Privacy via the Johnson-Lindenstrauss Transform

Randomness Efficient Fast-Johnson-Lindenstrauss Transform with Applications in Differential Privacy and Compressed Sensing

This paper resolves an open problem raised by Blocki et al. (FOCS 2012), i.e., whether other variants of the Johnson-Lindenstrauss transform preserves differential privacy or not? We prove that a general class of random projection matrices that satisfies the Johnson-Lindenstrauss lemma also preserves differential privacy. This class of random projection matrices requires only n Gaussian samples...

Circulant Matrices and Differential Privacy

This paper resolves an open problem raised by Blocki et al. (FOCS 2012), i.e., whether other variants of the Johnson-Lindenstrauss transform preserves differential privacy or not? We prove that a general class of random projection matrices that satisfies the Johnson-Lindenstrauss lemma also preserves differential privacy. This class of random projection matrices requires only n Gaussian samples...

The Fast Johnson-lindenstrauss Transform

While we omit the proof, we remark that it is constructive. Specifically, A is a linear map consisting of random projections onto subspaces of Rd. These projections can be computed by n matrix multiplications, which take time O(nkd). This is fast enough to make the Johnson-Lindenstrauss transform (JLT) a practical and widespread algorithm for dimensionality reduction, which in turn motivates th...

A Survey of Johnson Lindenstrauss Transform - Methods, Extensions and Applications

A Derandomized Sparse Johnson-Lindenstrauss Transform

Recent work of [Dasgupta-Kumar-Sarlós, STOC 2010] gave a sparse Johnson-Lindenstrauss transform and left as a main open question whether their construction could be efficiently derandomized. We answer their question affirmatively by giving an alternative proof of their result requiring only bounded independence hash functions. Furthermore, the sparsity bound obtained in our proof is improved. T...