In the era of digital economy, data serves as a pivotal production factor. This paper addresses the challenge of valuing multi-source transportation data in vertical federated learning (VFL)-based Mobility-as-a-Service (MaaS) platforms by proposing a data valuation method based on the Nucleolus, a solution concept from cooperative game theory. We quantify data contributions using conditional mutual information to define the characteristic function of the cooperative game. Theoretical analysis demonstrates that the game is convex, ensuring the core’s non-emptiness and the Nucleolus belonging to the core. Using an improved Kohlberg algorithm, which reduces computational complexity via balanced coalition checks and locked linear spaces, we efficiently derive the Nucleolus for data valuation in vertical federated learning. Validated on a real-world Kaggle traffic prediction dataset partitioned across three parties, the Nucleolus demonstrates fairer and more stable value distributions than Shapley values, while scaling to 30 participants with computation times under 23 s. Crucially, it suppresses data replication attacks with zero inflation in replicated values and minimal discontent increase (≤ 2%). By minimizing maximum coalition dissatisfaction, the Nucleolus establishes a robust foundation for market-based data pricing mechanisms, fostering sustainable MaaS ecosystems through enhanced data sharing and privacy preservation.

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The Nucleolus Solution for Data Valuation in Vertical Federated Learning-Based Mobility-as-a-Service Platforms

  • Shichong Xie,
  • Lijun Gao,
  • Yinlian Zeng

摘要

In the era of digital economy, data serves as a pivotal production factor. This paper addresses the challenge of valuing multi-source transportation data in vertical federated learning (VFL)-based Mobility-as-a-Service (MaaS) platforms by proposing a data valuation method based on the Nucleolus, a solution concept from cooperative game theory. We quantify data contributions using conditional mutual information to define the characteristic function of the cooperative game. Theoretical analysis demonstrates that the game is convex, ensuring the core’s non-emptiness and the Nucleolus belonging to the core. Using an improved Kohlberg algorithm, which reduces computational complexity via balanced coalition checks and locked linear spaces, we efficiently derive the Nucleolus for data valuation in vertical federated learning. Validated on a real-world Kaggle traffic prediction dataset partitioned across three parties, the Nucleolus demonstrates fairer and more stable value distributions than Shapley values, while scaling to 30 participants with computation times under 23 s. Crucially, it suppresses data replication attacks with zero inflation in replicated values and minimal discontent increase (≤ 2%). By minimizing maximum coalition dissatisfaction, the Nucleolus establishes a robust foundation for market-based data pricing mechanisms, fostering sustainable MaaS ecosystems through enhanced data sharing and privacy preservation.