Analysis of Eigenspace Dynamics with Applications to Array Processing
Bibliographic record
Abstract
Abstract : For an N-element array (Fig.1(a)), methods such as beamforming and singular value decomposition rely on estimation of the sample covariance matrix, computed from M independent data snapshots. As M , the sample covariance is a consistent estimator of the true population covariance. However, this ideal condition cannot be met in most practical situations,1-2 in which large-aperture arrays operate in the presence of fast maneuvering interferers, or with towed/drifting arrays strongly affected by deformation or array-depth perturbations. The long-term goal of this effort is the development of physically motivated models to statistically describe the eigenstructure (eigenvalues and eigenvectors) of sample covariance matrices in sample-starved settings, and the use of those models for performance analysis and improvement of array processing methods. To this end, mathematical tools developed in the context of Random Matrix Theory (RMT)3-6 (mostly focused in the regime NM) and High Dimension, Low Sample Size (HDLSS) array processing7-8 (which considers NM) are applied to obtain statistical descriptions of sample eigenvalues/eigenvectors and how those quantities differ from the (true) population eigenpairs. Additional long-term goals are exploiting the information carried by sample eigenvectors for the improvement of estimators of the sample covariance matrix (i.e., signal versus noise subspaces), and for quantifying local stationary in array data (Fig.1 (b)).
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".