Asymmetric Random Projections
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 computationall...
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| Abstract | 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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| AbstractList | 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. 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. |
| Author | Ryder, Nick Zohar Karnin Liberty, Edo |
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| BackLink | https://doi.org/10.48550/arXiv.1906.09489$$DView paper in arXiv |
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| Copyright | 2019. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
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| DOI | 10.48550/arxiv.1906.09489 |
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| Snippet | Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is... Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is... |
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| Title | Asymmetric Random Projections |
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