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Principal Component Analysis for Big Data

2018· other· en· W3166788073 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueWiley StatsRef: Statistics Reference Online · 2018
Typeother
Languageen
FieldMathematics
TopicStatistical Methods and Inference
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsPrincipal component analysisBig dataDimensionality reductionComputer scienceKernel principal component analysisSubspace topologyData scienceCausal inferenceSparse PCAInferenceFactor analysisData miningFocus (optics)Artificial intelligenceDimension (graph theory)AnalyticsData analysisStatistical inferenceRanking (information retrieval)Machine learningKernel methodMathematicsEconometricsStatisticsSupport vector machine

Abstract

fetched live from OpenAlex

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.

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.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.005
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: Not applicable
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.219
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.005
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.000
Bibliometrics0.0010.001
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0020.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0050.000

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.

Opus teacher head0.377
GPT teacher head0.454
Teacher spread0.078 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it