STATIS and DISTATIS: optimum multitable principal component analysis and three way metric multidimensional scaling
Bibliographic record
Abstract
Abstract STATIS 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, as in a variant called dual‐STATIS, multiple data tables where the same variables are measured on different sets of observations. STATIS proceeds in two steps:Firstit analyzes the between data table similarity structure and derives from this analysis an optimal set of weights that are used to compute a linear combination of the data tables called thecompromisethat best represents the information common to the different data tables;Second, the PCA of this compromise gives an optimal map of the observations. Each of the data tables also provides a map of the observations that is in the same space as the optimum compromise map. In this article, we present STATIS, explain the criteria that it optimizes, review the recent inferential extensions to STATIS and illustrate it with a detailed example. We also review, and present in a common framework, the main developments of STATIS such as (1)X‐STATIS or partial triadic analysis (PTA) which is used when all data tables collect the same variables measured on the same observations (e.g., at different times or locations), (2) COVSTATIS, which handles multiple covariance matrices collected on the same observations, (3) DISTATIS, which handles multiple distance matrices collected on the same observations and generalizes metric multidimensional scaling to three way distance matrices, (4) Canonical‐STATIS (CANOSTATIS), which generalizes discriminant analysis and combines it with DISTATIS to analyze multitable discriminant analysis problems, (5) power‐STATIS, which uses alternative criteria to find STATIS optimal weights, (6) ANISOSTATIS, which extends STATIS to give specific weights to each variable rather than to each whole table, (7) (K+ 1)‐STATIS (orexternal‐STATIS), which extends STATIS (and PLS‐methods and Tucker inter battery analysis) to the analysis of the relationships of several data sets and one external data set, and (8) double‐STATIS (or DO‐ACT), which generalizes (K+ 1)‐STATIS and analyzes two sets of data tables, and STATIS‐4, which generalizes double‐STATIS to more than two sets of data. These recent developments are illustrated by small examples.WIREs Comput Stat2012, 4:124–167. doi: 10.1002/wics.198 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Dimension Reduction Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data
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 | 0.012 | 0.040 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.007 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.001 | 0.005 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".