Generalization of the minimum covariance determinant algorithm for categorical and mixed data types
Bibliographic record
Abstract
Abstract The minimum covariance determinant (MCD) algorithm is one of the most common techniques to detect anomalous or outlying observations. The MCD algorithm depends on two features of multivariate data: the determinant of a matrix (i.e., geometric mean of the eigenvalues) and Mahalanobis distances (MD). While the MCD algorithm is commonly used, and has many extensions, the MCD is limited to analyses of quantitative data and more specifically data assumed to be continuous. One reason why the MCD does not extend to other data types such as categorical or ordinal data is because there is not a well-defined MD for data types other than continuous data. To address the lack of MCD-like techniques for categorical or mixed data we present a generalization of the MCD. To do so, we rely on a multivariate technique called correspondence analysis (CA). Through CA we can define MD via singular vectors and also compute the determinant from CA’s eigenvalues. Here we define and illustrate a generalized MCD on categorical data and then show how our generalized MCD extends beyond categorical data to accommodate mixed data types (e.g., categorical, ordinal, and continuous). We illustrate this generalized MCD on data from two large scale projects: the Ontario Neurodegenerative Disease Research Initiative (ONDRI) and the Alzheimer’s Disease Neuroimaging Initiative (ADNI), with genetics (categorical), clinical instruments and surveys (categorical or ordinal), and neuroimaging (continuous) data. We also make R code and toy data available in order to illustrate our generalized MCD.
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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 | 0.016 | 0.069 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".