Embedding and Trajectories of Temporal Networks
Bibliographic record
Abstract
Temporal network data are increasingly available in various domains, and often represent highly complex systems with intricate structural and temporal evolutions. Due to the difficulty of processing such complex data, it may be useful to coarse grain temporal network data into a numeric trajectory embedded in a low-dimensional space. We refer to such a procedure as temporal network embedding, which is distinct from procedures that aim at embedding individual nodes. Temporal network embedding is a challenging task because we often have access only to discrete time-stamped events between node pairs, and, in general, the events occur with irregular intervals, making the construction of the network at a given time a nontrivial question already. We propose a method to generate trajectories of temporal networks embedded in a low-dimensional space given a sequence of time-stamped events as input. We realize this goal by combining the landmark multidimensional scaling, which is an out-of-sample extension of the well-known multidimensional scaling method, and the framework of tie-decay temporal networks. This combination enables us to obtain a continuous-time trajectory describing the evolution of temporal networks. We then study mathematical properties of the proposed temporal network embedding framework. Finally, we showcase the method with empirical data of social contacts to find temporal organization of contact events and loss of them over a single day and across different days.
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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 | 0.000 | 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 | 0.000 |
| 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 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".