Robust clustering algorithms
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One of the most widely used techniques for data clustering is agglomerative clustering. Such algorithms have been long used across any different fields ranging from computational biology to social sciences to computer vision in part because they are simple and their output is easy to interpret. However, many of these algorithms lack any performance guarantees when the data is noisy, incomplete or has outliers, which is the case for most real world data. It is well known that standard linkage algorithms perform extremely poorly in presence of noise. In this work we propose two new robust algorithms for bottom-up agglomerative clustering and give formal theoretical guarantees for their robustness. We show that our algorithms can be used to cluster accurately in cases where the data satisfies a number of natural properties and where the traditional agglomerative algorithms fail. We also extend our algorithms to an inductive setting with similar guarantees, in which we randomly choose a small subset of points from a much larger instance space and generate a hierarchy over this sample and then insert the rest of the points to it to generate a hierarchy over the entire instance space. We then do a systematic experimental analysis of various linkage algorithms and compare their performance on a variety of real world data sets and show that our algorithms do much better at handling various forms of noise as compared to other hierarchical algorithms in the presence of noise.