(Invited) Diffusion Map Analysis of Multi-Channel Time Series Data
Bibliographic record
Abstract
Sensor data often come in the form of multichannel time series, for example, ECG, EEG, and structural vibration monitoring to name a few. Conventionally, such multichannel time series data are analysed by using FFT for each channel, and/or by computing inter-channel correlations. Mathematically, however, these signals are better represented by dynamical systems, which are sets of differential equations. The behaviour of a dynamical system may be visualised as a trajectory in the so-called phase space. For example, the state of a weight suspended by a spring can be fully described by the weight’s position x and its velocity v, hence its temporal behaviour creates a trajectory in its phase space (x, v). It works similarly for real systems that produce time series data. From a single channel of time series x(t) it is possible to reconstruct the phase space trajectory using lagged variables x(t), x(t-1), x(t-2),…., x(t-n). It is, however, very difficult to find and analyse the trajectory because the dimensionality of the phase space is very large in general. In this presentation, we will show that a method called the diffusion map can extract the lower dimensional manifold in which the trajectory resides, and reveal the structure of the dynamics. Using some toy models we will demonstrate how our technique can be used to extract various useful information about the nature of the dynamics, including identification of anomalies, especially signs for imminent catastrophic changes such as phase transitions or structural collapse.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 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".