A fast algorithm to factorize high-dimensional tensor product matrices used in genetic models.

Area of Science:

• Genetics
• Computational Biology
• Statistical Genetics

Background:

• Genetic models, including those for epistasis and gene-by-environment interactions, often rely on covariance structures represented by Hadamard products of low-rank matrices.
• Factorizing these large Hadamard product matrices is computationally intensive and poses a challenge for big data analyses using current algorithms.

Purpose of the Study:

• To develop a computationally efficient algorithm for factorizing large Hadamard product matrices.
• To enable the feasible application of complex genetic models to large sample sizes.

Main Methods:

• The study proposes a novel algorithm based on the properties of Hadamard and Kronecker products to achieve approximate matrix decomposition.
• The algorithm's performance is benchmarked against standard eigenvalue decomposition methods.
• The method is implemented in the open-source "tensorEVD" R package.

Main Results:

• The proposed algorithm offers an approximate decomposition that is orders of magnitude faster than standard eigenvalue decomposition.
• Benchmarks demonstrate significant speed improvements, making large-scale genetic analyses more feasible.
• The algorithm was successfully applied to analyze data from the Genomes to Fields Initiative (n ≈ 60,000).

Conclusions:

• The developed algorithm provides a scalable solution for factorizing large Hadamard product matrices.
• This advancement facilitates the use of sophisticated genetic models in the era of big data.
• The "tensorEVD" R package makes this efficient method accessible to researchers.