Well-separated pair decomposition (WSPD) is a well known geometric decomposition used for encoding distances, introduced in a seminal paper by Paul B. Callahan and S. Rao Kosaraju in 1995. WSPD compresses
pairwise distances of
n given points from
in
space for a fixed dimension
d. However, the main problem with this remarkable decomposition is the “hidden” dependence on the dimension
d, which in practice does not allow for the computation of a WSPD for any dimension
or
at best. In this work, I will show how to compute a WSPD for points in
and for any dimension
d. Instead of computing a WSPD directly in
, I propose to learn nonlinear mapping and transform the data to a lower-dimensional space
,
or
, since only in such low-dimensional spaces can a WSPD be efficiently computed. Furthermore, I estimate the quality of the computed WSPD in the original
space. My experiments show that for different synthetic and real-world datasets my approach allows that a WSPD of size
can still be computed for points in
for dimensions
d much larger than two or three in practice.
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