Matrix-based decomposition algorithms for engineering applications: the survey and generic framework
Bibliographic record
Abstract
This paper focuses on the issue of matrix-based decomposition, which has already been recognised as an effective means to address a system's complexity. For instance, a Design Structure Matrix (DSM) has been applied to tackle the complexity involved in product architecture and project management. As matrix-based decomposition has been studied and applied in different engineering contexts, the corresponding algorithms are rather scattered and often address only specific, context-dependent problems. Therefore, this paper is intended to contribute to matrix-based decomposition in two aspects. First, the research efforts in different domains are surveyed to identify the fundamental algorithmic techniques that are relevant to matrix-based decomposition. Second, a generic framework that allows the customisation of algorithms is proposed as an integrated tool to address different problems in matrix-based decomposition. Four matrix examples have been used to illustrate the framework's feasibility and applicability. The example results support that the proposed framework is capable of addressing four common matrix types in engineering applications, namely, symmetric DSM, non-symmetric DSM, directed DSM and rectangular matrix.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.007 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.003 |
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".