Data Analysis and Efficiency
Thursday, 10:30 AM – 12:00 PM
Chairs: Michael Mahoney
b-Bit Minwise Hashing
Ping Li, Christian Konig
This paper establishes the theoretical framework of b-bit minwise hashing. The original minwise hashing method has become a standard technique for estimating set similarity (e.g., resemblance) with applications in information retrieval, data management, computational advertising, etc. By only storing $b$ bits of each hashed value (e.g., b=1 or 2), we gain substantial advantages in terms of storage space. We prove the basic theoretical results and provide an unbiased estimator of the resemblance for any b. We demonstrate that, even in the least favorable scenario, using b=1 may reduce the storage space at least by a factor of 21.3 (or 10.7) compared to b=64 (or b=32), if one is interested in resemblance >0.5.
Max-Cover in Map-Reduce
Flavio Chierichetti, Ravi Kumar, Andrew Tomkins
The NP-hard Max-k-cover problem requires selecting k sets from a collection so as to maximize the size of the union. This classic problem occurs commonly in many settings in web search and advertising. For moderately-sized instances, a greedy algorithm gives an approximation of (1-1/e). However, the greedy algorithm requires updating scores of arbitrary elements after each step, and hence becomes intractable for large datasets. We give the first max cover algorithm designed for today’s large-scale commodity clusters. Our algorithm has provably almost the same approximation as greedy, but runs much faster. Furthermore, it can be easily expressed in the MapReduce programming paradigm, and requires only polylogarithmically many passes over the data. Our experiments on five large problem instances show that our algorithm is practical and can achieve good speedups compared to the sequential greedy algorithm.
Distributed Nonnegative Matrix Factorization for Web-Scale Dyadic Data Analysis on MapRedduce
Chao Liu, Hung-chih Yang, Jinliang Fan, Li-Wei He, Yi-Min Wang
The Web abounds with dyadic data that keeps increasing by every single second. Previous work has repeatedly shown the usefulness of extracting the interaction structure inside dyadic data [21, 9, 8]. A commonly used tool in extracting the underlying structure is the matrix factorization, whose fame was further boosted in the Netflix challenge [26]. When we were trying to replicate the same success on real-world Web dyadic data, we were seriously challenged by the scalability of available tools. We therefore in this paper report our efforts on scaling up the nonnegative matrix factorization (NMF) technique. We show that by carefully partitioning the data and arranging the computations to maximize data locality and parallelism, factorizing a tens of millions by hundreds of millions matrix with billions of nonzero cells can be accomplished within tens of hours. This result effectively assures practitioners of the scalability of NMF on Web-scale dyadic data.
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