Multiple factor analysis: principal component analysis for multitable and multiblock data sets
Bibliographic record
Abstract
Abstract Multiple factor analysis (MFA, also called multiple factorial analysis) is an extension of principal component analysis (PCA) tailored to handle multiple data tables that measure sets of variables collected on the same observations, or, alternatively, (in dual‐MFA) multiple data tables where the same variables are measured on different sets of observations. MFA proceeds in two steps: First it computes a PCA of each data table and ‘normalizes’ each data table by dividing all its elements by the first singular value obtained from its PCA. Second , all the normalized data tables are aggregated into a grand data table that is analyzed via a (non‐normalized) PCA that gives a set of factor scores for the observations and loadings for the variables. In addition, MFA provides for each data table a set of partial factor scores for the observations that reflects the specific ‘view‐point’ of this data table. Interestingly, the common factor scores could be obtained by replacing the original normalized data tables by the normalized factor scores obtained from the PCA of each of these tables. In this article, we present MFA, review recent extensions, and illustrate it with a detailed example. WIREs Comput Stat 2013, 5:149–179. doi: 10.1002/wics.1246 This article is categorized under: Data: Types and Structure > Categorical Data Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis Statistical and Graphical Methods of Data Analysis > Multivariate Analysis
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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 | 0.026 | 0.101 |
| Meta-epidemiology (narrow) | 0.004 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.008 | 0.012 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.005 | 0.006 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.014 | 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".