A heterogeneous information network (HIN) is one whose nodes model objects of different types and whose links model objects’ relationships. To enrich its information, objects in an HIN are typically associated with additional attributes. We call such an HIN an Attributed HIN or AHIN. We study the problem of clustering objects in an AHIN, taking into account objects’ similarities with respect to both object attribute values and their structural connectedness in the network. We show how supervision signal, expressed in the form of a must-link set and a cannot-link set, can be leveraged to improve clustering results. We put forward the SCHAIN algorithm to solve the clustering problem, and two highly efficient variants, SCHAIN-PI and SCHAIN-IRAM, which employ the power iteration based method and the implicitly restarted Arnoldi method respectively to compute eigenvectors of a matrix. We conduct extensive experiments comparing SCHAIN-based algorithms with other state-of-the-art clustering algorithms. Our results show that SCHAIN-IRAM outperforms other competitors in terms of clustering effectiveness and is highly efficient.