Multi-scale clustering by building a robust and self correcting ultrametric topology on data points

Area of Science:

• Computational Biology
• Data Science
• Bioinformatics

Background:

• High-throughput technologies generate vast, complex biological datasets.
• Extracting meaningful biological functions from this data is a significant challenge.
• Understanding the inherent multi-scale geometry of data is crucial for knowledge discovery.

Purpose of the Study:

• To develop a novel methodology for analyzing complex biological data clouds.
• To effectively capture and represent the multi-scale geometric structure of data.
• To provide a more robust and accurate tool for biological data analysis.

Main Methods:

• Introduced the data cloud geometry-tree (DCG-tree) methodology.
• Derived a hierarchy of clustering configurations from empirical similarity measurements.
• Transformed the hierarchy into an ultrametric space represented by an ultrametric tree or Parisi matrix.
• Incorporated a self-correcting mechanism for clustering membership across tree levels.

Main Results:

• DCG-trees successfully capture the geometric structure of data clouds.
• The method demonstrated robustness and reduced sensitivity to measurement errors compared to standard Hierarchical Clustering.
• DCG-trees provided better quantification of multi-scale geometric structures across diverse datasets (fMRI, genomics, social networks).

Conclusions:

• DCG-tree is an effective tool for analyzing complex biological data.
• The methodology enhances the assimilation of large datasets into conceptual frameworks for deciphering biological functions.
• DCG-trees offer improved insights into the multi-scale geometry embedded within biological data.