An apparatus in one embodiment comprises a plurality of container host devices of at least one processing platform. The container host devices implement a plurality of containers for executing applications on behalf of one or more tenants of cloud infrastructure. One or more of the container host devices are each configured to compute distance measures between respective pairs of the containers and to assign the containers to container clusters based at least in part on the distance measures. The distance measures may be computed as respective content-based distance measures between hash identifiers of respective layers of layer structures of the corresponding containers. The apparatus may further comprise an interface configured to present a visualization of the container clusters. User feedback received via the interface is utilized to alter at least one parameter of the computation of distance measures and the assignment of clusters to container clusters.