randPedPCA: rapid approximation of principal components from large pedigrees.

Area of Science:

• Genetics
• Bioinformatics
• Computational Biology

Background:

• Modern breeding programs involve millions of pedigree records, posing visualization challenges.
• Pedigree data can be represented as relationship matrices, enabling visualization through principal component analysis (PCA).
• Naive PCA methods face computational and memory constraints with large pedigrees.

Purpose of the Study:

• To develop an efficient method for visualizing the structure of large pedigrees.
• To overcome computational limitations of traditional PCA for extensive pedigree datasets.

Main Methods:

• Developed the open-access R package randPedPCA for rapid pedigree PCA.
• Utilized sparse matrices and implicit matrix-vector multiplications with the inverse relationship factor.
• Implemented randomized singular value decomposition and Eigen decomposition via the RSpectra library.

Main Results:

• The randPedPCA package achieves speed-ups exceeding 10,000 times compared to naive PCA on simulated data.
• Randomized PCA methods enable analyses previously impossible due to computational constraints.
• Demonstrated analysis of a UK Kennel Club Labrador Retriever pedigree with nearly 1.5 million individuals, showing significant time reduction.

Conclusions:

• Leading principal components of pedigree matrices can be efficiently computed using randomized methods.
• Scatter plots of PCA scores provide intuitive visualizations for large pedigrees.
• This approach is substantially faster than traditional pedigree graph rendering for large datasets.