It is interesting that much of the literature about random projections is to make them less data oblivious. That goal is in large part driven by our stinginess on the complexity of computing these Random Projections. What if the number of Random Projections were not capped? What if, instead of metering the number of random projections to get the most out of it, one were given plenty of them in one fell swoop? This is what we are trying to do at LightOn: use Light to provide plenty of random projections. How much is plenty? Let's put it this way, having a Random Projection of size 1 or 1 million using our OPU requires the same effort. We are running a Cloud service where you can try our technology, it's here: https://www.lighton.ai/lighton-cloud/
In the meantime, let us take a look at these interesting asymmetric RPs:
Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of information about the data. In this paper, we provide a computationally light way to extract statistics from the data that allows designing a data dependent RP with superior performance compared to data-oblivious RP. We tackle scenarios such as matrix multiplication and linear regression/classification in which we wish to estimate inner products between pairs of vectors from two possibly different sources. Our technique takes advantage of the difference between the sources and is provably superior to oblivious RPs. Additionally, we provide extensive experiments comparing RPs with our approach showing significant performance lifts in fast matrix multiplication, regression and classification problems.
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