  Standard clustering techniques assume a common configuration for all features
in a dataset. However, when dealing with multi-view or longitudinal data, the
clusters' number, frequencies, and shapes may need to vary across features to
accurately capture dependence structures and heterogeneity. In this setting,
classical model-based clustering fails to account for within-subject dependence
across domains. We introduce conditional partial exchangeability, a novel
probabilistic paradigm for dependent random partitions of the same objects
across distinct domains. Additionally, we study a wide class of Bayesian
clustering models based on conditional partial exchangeability, which allows
for flexible dependent clustering of individuals across features, capturing the
specific contribution of each feature and the within-subject dependence, while
ensuring computational feasibility.
