JL Lemma Based Dimensionality Reduction: On Using CDS Based Partial Fourier Matrices

Abstract

In the Big Data regime, Dimensionality Reduction (DR) has a fundamental role towards facilitating useful analytics on the data. Quite recently, Johnson Lindenstrauss (JL) Lemma-based DR is actively researched from both theoretical and application perspectives. In this paper, we provide some preliminary results demonstrating the utility of the deterministic partial Fourier matrices with the rows picked according to an appropriate Cyclic Difference Set (CDS), for projecting the data vectors into the lower dimension. Apart from bringing out the fact that these matrices preserve the pair-wise distances among the vectors equally well as their random counterparts, results are also provided for their applicability in image classification and clustering.