text: Recently, the method of b-bit minwise hashing has been applied to large-scale linear learning and sublinear time near-neighbor search. The major drawback of minwise hashing is the expensive preprocessing cost, as the method requires applying (e.g.,) k=200 to 500 permutations on the data. The testing time can also be expensive if a new data point (e.g., a new document or image) has not been processed, which might be a significant issue in user-facing applications. We develop a very simple solution based on one permutation hashing. Conceptually, given a massive binary data matrix, we permute the columns only once and divide the permuted columns evenly into k bins; and we simply store, for each data vector, the smallest nonzero location in each bin. The interesting probability analysis (which is validated by experiments) reveals that our one permutation scheme should perform very similarly to the original (k-permutation) minwise hashing. In fact, the one permutation scheme can be even slightly more accurate, due to the "sample-without-replacement" effect. Our experiments with training linear SVM and logistic regression on the webspam dataset demonstrate that this one permutation hashing scheme can achieve the same (or even slightly better) accuracies compared to the original k-permutation scheme. To test the robustness of our method, we also experiment with the small news20 dataset which is very sparse and has merely on average 500 nonzeros in each data vector. Interestingly, our one permutation scheme noticeably outperforms the k-permutation scheme when k is not too small on the news20 dataset. In summary, our method can achieve at least the same accuracy as the original k-permutation scheme, at merely 1 k of the original preprocessing cost.
  @cite_19: Minwise hashing is a standard technique in the context of search for efficiently computing set similarities. The recent development of b-bit minwise hashing provides a substantial improvement by storing only the lowest b bits of each hashed value. In this paper, we demonstrate that b-bit minwise hashing can be naturally integrated with linear learning algorithms such as linear SVM and logistic regression, to solve large-scale and high-dimensional statistical learning tasks, especially when the data do not fit in memory. We compare b-bit minwise hashing with the Count-Min (CM) and Vowpal Wabbit (VW) algorithms, which have essentially the same variances as random projections. Our theoretical and empirical comparisons illustrate that b-bit minwise hashing is significantly more accurate (at the same storage cost) than VW (and random projections) for binary data.
  @cite_16: We have developed an efficient way to determine the syntactic similarity of files and have applied it to every document on the World Wide Web. Using this mechanism, we built a clustering of all the documents that are syntactically similar. Possible applications include a "Lost and Found" service, filtering the results of Web searches, updating widely distributed web-pages, and identifying violations of intellectual property rights.
  @cite_17: 
summary: Interestingly, in the original minwise hashing'' paper @cite_16 (we use quotes because the scheme was not called minwise hashing'' at that time), only one permutation was used and a sample was the first @math nonzeros after the permutation. After the authors of @cite_16 realized that the estimators could not be written as an inner product and hence the scheme was not suitable for many applications such as sublinear time near neighbor search using hash tables, they quickly moved to the @math -permutation minwise hashing scheme @cite_17 . In the context of large-scale linear learning, the importance of having estimators which are inner products should become more obvious after @cite_19 introduced the idea of using ( @math -bit) minwise hashing for linear learning.