Estimating the Number of Correlated Components Based on Random Projections

Abstract

Estimating the number of correlated components between two data sets is a challenging task in the case of small sample support. Typically, a rank-reduction preprocessing step based on principal component analysis (PCA) is carried out on each data set individually to reduce the dimensionality before analyzing correlation between the data sets. However, PCA retains the components with the largest variance within a data set, and therefore fails when these components are not the ones that account for the correlation between the data sets. To overcome this, we propose an alternative technique that, instead of projecting the data into a single subspace, uses a large number of random projections.