On low dimensional random projections and similarity search

Abstract

Random projection (RP) is a common technique for dimensionality reduction under L2 norm for which many significant space embedding results have been demonstrated. However, many similarity search applications often require very low dimension embeddings in order to reduce overhead and boost performance. Inspired by the use of symmetric probability distributions in previous work, we propose a novel RP algorithm, Beta Random Projection, and give its probabilistic analyses based on Beta and Gaussian approximations. We evaluate the algorithm in terms of standard similarity metrics with other RP algorithms as well as the singular value decomposition (SVD). Our experimental results show that BRP preserves both similarity metrics well and, under various dataset types including random point sets, text (TREC5) and images, provides sharper and consistent performance.

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“…A wide range of distributions have been shown to yield good results with high probability, for example almost all zero mean, unit variance distributions can be used [5]. Lu and Lió studied random projection in low dimensions [10] and showed, perhaps unsurprisingly, that the distortion introduced when q is small can be negligible if the intrinsic dimensionality of the original space is low. Random projection and related methods have subsequently become an important tool in highdimensional statistics and machine learning, and have been applied to a range of problems, including regression [17], mixture modeling [5], text analysis [3], and medical imaging [11].…”