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- W2970329193 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 R^n into a much lower-dimensional space 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 l_infinity-to-l_2 norm ratio. Recently, Freksen, Kamma, and Larsen (NeurIPS '18) closed this line of work by proving a tight tradeoff between l_infinity-to-l_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 l_infinity-to-l_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.
- W2970329193 created "2019-09-05" @default.
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- W2970329193 date "2019-03-08" @default.
- W2970329193 modified "2023-10-18" @default.
- W2970329193 title "Understanding Sparse JL for Feature Hashing" @default.
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