Clustering by soft-constraint affinity propagation: Applications to gene-expression data

Motivation: Similarity-measure based clustering is a crucial problem appearing throughout scientific data analysis. Recently, a powerful new algorithm called Affinity Propagation (AP) based on message-passing techniques was proposed by Frey and Dueck \cite{Frey07}. In AP, each cluster is identified by a common exemplar all other data points of the same cluster refer to, and exemplars have to refer to themselves. Albeit its proved power, AP in its present form suffers from a number of drawbacks. The hard constraint of having exactly one exemplar per cluster restricts AP to classes of regularly shaped clusters, and leads to suboptimal performance, {\it e.g.}, in analyzing gene expression data. Results: This limitation can be overcome by relaxing the AP hard constraints. A new parameter controls the importance of the constraints compared to the aim of maximizing the overall similarity, and allows to interpolate between the simple case where each data point selects its closest neighbor as an exemplar and the original AP. The resulting soft-constraint affinity propagation (SCAP) becomes more informative, accurate and leads to more stable clustering. Even though a new {\it a priori} free-parameter is introduced, the overall dependence of the algorithm on external tuning is reduced, as robustness is increased and an optimal strategy for parameter selection emerges more naturally. SCAP is tested on biological benchmark data, including in particular microarray data related to various cancer types. We show that the algorithm efficiently unveils the hierarchical cluster structure present in the data sets. Further on, it allows to extract sparse gene expression signatures for each cluster.

💡 Research Summary

The paper addresses a fundamental limitation of Affinity Propagation (AP), a message‑passing clustering algorithm that has become popular for similarity‑based data analysis, especially in high‑dimensional biological contexts such as gene‑expression profiling. In standard AP each cluster is represented by a single exemplar and the algorithm enforces a hard constraint that every data point must either be an exemplar or point to exactly one exemplar. While this formulation yields elegant and often accurate results, the strict “one‑exemplar‑per‑cluster” rule hampers the detection of irregularly shaped clusters and obscures hierarchical relationships that are common in genomic data sets.

To overcome this, the authors introduce Soft‑Constraint Affinity Propagation (SCAP). The key idea is to relax the hard constraint by assigning a finite penalty to violations of the exemplar rule. A new scalar parameter λ∈