Abstract:
Machine learning libraries need static and dynamic clustering algorithms. The sliding window model or simpler models have dominated dynamic machine learning and data mining algorithm development. Many real-world applications require arbitrary deletions and insertions. Because of inappropriate content or privacy concerns, one may need to remove data items that are not the oldest. Clustering trajectory data may involve general update operations. The fully dynamic adversarial model yields a (2+)-approximation algorithm for the k-center clustering problem with “small” amortized cost. If the adversary doesn’t know our algorithm’s random choices, points can be added or removed arbitrarily. The amortized cost of our algorithm is poly-logarithmic when the ratio between the maximum and minimum distance between any two points in input is bounded by a polynomial and k and are constant. Our fully dynamic algorithm’s memory requirement is greatly reduced, but its approximation ratio is 4+. Our approach is validated by extensive experimental evaluation on dynamic data from Twitter, Flickr, and trajectory data.
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