Rigid geometry solves "curse of dimensionality" effects in clustering methods: An application to omics data

Area of Science:

• Biochemistry
• Computational Biology
• Data Science

Background:

• Long-term sample preservation at ultralow temperatures requires robust analytical methods.
• Understanding protein degradation and metabolism at subfreezing temperatures is crucial.
• Existing clustering methods struggle with high-dimensional biological data, like that from liquid chromatography-mass spectrometry (LC/MS).

Purpose of the Study:

• To develop a strategy for analyzing protein degradation and metabolism in samples stored at ultralow temperatures.
• To overcome the limitations of traditional clustering methods when applied to complex biological datasets.
• To improve the reproducibility and reliability of sample analysis in long-term ultralow temperature storage.

Main Methods:

• Acquisition of liquid chromatography-mass spectrometry (LC/MS) data for protein signal intensities in HEK-293 cells.
• Application of a novel clustering approach using rigid geometry and a prime ideal I-adic (p-adic) metric.
• Testing the method's efficacy on expression array data.

Main Results:

• The novel p-adic metric approach successfully rearranged sample clusters into a meaningful and reproducible order.
• Clustering results were consistent across different analytical methods, unlike initial attempts.
• The method effectively eliminated the "curse of dimensionality" for clustering biological data.
• Successful application to expression array data demonstrated broader utility.

Conclusions:

• The developed p-adic metric method provides a robust solution for analyzing high-dimensional biological data from ultralow temperature preserved samples.
• This approach enhances the reproducibility and reliability of sample analysis, overcoming common dimensionality challenges.
• The methodology may offer a characteristic value for systems adhering to Boltzmann distribution principles.