Random Projection for Fast and Efficient Multivariate Correlation Analysis of High-Dimensional Data: A New Approach

Abstract

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 expensive in applications involving large numbers of variables, as required, for example, in genetic neuroimaging. 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 PLSC 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.

On randomized sketching algorithms and the Tracy–Widom law

“…The bounds in Table 1 only give qualitative guidance about the embedding probability. Users will benefit from more prescriptive results in order to choose the sketch size k, and the type of sketch for applications (Grellmann et al 2016;Geppert et al 2017;Ahfock et al 2020;Falcone et al 2021).…”

Tuning Database-Friendly Random Projection Matrices for Improved Distance Preservation on Specific Data

“…As we can observe, the proposed DT-RP algorithm outperforms RP for all datasets. The average Recall 4 Note that the recall metric used here is different from the common classification recall (sensitivity, true positive rate) commonly used in categorization problems together with the precision score. For more details about the recall score used in approximate nearest neighbor search see [40].…”

“…Thanks to this property, Random Projection has become a widespread tool for dimensionality reduction, especially in large-scale applications where the volume of data or the dimensionality of samples is too big for alternative methods. For instance, Random Projection has been successfully used to accelerate tasks such as multivariate correlation analysis [4], high-dimensional data clustering [5,6], image search [7] or texture classification [8], among many others.…”

Random projections: Data perturbation for classification problems

“…Broadly speaking, random projections offer a universal and flexible approach to complex statistical problems. They are a particularly useful tool in large‐scale settings, such as high‐dimensional classification (Cannings & Samworth, 2017; Durrant & Kabán, 2013, 2015), clustering (Dasgupta, 1999; Fern & Brodley, 2003; Heckel, Tschannen, & Bölcskei, 2017), precision matrix estimation (Marzetta, Tucci, & Simon, 2011), regression (Ahfock, Astle, & Richardson, 2017; Dobriban & Liu, 2019; Heinze, McWiliams, & Meinshausen, 2016; Klanke, Vijayakumar, & Schaal, 2008; McWilliams, Heinze, Meinshausen, Krummenacher, & Vanchinathan, 2014; Mukhopadhyay & Dunson, 2019; Slawski, 2018; Thanei, Heinze, & Meinshausen, 2017; Thanei, Meinshausen, & Shah, 2018), sparse principal component analysis (Gataric, Wang, & Samworth, 2019), hypothesis testing (Lopes, Jacob, & Wainwright, 2011; Shi, Lu, & Song, 2019), correlation estimation (Grellmann et al, 2016), dimension reduction (Bingham & Mannilla, 2001; Omidiran & Wainwright, 2010; Reeve, Mu, & Brown, 2018), and matrix decomposition (Halko, Martinsson, & Tropp, 2011).…”

“…, sparse principal component analysis (Gataric, Wang, & Samworth, 2019), hypothesis testing (Lopes, Jacob, & Wainwright, 2011;Shi, Lu, & Song, 2019), correlation estimation (Grellmann et al, 2016), dimension reduction (Bingham & Mannilla, 2001;Omidiran & Wainwright, 2010;Reeve, Mu, & Brown, 2018), and matrix decomposition (Halko, Martinsson, & Tropp, 2011).…”