Preconditioned Data Sparsification for Big Data with Applications to PCA and K-means

We analyze a compression scheme for large data sets that randomly keeps a small percentage of the components of each data sample. The benefit is that the output is a sparse matrix and therefore subsequent processing, such as PCA or K-means, is significantly faster, especially in a distributed-data setting. Furthermore, the sampling is single-pass and applicable to streaming data. The sampling mechanism is a variant of previous methods proposed in the literature combined with a randomized preconditioning to smooth the data. We provide guarantees for PCA in terms of the covariance matrix, and guarantees for K-means in terms of the error in the center estimators at a given step. We present numerical evidence to show both that our bounds are nearly tight and that our algorithms provide a real benefit when applied to standard test data sets, as well as providing certain benefits over related sampling approaches.Comment: 28 pages, 10 figure

Efficient & Effective Selective Query Rewriting with Efficiency Predictions

To enhance effectiveness, a user's query can be rewritten internally by the search engine in many ways, for example by applying proximity, or by expanding the query with related terms. However, approaches that benefit effectiveness often have a negative impact on efficiency, which has impacts upon the user satisfaction, if the query is excessively slow. In this paper, we propose a novel framework for using the predicted execution time of various query rewritings to select between alternatives on a per-query basis, in a manner that ensures both effectiveness and efficiency. In particular, we propose the prediction of the execution time of ephemeral (e.g., proximity) posting lists generated from uni-gram inverted index posting lists, which are used in establishing the permissible query rewriting alternatives that may execute in the allowed time. Experiments examining both the effectiveness and efficiency of the proposed approach demonstrate that a 49% decrease in mean response time (and 62% decrease in 95th-percentile response time) can be attained without significantly hindering the effectiveness of the search engine