Principal Component Analysis for Big Data
Bibliographic record
Abstract
Abstract Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting statistical inference. Principal component analysis, commonly referred to as PCA, has become an essential tool for multivariate data analysis and unsupervised dimension reduction, the goal of which is to find a lower dimensional subspace that captures most of the variation in the dataset. This article provides an overview of methodological and theoretical developments of PCA over the past decade, with focus on its applications to big data analytics. We first review the mathematical formulation of PCA and its theoretical development from the view point of perturbation analysis. We then briefly discuss the relationship between PCA and factor analysis as well as its applications to large covariance estimation and multiple testing. PCA also finds important applications in many modern machine learning problems, and in this article, we focus on community detection, ranking, mixture model, and manifold learning.
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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 | 0.006 | 0.033 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.009 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.006 |
| 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".