Published 2026-08-06 | Version v1.0
Policy BriefOpenPublished

The Evolving Structure of the U.S.–Iran–Israel Conflict

MCEA and NMF Analysis of Analytical Days 1–159 Using MCCM v2.3.4

Description

This policy brief examines the evolving structure of the U.S.–Iran–Israel conflict across 159 analytical days using MCCM v2.3.4, the Multi-Component Escalation Assessment (MCEA), non-negative matrix factorization (NMF), and exploratory k-means clustering. It finds that Phase III marked the principal structural break, with mean MCEA rising from 0.716 in Phase II to 0.840 in Phase III and peaking at 0.980 on Day 140. The analysis shows that escalation was systemic rather than purely kinetic: military pressure, institutional contestation, narrative amplification, uncertainty, resilience erosion, transmission dynamics, and external-node exposure intensified together. The brief argues that effective warning requires monitoring cross-layer configurations, latent mechanism composition, and resilience loss rather than visible strike intensity alone.

Abstract

This policy brief examines the evolving structure of the U.S.–Iran–Israel conflict across 159 analytical days using the Multi-Domain Conflict and Coupling Model (MCCM) v2.3.4, the Multi-Component Escalation Assessment (MCEA), non-negative matrix factorization (NMF), and exploratory k-means clustering. The results show a limited rise from Phase I to Phase II, followed by a decisive structural break in Phase III. Mean MCEA increased from 0.699 in Phase I to 0.716 in Phase II, then rose to 0.840 in Phase III, 17.27% above Phase II. The series peaked at 0.980 on Day 140. The Phase III rise was not a simple increase in military activity. Escalation dynamics, rule and institutional contestation, narrative warfare, uncertainty, transmission mechanisms, resilience erosion, and external strategic-node dependency intensified together. Exploratory NMF identifies four recurring co-activation patterns: kinetic escalation and physical disruption; rule-order and external-node coupling; resilience and normative-stability erosion; and institutional-information network pressure. Three daily clusters show that similar aggregate pressure levels can conceal different internal configurations. The central policy conclusion is that systemic escalation occurs when military, political, informational, institutional, economic, and network pressures reinforce one another while resilience mechanisms weaken. Effective warning therefore requires monitoring mechanism configurations, not only individual strikes or headline military indicators.

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Keywords

  • U.S.–Iran–Israel conflict
  • MCCM v2.3.4
  • Multi-Domain Conflict and Coupling Model
  • MCEA
  • Multi-Component Escalation Assessment
  • NMF
  • non-negative matrix factorization
  • k-means clustering
  • Phase III
  • systemic escalation
  • conflict monitoring
  • cross-layer configuration
  • ten-layer topography
  • mechanism co-activation
  • latent uncertainty
  • state risk signaling
  • aggregate strategic stress
  • rule contestation
  • narrative polarization
  • information amplification
  • actor coupling
  • resilience erosion
  • external strategic node dependency
  • negotiation feasibility index
  • threshold risk
  • EPINOVA

Subjects

  • International security
  • Strategic studies
  • Conflict analysis
  • Systems analysis
  • Computational social science
  • Security studies
  • Networked warfare
  • Middle East security
  • U.S.–Iran relations
  • Israel security
  • Crisis monitoring
  • Public policy
  • Data-driven policy analysis

Recommended citation

Wu, Shaoyuan (2026), The Evolving Structure of the U.S.–Iran–Israel Conflict: MCEA and NMF Analysis of Analytical Days 1–159 Using MCCM v2.3.4, Policy Brief No. EPINOVA–2026–PB–66, Global AI Governance and Policy Research Center, EPINOVA LLC. https://doi.org/10.67037/epinova.pb.2026.066

APA citation

Wu, S. (2026). The evolving structure of the U.S.–Iran–Israel conflict: MCEA and NMF analysis of Analytical Days 1–159 using MCCM v2.3.4. EPINOVA Policy Brief Series, EPINOVA-PB-2026-066. Global AI Governance and Policy Research Center, EPINOVA LLC. https://doi.org/10.67037/epinova.pb.2026.066.

Alternate identifiers

SchemeIdentifierDescription
URLhttps://epinova.org/policy-brief-1Official EPINOVA publication page
EPINOVA policy brief numberEPINOVA–2026–PB–66Policy brief number printed in the PDF
File nameThe Evolving Structure of the U.S.–Iran–Israel Conflict MCEA and NMF Analysis of Analytical Days 1–159 Using MCCM v2.3.4.pdfSource PDF file name
Short titleThe Evolving Structure of the U.S.–Iran–Israel ConflictShort form of the policy brief title
Analytical modelMCCM v2.3.4Multi-Domain Conflict and Coupling Model version 2.3.4 used as the conflict-monitoring framework
Analytical indicatorMCEAMulti-Component Escalation Assessment, an equal-weight daily systemic-pressure measure derived from 35 risk-oriented MCCM mechanisms
Analytical methodNMFNon-negative matrix factorization used to identify recurring mechanism co-activation patterns
Temporal coverageAnalytical Days 1–159Conflict-monitoring window using analytical days from 12:00 p.m. Eastern Time to 12:00 p.m. Eastern Time the following day

Related works

RelationIdentifierTypeDescription
IsPartOfhttps://epinova.org/policy-brief-1Publication seriesEPINOVA Policy Brief Series
IsSupplementedByhttps://github.com/EPINOVALLC/EPINOVA-ResearchRepositorySupplementary repository and structural archive
ReferencesLee and Seung (1999). Learning the parts of objects by non-negative matrix factorizationJournal articleReferenced for non-negative matrix factorization
ReferencesLloyd (1982). Least squares quantization in PCMJournal articleReferenced for k-means clustering
ReferencesRousseeuw (1987). SilhouettesJournal articleReferenced for silhouette coefficient and cluster validation
ReferencesPedregosa et al. (2011). Scikit-learnJournal articleReferenced for scikit-learn implementation

References

  1. Gordon, P. H. (2026, June 10). How the Iran war will change the Middle East. Brookings Institution. https://www.brookings.edu/articles/how-the-iran-war-will-change-the-middle-east/
  2. Govella, K., & Nakano, J. (2026, March 20). What are the implications of the Iran conflict for Japan? Center for Strategic and International Studies. https://www.csis.org/analysis/what-are-implications-iran-conflict-japan
  3. Lee, D. D., & Seung, H. S. (1999). Learning the parts of objects by non-negative matrix factorization. Nature, 401(6755), 788–791. https://doi.org/10.1038/44565
  4. Lloyd, S. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129–137. https://doi.org/10.1109/TIT.1982.1056489
  5. Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., VanderPlas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., & Duchesnay, E. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12, 2825–2830. https://www.jmlr.org/papers/v12/pedregosa11a.html
  6. Rousseeuw, P. J. (1987). Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20, 53–65. https://doi.org/10.1016/0377-0427(87)90125-7
  7. Yacoubian, M. (2026a, July 20). Is the Iran war entering a dangerous new phase? Center for Strategic and International Studies. https://www.csis.org/analysis/iran-war-entering-dangerous-new-phase
  8. Yacoubian, M. (2026b, June 8). Can Iran negotiations survive Israel-Iran escalation? Center for Strategic and International Studies. https://www.csis.org/analysis/can-iran-negotiations-survive-israel-iran-escalation