  Multiple datasets containing different types of features may be available for
a given task. For instance, users' profiles can be used to group users for
recommendation systems. In addition, a model can also use users' historical
behaviors and credit history to group users. Each dataset contains different
information and suffices for learning. A number of clustering algorithms on
multiple datasets were proposed during the past few years. These algorithms
assume that at least one dataset is complete. So far as we know, all the
previous methods will not be applicable if there is no complete dataset
available. However, in reality, there are many situations where no dataset is
complete. As in building a recommendation system, some new users may not have a
profile or historical behaviors, while some may not have a credit history.
Hence, no available dataset is complete. In order to solve this problem, we
propose an approach called Collective Kernel Learning to infer hidden sample
similarity from multiple incomplete datasets. The idea is to collectively
completes the kernel matrices of incomplete datasets by optimizing the
alignment of the shared instances of the datasets. Furthermore, a clustering
algorithm is proposed based on the kernel matrix. The experiments on both
synthetic and real datasets demonstrate the effectiveness of the proposed
approach. The proposed clustering algorithm outperforms the comparison
algorithms by as much as two times in normalized mutual information.
