Riemannian Distances for Signal Classification by Power Spectral Density
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Bibliographic record
Abstract
Signal classification is an important issue in many branches of science and engineering. In signal classification, a feature of the signals is often selected for similarity comparison. A distance metric must then be established to measure the dissimilarities between different signal features. Due to the natural characteristics of dynamic systems, the power spectral density (PSD) of a signal is often used as a feature to facilitate classification. We reason in this paper that PSD matrices have structural constraints and that they describe a manifold in the signal space. Thus, instead of the widely used Euclidean distance (ED), a more appropriate measure is the Riemannian distance (RD) on the manifold. Here, we develop closed-form expressions of the RD between two PSD matrices on the manifold and study some of the properties. We further show how an optimum weighting matrix can be developed for the application of RD to signal classification. These new distance measures are then applied to the classification of electroencephalogram (EEG) signals for the determination of sleep states and the results are highly encouraging.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 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 it