Beta Random Projection

Random projection (RP) is a common technique for dimensionality reduction under L
₂
norm for which many significant space embedding results have been demonstrated. In particular, random projection techniques could yield sharp results for R
^d
under L
₂
norm in time linear to the number of data points and dimensionality in question only. Inspired by the use of symmetric probability distributions in previous work, we propose a RP algorithm based on the hyper- spherical symmetry and give its probabilistic analyses based on beta and Gaussian distribution. Later, we present evaluations of our algorithm with other RP algorithms as well as the singular value decomposition (SVD). In particular, we benchmark our results via cosine similarity and L
₂
norm on a image collection.