Precision and Accuracy of Length and Variance Fractal Dimensions Computed from Fractional Self-Affine Signals
Bibliographic record
Abstract
Many digital signal processing algorithms are based on mono-scale analysis. Since the reshuffling of any data value does not change the probability distribution, the sense of correlation or covariance in the data is lost, especially when dealing with self-affine time series. An alternative approach is to use poly-scale analysis. This paper describes two poly-scale algorithms: the length fractal dimension and variance fractal dimension and evaluates their accuracy and precision. First, we generate white Gaussian noise and fractal Brownian motion using the concepts of fractional Brownian motion and the discrete Fourier transform. Next, we evaluate the performance of these measures. Since many processes are nonstationary, we also present a stationarity-frame detection technique based on the One-Way ANOVA and Bartlett tests. Our results show that these poly-scale techniques can always be used as reliable tools for different purposes in self-affine data analysis.
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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 | 0.004 | 0.033 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.004 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 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".