Główne pojęcia
The authors propose a method using deep random features to compress point sets efficiently while preserving pairwise distances with high probability.
Streszczenie
The content introduces a novel approach to compressing point sets by constructing random nonlinear maps that maintain approximate distances between points. The method offers advantages over existing techniques and provides insights into the compression of data sets. The theoretical foundation, practical applications, and comparisons with other methods are discussed in detail.
Statystyki
For a point set S, the map ϕℓ : Rd → N −1/2{−1, 1}N has the property that storing ϕℓ(S) (a sketch of S) allows one to report pairwise squared distances between points in S up to some multiplicative (1 ± ǫ) error.
Compared to existing techniques, the maps offer several advantages.
The number of bits of the sketch is Θ n log n ǫ2 (log 1 m)2 log2(π/√ 2).
Cytaty
"The main advantage of our maps ϕℓ over random linear maps is that ours map point sets directly into the discrete cube N −1/2{−1, 1}N."
"Our main result shows that this is possible in certain cases."