The depth problem: identifying the most representative units in a data group.

Area of Science:

• Data Science
• Biostatistics
• Bioinformatics

Background:

• Identifying central units in data clusters is challenging, especially when data points may not belong to any single group.
• This is critical in biomedical data analysis, including tumor classification and gene expression profiling, to understand pathological processes.
• Current methods struggle with non-continuous data common in biological and clinical datasets.

Purpose of the Study:

• To develop a novel statistical approach for identifying the most central and representative units within data clusters.
• To provide a robust method applicable to diverse multivariate data, including non-continuous biomedical data.
• To enhance the characterization of data groups and improve the identification of key samples in pathological processes.

Main Methods:

• A new depth function is proposed to quantify the centrality of units within clusters.
• The method utilizes pairwise distance or dissimilarity measures, allowing flexibility with various data types.
• Validation was performed using both artificial datasets and real-world empirical data.

Main Results:

• The proposed depth function effectively identifies central units that best characterize each cluster.
• The approach demonstrates good performance across different data types, including binary and multiattribute data.
• Application to empirical data confirmed the statistical approach's efficacy in real-world scenarios.

Conclusions:

• The novel depth function offers a valuable tool for cluster analysis in multivariate data.
• This method significantly improves the identification of central units, aiding in the interpretation of complex biomedical datasets.
• The approach is broadly applicable to various fields requiring robust cluster characterization, particularly in medicine and biology.