StreamKM++: A Clustering Algorithm for Data Streams∗

We develop a new k-means clustering algorithm for data streams, which we call StreamKM++. Our algorithm computes a small weighted sample of the data stream and solves the problem on the sample using the k-means++ algorithm [1]. To compute the small sample, we propose two new techniques. First, we use a non-uniform sampling approach similar to the k-means++ seeding procedure to obtain small coresets from the data stream. This construction is rather easy to implement and, unlike other coreset constructions, its running time has only a low dependency on the dimensionality of the data. Second, we propose a new data structure which we call a coreset tree. The use of these coreset trees signi cantly speeds up the time necessary for the non-uniform sampling during our coreset construction. We compare our algorithm experimentally with two well-known streaming implementations (BIRCH [16] and StreamLS [4, 9]). In terms of quality (sum of squared errors), our algorithm is comparable with StreamLS and signi cantly better than BIRCH (up to a factor of 2). In terms of running time, our algorithm is slower than BIRCH. Comparing the running time with StreamLS, it turns out that our algorithm scales much better with increasing number of centers. We conclude that, if the rst priority is the quality of the clustering, then our algorithm provides a good alternative to BIRCH and StreamLS, in particular, if the number of cluster centers is large. We also give a theoretical justi cation of our approach by proving that our sample set is a small coreset in low