randPedPCA: rapid approximation of principal components from large pedigrees
Bibliographic record
Abstract
Abstract Background Pedigrees continue to be extremely important in agriculture and conservation genetics, with the pedigrees of modern breeding programmes easily comprising millions of records. This size can make visualising the structure of such pedigrees challenging. Being graphs, pedigrees can be represented as matrices, including, most commonly, the additive (numerator) relationship matrix, $$\varvec{A}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> , and its inverse. With these matrices, the structure of pedigrees can then, in principle, be visualised via principal component analysis (PCA). However, the naive PCA of matrices for large pedigrees is challenging due to computational and memory constraints. Furthermore, computing a few leading principal components is usually sufficient for visualising the structure of a pedigree. Results We present the open-access R package for rapid pedigree PCA using sparse matrices. Our rapid pedigree PCA builds on the fact that matrix-vector multiplications with the additive relationship matrix can be carried out implicitly using the extremely sparse inverse relationship factor, $$\varvec{L}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> , which can be directly obtained from a given pedigree. We implemented two methods. Randomised singular value decomposition tends to be faster when very few principal components are requested, and Eigen decomposition via the library tends to be faster when more principal components are of interest. On simulated data, our package delivers a speed-up greater than 10,000 times compared to naive PCA. It further enables analyses that are impossible with naive PCA. When only two principal components are desired, the randomised PCA method can half the running time required compared to , which we demonstrate by analysing the pedigree of the UK Kennel Club registered Labrador Retriever population of almost 1.5 million individuals. Conclusions The leading principal components of pedigree matrices can be efficiently obtained using randomised singular value decomposition and other methods. Scatter plots of these scores allow for intuitive visualisation of large pedigrees. For large pedigrees, this is considerably faster than rendering plots of a pedigree graph.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.014 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.011 | 0.007 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".