Discriminant analysis based on modified generalised singular value decomposition and its numerical error analysis
Bibliographic record
Abstract
Generalised singular value decomposition (GSVD) has been used in the literature for linear discriminant analysis (LDA) to solve the small sample size problem in pattern recognition. However, this method, commonly known as LDA/GSVD algorithm, suffers from excessive computational load when the sample dimension is high. Here the GSVD framework used in the LDA/GSVD algorithm is modified by replacing the SVD of a high-dimension matrix with the eigen-decomposition of a small size inner product matrix, thus circumventing the direct calculation of a high-dimension singular vector matrix. It is established by a theorem that if the samples are linearly independent in the feature space, the samples in each class are degenerated into a distinct single point of a discriminative space derived from the GSVD-based algorithms, and the distances between the points depend only on the respective numbers of the samples in the corresponding classes. In order to overcome the over-fitting problem, a method to orthogonalise the basis of the discriminative subspace is proposed. The proposed linear algorithm is kernelised for the discriminant analysis of samples that are not linearly independent as the non-linear kernel mapping can establish linear independence. The results of the above theorem are used to develop a method to measure the numerical error. This measure can also be used to decide the kernel parameters to minimise the numerical error in the non-linear algorithm.
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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".