Wasserstein-Distance-Based Gaussian Mixture Reduction
Bibliographic record
Abstract
Gaussian mixtures (GMs) are widely used in signal processing applications to capture the multimodal behavior of dynamic systems. Due to an exponential increase in the number of GM components in such applications, Gaussian mixture reduction (GMR) approaches are deemed necessary. Traditionally, the Kullback-Leibler divergence (KLD) is used for GMR along with a moment-matching merging approach to minimize the information loss. However, in certain applications such as image retrieval, preserving the geometric shape of the GM is more appealing. For such applications, this work prescribes the use of the Wasserstein distance (WD), which quantifies the minimum cost of converting one density into another and, therefore, is mostly concerned with the shape difference between the densities. To minimize the change in the shape of the GM, first, similar GM components are identified utilizing the WD. Next, these components are merged by proposing a novel WD-based averaging method. The simulation results confirm the success of the proposed WD-based GMR techniques in providing a better approximation of the original GM in the WD sense as compared to KLD-based methods.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| 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".