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• W2921052765 abstract "Feature hashing and other random projection schemes are commonly used to reduce the dimensionality of feature vectors. The goal is to efficiently project a high-dimensional feature vector living in $mathbb{R}^n$ into a much lower-dimensional space $mathbb{R}^m$, while approximately preserving Euclidean norm. These schemes can be constructed using sparse random projections, for example using a sparse Johnson-Lindenstrauss (JL) transform. A line of work introduced by Weinberger et. al (ICML '09) analyzes the accuracy of sparse JL with sparsity 1 on feature vectors with small $ell_infty$-to-$ell_2$ norm ratio. Recently, Freksen, Kamma, and Larsen (NeurIPS '18) closed this line of work by proving a tight tradeoff between $ell_infty$-to-$ell_2$ norm ratio and accuracy for sparse JL with sparsity $1$. In this paper, we demonstrate the benefits of using sparsity $s$ greater than $1$ in sparse JL on feature vectors. Our main result is a tight tradeoff between $ell_infty$-to-$ell_2$ norm ratio and accuracy for a general sparsity $s$, that significantly generalizes the result of Freksen et. al. Our result theoretically demonstrates that sparse JL with $s > 1$ can have significantly better norm-preservation properties on feature vectors than sparse JL with $s = 1$; we also empirically demonstrate this finding." @default.
• W2921052765 created "2019-03-22" @default.
• W2921052765 creator A5005798722 @default.
• W2921052765 date "2019-03-08" @default.
• W2921052765 modified "2023-09-23" @default.
• W2921052765 title "Understanding Sparse JL for Feature Hashing" @default.
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