic dataset from the stochastic block model and a real network from theWonderNetwork website.

K-sets+: a Linear-time Clustering Algorithm for Data Points with a Sparse Similarity Measure