Identification of ordinal relations and alternative suborders within high-dimensional molecular data

Ana Stolnicu¹Peter Eckhardt-Bellmann¹Hans A. Kestler^2*

• ¹Universitat Ulm, Ulm, Germany
• ²University of Ulm, Ulm, Germany

Numerous biological systems exhibit ordinal connections between categories. Developmental and time-series information inherently depict sequences like 'early', 'intermediate', and 'late' phases, showing that these specific processes follow a progression. Ordinal classification techniques are often applied in biological and medical contexts, ranging from the evaluation of pain intensity, to the detection of evolving diseases, such as cancer. These ranking systems may assist clinicians in establishing diagnoses and developing tailored treatment plans. For instance, tumor staging might guide early detection strategies and targeted therapies, improving patient outcomes. However, applying ordinal classification to biological data presents considerable challenges. In addition to their high dimensionality, these datasets can be highly heterogeneous, often reflecting branching processes that occur simultaneously during progression. Factors such as intratumoral diversity, asynchronous progress, and context-specific signaling activity may interfere with the identification of such alternative development routes. To address these challenges, we propose a framework for uncovering ordinal relationships within molecular data. Specifically, directed threshold classifiers are introduced as base learners for ordinal classifier cascades, enabling the detection of both total and partial orderings between molecular states. This approach preserves the inherent ordinal structure by projecting high-dimensional data onto one single dimension while simultaneously decreasing complexity. Additionally, the distinct features of the resulting thresholds allow the prediction of potential alternative paths among the suborders.