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In recent years, the advent of great technological advances has produced a wealth of very high-dimensional data, and combining high-dimensional information from multiple sources is becoming increasingly important in an extending range of scientific disciplines. Partial Least Squares Correlation (PLSC) is a frequently used method for multivariate multimodal data integration. It is, however, computationally extensive in applications involving large numbers of variables, as required, for example, in functional genomics. To handle high-dimensional problems, dimension reduction might be implemented as pre-processing step. We propose a new approach that incorporates Random Projection (RP) for dimensionality reduction into Partial Least Squares Correlation to efficiently solve high-dimensional multimodal problems like genotype-phenotype associations.We name our new method PLSC-RP. Using simulated and experimental data sets containing whole genome SNP measures as genotypes and whole brain neuroimaging measures as phenotypes, we demonstrate that PLSC-RP is drastically faster than traditional PLSC while providing statistically equivalent results. We also provide evidence that dimensionality reduction using RP is data type independent. Therefore, PLSC-RP opens up a wide range of possible applications. It can be used for any integrative analysis that combines information from multiple sources.