  Independent and identically distributed (i.i.d.) data is essential to many
data analysis and modeling techniques. In the medical domain, collecting data
from multiple sites or institutions is a common strategy that guarantees
sufficient clinical diversity, determined by the decentralized nature of
medical data. However, data from various sites are easily biased by the local
environment or facilities, thereby violating the i.i.d. rule. A common strategy
is to harmonize the site bias while retaining important biological information.
The ComBat is among the most popular harmonization approaches and has recently
been extended to handle distributed sites. However, when faced with situations
involving newly joined sites in training or evaluating data from unknown/unseen
sites, ComBat lacks compatibility and requires retraining with data from all
the sites. The retraining leads to significant computational and logistic
overhead that is usually prohibitive. In this work, we develop a novel Cluster
ComBat harmonization algorithm, which leverages cluster patterns of the data in
different sites and greatly advances the usability of ComBat harmonization. We
use extensive simulation and real medical imaging data from ADNI to demonstrate
the superiority of the proposed approach. Our codes are provided in
https://github.com/illidanlab/distributed-cluster-harmonization.
