Explicit Sensor Network Localization using Semidefinite Representations\n and Facial Reductions
Bibliographic record
Abstract
The sensor network localization, SNL, problem in embedding dimension r,\nconsists of locating the positions of wireless sensors, given only the\ndistances between sensors that are within radio range and the positions of a\nsubset of the sensors (called anchors). Current solution techniques relax this\nproblem to a weighted, nearest, (positive) semidefinite programming, SDP,\ncompletion problem, by using the linear mapping between Euclidean distance\nmatrices, EDM, and semidefinite matrices. The resulting SDP is solved using\nprimal-dual interior point solvers, yielding an expensive and inexact solution.\n This relaxation is highly degenerate in the sense that the feasible set is\nrestricted to a low dimensional face of the SDP cone, implying that the Slater\nconstraint qualification fails. Cliques in the graph of the SNL problem give\nrise to this degeneracy in the SDP relaxation. In this paper, we take advantage\nof the absence of the Slater constraint qualification and derive a technique\nfor the SNL problem, with exact data, that explicitly solves the corresponding\nrank restricted SDP problem. No SDP solvers are used. For randomly generated\ninstances, we are able to efficiently solve many huge instances of this NP-hard\nproblem to high accuracy, by finding a representation of the minimal face of\nthe SDP cone that contains the SDP matrix representation of the EDM. The main\nwork of our algorithm consists in repeatedly finding the intersection of\nsubspaces that represent the faces of the SDP cone that correspond to cliques\nof the SNL problem.\n
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 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".