Bibliographic record
Abstract
Dimensionality reduction is the process by which a set of data points in a higher dimensional space are mapped to a lower dimension while maintaining certain properties of these points relative to each other. One important property is the preservation of the three angles formed by a triangle consisting of three neighboring points in the high dimensional space. If this property is maintained for those same points in the lower dimensional embedding then the result is a conformal map. However, many of the commonly used nonlinear dimensionality reduction techniques, such as Locally Linear Embedding (LLE) or Laplacian Eigenmaps (LEM), do not produce conformal maps. Post-processing techniques formulated as instances of semi-definite programming (SDP) problems can be applied to the output of either LLE or LEM to produce a conformal map. However, the effectiveness of this approach is limited by the computational complexity of SDP solvers. This paper will propose an alternative post-processing algorithm that produces a conformal map but does not require a solution to a SDP problem and so is more computationally efficient thus allowing it to be applied to a wider selection of datasets. Using this alternative solution, the paper will also propose a new algorithm for 3D object classification. An interesting feature of the 3D classification algorithm is that it is invariant to the scale and the orientation of the surface.
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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 0.003 |
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".