DOI: 10.5176/2251-1911_CMCGS16.1

Authors: Keegan Kang and Giles Hooker

Abstract: Efficient random projections were first introduced for high dimensional data, as a method of preserving lengths and inner products with high probability by Achlioptas [1], which in turn lead to natural applications in clustering problems [2], [3]. Extensions in the theory led to random projections being used for various purposes such as Principal Component Analysis (PCA) [4], [5], Support Vector Machines [6], or even constructing t tests in high dimensions [7], [8]. We propose BCD (Block Correlated Deterministic) random projections which extend the work of [9] and [10] by taking into account properties of our data. We focus on constructing random projections with two parameters, which may lead to more accurate estimates of other parameters of interests, by reducing the variance of our estimates. We present the construction of BCD random projections, and subsequent theoretical variance results for the Euclidean distance and the inner product.

Keywords: Random Projections, Variance Reduction

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