Matrix Factorization-Based Dimensionality Reduction Algorithms─A Comparative Study on Spectroscopic Profiling Data

Area of Science:

• Analytical Chemistry
• Data Science
• Computational Science

Background:

• High-dimensional spectroscopic profiling data presents challenges due to the curse of dimensionality.
• Dimensionality reduction (DR) is crucial for managing complex datasets in analytical chemistry.
• Many DR algorithms can be unified under a matrix factorization (MF) framework.

Purpose of the Study:

• To theoretically reformulate various DR algorithms within a unified MF perspective.
• To develop and release an open-sourced toolkit integrating these MF-based DR algorithms.
• To conduct a comparative study of MF-based DR algorithms using real-world spectroscopic data.

Main Methods:

• Theoretical reformulation of DR algorithms (PCA, NMF, LAE, RP, SRP, VQ, AA, ICA) under MF.
• Development of an open-sourced toolkit with a unified API for integrated DR algorithms.
• Comparative analysis using time-of-flight (TOF) mass spectra, evaluating metrics like reconstruction error, topological preservation, and computational cost.

Main Results:

• Independent Component Analysis (ICA) demonstrated the highest reconstruction quality (<2% error).
• Principal Component Analysis (PCA) best preserved pairwise distance and ranking properties.
• Random Projection (RP) and Sparse Random Projection (SRP) offered superior computational performance (10-100x faster) for edge computing scenarios where reconstruction is not critical.

Conclusions:

• Guidelines for DR algorithm selection based on specific needs (reconstruction quality, topological structure preservation, computational efficiency) are provided.
• The unified MF perspective simplifies the understanding and application of diverse DR techniques.
• The developed toolkit and comparative study offer valuable resources for researchers dealing with high-dimensional spectroscopic data.