# Random projections of random manifolds

@article{Lahiri2016RandomPO, title={Random projections of random manifolds}, author={Subhaneil Lahiri and Peiran Gao and Surya Ganguli}, journal={ArXiv}, year={2016}, volume={abs/1607.04331} }

Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on how many projections are needed to accurately preserve the geometry of these manifolds, given their intrinsic dimensionality, volume and curvature. However, such works employ definitions of volume and curvature that are inherently difficult to compute…

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