Nesterov Accelerated Gradient Descent for Optimizing Fast Harmonic Mean Linear Discriminant Analysis
Bibliographic record
Abstract
Dimension reduction algorithms have become widespread in data science due to the prevalence of High-Dimensional Data (HDD).In recent years, many versions of Linear Discriminant Analysis (LDA) have been developed for dimensionality reduction.Among them, the Fast Harmonic mean-based LDA (FHLDA) and FHLDA-pairwise (FHLDAp) algorithms reduce HDD by adopting joint diagonalization based on Taylor expansion to generate discriminants.However, the Stiefel manifold gradient scheme in these algorithms involves many matrix multiplications, leading to high computational time complexity (𝑂(𝑝 2 )).Thus, this manuscript proposes an Accelerated Optimization (AO) approach for FHLDA and FHLDAp algorithms to reduce the complexity of the Stiefel manifold gradient scheme to 𝑂(√𝑝) .A Nesterov accelerated gradient descent scheme is introduced to optimize functions on the Stiefel manifold by constructing a sequence of proximal points satisfying manifold constraints.This achieves asymptotically optimal error for L-smooth convex, as well as L-smooth and 𝜇-strongly convex functions, provided step size satisfies the Lipschitz smoothness condition.So, it is ensured to converge and achieve an accelerated rate after the solution is nearer to the local.After applying this scheme, joint diagonalization via Taylor expansion recovers the discriminant vector from the manifold.Experimental results demonstrate that the AOFHLDA and AOFHLDAp algorithms outperform LDA, FHLDA, and FHLDAp on both single and multi-label datasets, achieving significant accuracy improvements.Specifically, AOFHLDA improves accuracy by 17.87%, 14.14%, 14.65%, and 15.28% on the PIE, UMIST, Barcelona, and MediaMill datasets, respectively.Similarly, AOFHLDAp improves accuracy by 19.32%, 15.13%, 15.61%, and 16.44% on the PIE, UMIST, Barcelona, and MediaMill datasets, respectively.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".