  Random projection (RP) is a powerful dimension reduction technique widely
used in the analysis of high dimensional data. We demonstrate how this
technique can be used to improve the computational efficiency of gravitational
wave searches from compact binaries of neutron stars or black holes.
Improvements in low-frequency response and bandwidth due to detector hardware
upgrades pose a data analysis challenge in the advanced LIGO era as they result
in increased redundancy in template databases and longer templates due to the
higher number of signal cycles in-band. The RP-based methods presented here
address both these issues within the same broad framework. We first use RP for
an efficient, singular value decomposition inspired template matrix
factorization and develop a geometric intuition for why this approach works. We
then use RP to calculate approximate time-domain match correlations in a lower
dimensional vector space. For searches over parameters corresponding to
non-spinning binaries with a neutron star and a black hole, a combination of
the two methods can reduce the total on-line computational cost by an order of
magnitude over a nominal baseline. This can, in turn, help free-up
computational resources needed to go beyond current spin-aligned searches to
more complex ones involving generically spinning waveforms.
