  The effectiveness of machine learning (ML) algorithms is deeply intertwined
with the quality and diversity of their training datasets. Improved datasets,
marked by superior quality, enhance the predictive accuracy and broaden the
applicability of models across varied scenarios. Researchers often integrate
data from multiple sources to mitigate biases and limitations of single-source
datasets. However, this extensive data amalgamation raises significant ethical
concerns, particularly regarding user privacy and the risk of unauthorized data
disclosure. Various global legislative frameworks have been established to
address these privacy issues. While crucial for safeguarding privacy, these
regulations can complicate the practical deployment of ML technologies.
Privacy-Preserving Machine Learning (PPML) addresses this challenge by
safeguarding sensitive information, from health records to geolocation data,
while enabling the secure use of this data in developing robust ML models.
Within this realm, the Non-Readily Identifiable Data Collaboration (NRI-DC)
framework emerges as an innovative approach, potentially resolving the 'data
island' issue among institutions through non-iterative communication and robust
privacy protections. However, in its current state, the NRI-DC framework faces
model performance instability due to theoretical unsteadiness in creating
collaboration functions. This study establishes a rigorous theoretical
foundation for these collaboration functions and introduces new formulations
through optimization problems on matrix manifolds and efficient solutions.
Empirical analyses demonstrate that the proposed approach, particularly the
formulation over orthogonal matrix manifolds, significantly enhances
performance, maintaining consistency and efficiency without compromising
communication efficiency or privacy protections.
