Optimality of the Johnson-Lindenstrauss Lemma

For any d, n ≥ 2 and 1=(min{n, d})0.4999

[1]  Lloyd R. Welch,et al.  Lower bounds on the maximum cross correlation of signals (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[2]  W. B. Johnson,et al.  Extensions of Lipschitz mappings into Hilbert space , 1984 .

[3]  G. Pisier.  The volume of convex bodies and Banach space geometry , 1989 .

[4]  Noga Alon,et al.  Simple construction of almost k-wise independent random variables , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[5]  B. Bollobás.  THE VOLUME OF CONVEX BODIES AND BANACH SPACE GEOMETRY (Cambridge Tracts in Mathematics 94) , 1991 .

[6]  Noga Alon,et al.  Simple Construction of Almost k-wise Independent Random Variables , 1992, Random Struct. Algorithms.

[7]  Rafail Ostrovsky,et al.  Efficient search for approximate nearest neighbor in high dimensional spaces , 1998, STOC '98.

[8]  S. Muthukrishnan,et al.  Data streams: algorithms and applications , 2005, SODA '03.

[9]  Noga Alon,et al.  Problems and results in extremal combinatorics--I , 2003, Discret. Math..

[10]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[11]  Nikhil Srivastava,et al.  Graph sparsification by effective resistances , 2008, SIAM J. Comput..

[12]  Daniel M. Kane,et al.  Almost Optimal Explicit Johnson-Lindenstrauss Families , 2011, APPROX-RANDOM.

[13]  Piotr Indyk,et al.  Approximate Nearest Neighbor: Towards Removing the Curse of Dimensionality , 2012, Theory Comput..

[14]  David P. Woodruff,et al.  On Deterministic Sketching and Streaming for Sparse Recovery and Norm Estimation , 2012, APPROX-RANDOM.

[15]  David P. Woodruff,et al.  Optimal Bounds for Johnson-Lindenstrauss Transforms and Streaming Problems with Subconstant Error , 2011, TALG.

[16]  David P. Woodruff.  Sketching as a Tool for Numerical Linear Algebra , 2014, Found. Trends Theor. Comput. Sci..

[17]  David P. Woodruff,et al.  On deterministic sketching and streaming for sparse recovery and norm estimation , 2014 .

[18]  Michael B. Cohen,et al.  Dimensionality Reduction for k-Means Clustering and Low Rank Approximation , 2014, STOC.

[19]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[20]  Christos Boutsidis,et al.  Randomized Dimensionality Reduction for $k$ -Means Clustering , 2011, IEEE Transactions on Information Theory.

[21]  Kasper Green Larsen,et al.  The Johnson-Lindenstrauss lemma is optimal for linear dimensionality reduction , 2014, ICALP.

[22]  Noga Alon,et al.  Optimal Compression of Approximate Inner Products and Dimension Reduction , 2016, 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS).