Orthogonalized discriminant analysis based on generalized singular value decomposition
Bibliographic record
Abstract
Generalized singular value decomposition (GSVD) has been used for linear discriminant analysis (LDA) to solve the small sample size problem in pattern recognition. However, this algorithm may suffer from the over-fitting problem. In this paper, we propose a novel orthogonalization technique for the LDA/GSVD algorithm to address the over-fitting problem. In this technique, an orthogonalization of the basis of the discriminant subspace derived from the LDA/GSVD algorithm is carried out through an eigen-decomposition of a small size inner product matrix. It is computationally efficient when data are high dimensional. The technique is further applied to the kernelized LDA/GSVD algorithm, mGSVD-KDA, leading to a new algorithm, referred to as GSVD-OKDA. It is shown that with linear and nonlinear kernels, this new algorithm successfully overcomes the over-fitting problem of the LDA/GSVD and mGSVD-KDA algorithms. Simulation results show that the proposed algorithms provide high recognition accuracy with low computational complexity.
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 distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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.
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 teacher head, 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".