Efficient method reveals patterns in complex discrete data sets
Efficient and Generalizable Archetypal Analysis for Discrete Data
Machine Learning
Summary
Many datasets have complex and discrete types of data like counts or categories, which are hard to summarize clearly. The authors developed a new way to break down such data into simple, understandable building blocks called archetypes. Their method uses probability-based models to work well with different kinds of discrete data and runs efficiently on large datasets. It also helps to automatically pick the right number of archetypes, making the summaries more reliable. This approach was tested on biological data, showing that the identified patterns make sense and fit the data well.
What this means in practice
- •For bioinformatics teams: Identify interpretable cell or mutation profiles from large-scale biological count or categorical data to aid research and analysis.
- •For microbiome data analysts: Extract meaningful microbial community patterns from compositional discrete data for ecological or health-related studies.
Authors
A. Emilie J. Wedenborg, Jesper Løve Hinrich, Morten Mørup
Abstract
Archetypal Analysis (AA) represents observations as convex combinations of extremal data-driven profiles, yielding interpretable low-dimensional descriptions of complex datasets. Classical AA relies on a least-squares objective, which is poorly suited to discrete observations such as binary, count, and categorical data. We introduce an efficient likelihood-based framework for AA supporting Bernoulli, Poisson, and multinomial observation models. Our optimization scheme employs local quadratic approximations of the negative log-likelihood, enabling constrained updates through sequential minimal optimization (SMO) and an active-set method. Scalability is improved by bounding the active set while preserving simplex feasibility. We further introduce a cross-validated predictive likelihood criterion for selecting the number of archetypes, providing a principled alternative to reconstruction-error heuristics and stability-based diagnostics. Synthetic experiments demonstrate computational efficiency and accurate recovery of model complexity. Applications to single-cell RNA sequencing, microbiome composition, and somatic mutation data show that the learned archetypes capture interpretable domain-specific structures while achieving competitive likelihood fits and stable solutions. Overall, the proposed framework enables efficient likelihood-based archetypal analysis of discrete data, complemented by predictive likelihood-based model selection.