Theory of Lehmer transform and its applications in identifying the electroencephalographic signature of major depressive disorder
Bibliographic record
Abstract
We propose a novel transformation called Lehmer transform and establish a theoretical framework used to compress and characterize large volumes of highly volatile time series data. The proposed method is a powerful data-driven approach for analyzing extreme events in non-stationary and highly oscillatory stochastic processes like biological signals. The proposed Lehmer transform decomposes the information contained in a function of the data sample into a domain of some statistical moments. The mentioned statistical moments, referred to as suddencies, can be perceived as the moments that generate all possible statistics when used as inputs of the transformation. Besides, the appealing analytical properties of Lehmer transform makes it a natural candidate to take on the role of a statistic-generating function, a notion that we define in this work for the first time. Possible connections of the proposed transformation to the frequency domain will be briefly discussed, while we extensively study various aspects of developing methodologies based on the time-suddency decomposition framework. In particular, we demonstrate several superior features of the Lehmer transform over the traditional time-frequency methods such as Fourier and Wavelet transforms by analyzing the challenging electroencephalogram signals of the patients suffering from the major depressive disorder. It is shown that our proposed transformation can successfully lead to more robust and accurate classifiers developed for discerning patients from healthy controls.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".