Given a large collection of objects, finding all pairs of similar objects, namely similarity join, is widely used to solve various problems in many application domains.Computation time of similarity join is critical issue, since similarity join requires computing similarity values for all possible pairs of objects. Several existing algorithms adopt prefix filtering to avoid unnecessary similarity computation; however, existing algorithms implementing the prefix filtering have inefficiency in filtering out object pairs, in particular, when aggregate weighted similarity function, such as cosine similarity, is used to quantify similarity values between objects. This is mostly caused by large prefixes the algorithms select. In this paper, we propose an alternative method to select small prefixes by exploiting the relationship between arithmetic mean and geometric mean of elements' weights. A new algorithm, MMJoin, implementing the proposed methods dramatically reduces the average size of prefixes without much overhead. Finally, it saves much computation time. We demonstrate that our algorithm outperforms a state-of-the-art one with empirical evaluation on large-scale real world datasets.
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