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• W1969281479 abstract "We show there is a distribution over linear mappings R:l1n -> l1O(d log d), such that with arbitrarily large constant probability, for any fixed d-dimensional subspace L, for all x ∈ L we have |x|1 ≤ |Rx|1 = O(d log d)|x|1. This provides the first analogue of the ubiquitous subspace Johnson-Lindenstrauss embedding for the l1-norm. Importantly, the target dimension and distortion are independent of the ambient dimension n. We give several applications of this result. First, we give a faster algorithm for computing well-conditioned bases. Our algorithm is simple, avoiding the linear programming machinery required of previous algorithms. We also give faster algorithms for least absolute deviation regression and l1-norm best fit hyperplane problems, as well as the first single pass streaming algorithms with low space for these problems. These results are motivated by practical problems in image analysis, spam detection, and tatistics, where the l1-norm is used in studies where outliers may be safely and effectively ignored. This is because the l1-norm is more robust to outliers than the l2-norm." @default.
• W1969281479 created "2016-06-24" @default.
• W1969281479 creator A5024805876 @default.
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• W1969281479 date "2011-06-06" @default.
• W1969281479 modified "2023-09-30" @default.
• W1969281479 title "Subspace embeddings for the L ₁ -norm with applications" @default.
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• W1969281479 doi "https://doi.org/10.1145/1993636.1993736" @default.
• W1969281479 hasPublicationYear "2011" @default.
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