Study of Sparsity Emanating from NKPD and its Utilization to Enhance NKPD based Adaptive Algorithms
Bibliographic record
Abstract
Recently, the nearest Kronecker product (NKP) decomposition has become popular in several adaptive filtering (AF) applications owing to its fast convergence and tracking ability. In this paper, we study the nature of the smaller weight vectors resulting from NKP decomposition (NKPD) of a wide range of acoustic impulse responses (IRs). The study shows that the smaller weight vectors resulting from NKPD exhibit moderate to high degree of sparsity. To exploit this knowledge in AF problems, we propose a class of proportionate update based NKP normalized least-mean-square (NKP-NLMS) type algorithms: namely, the improved proportionate NKP-NLMS (NKP-IPNLMS) algorithm which uses the$\ell_{1}$-norm of the smaller weight vectors and the NKP- IPNLMS$-\ell_{0}$which uses an approximation of the$\ell_{0}$-norm. Further, we propose a new approximation of the$\ell_{0}$-norm with reduced computational complexity, using which we also propose the$\text{NKP}-\text{IPNLMS}-\ell_{0}-2$algorithm. Next, we present a comparison of computational complexity of the proposed algorithms. Simulation results show the improved performance achieved by the proposed algorithms, showing the advantage of exploiting sparsity in the smaller weight vectors in NKPD based adaptive algorithms.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".