Matrix Recovery Algorithm for Reconstructing Mixing Matrices From Raw Observations and Ordinary Least Squares Unmixed...

Area of Science:

• Flow Cytometry
• Computational Biology
• Data Science

Background:

• Accurate spectral unmixing in flow cytometry relies on the mixing matrix (M) to deconvolve overlapping fluorescent signals.
• Current Flow Cytometry Standard (FCS) formats lack adequate support for storing M, compromising analytical reproducibility and transparency.
• This limitation hinders retrospective analysis and validation of flow cytometry experiments.

Purpose of the Study:

• To develop and validate a novel matrix recovery (MR) algorithm for computationally reconstructing the mixing matrix (M).
• To address the inadequate storage of M in existing FCS data formats.
• To enhance analytical reproducibility and method transparency in flow cytometry.

Main Methods:

• A matrix recovery (MR) algorithm was developed to reconstruct the mixing matrix (M) from raw detector observations and unmixed abundance values.
• The algorithm utilizes a closed-form solution for ordinary least squares (OLS) unmixing: M = (A · O+)+, where A is unmixed abundance and O is raw observations.
• The algorithm was validated across six commercial cytometric platforms with varying detector channels and fluorochrome panels.

Main Results:

• The MR algorithm achieved mathematically exact recovery of M for OLS methodologies with numerical errors below 10^-4.
• Comprehensive validation confirmed the algorithm's accuracy across diverse cytometric platforms and experimental conditions.
• Weighted least squares (WLS) recovery is theoretically possible but currently computationally intractable for practical applications.

Conclusions:

• The developed matrix recovery algorithm provides a critical tool for retrospective analysis of flow cytometry data when M is not provided.
• This approach significantly improves analytical reproducibility and method transparency.
• Systematic inclusion of M within FCS file specifications remains the optimal long-term solution for flow cytometry data integrity.