Heterogeneous transfer clustering can translate knowledge from some related heterogeneous source domains to the target domain without any supervision. Existing works usually use a large amount of complete co-occurrence data to learn the projection functions mapping heterogeneous data to a common latent feature subspace. However, in many real applications, it is not practical to collect abundant co-occurrence data, while the available co-occurrence data are always incomplete. Another commonly encountered problem is that the complex structure of real heterogeneous data may result in substantial degeneration in clustering performance. To address these issues, we propose a heterogeneous transfer clustering method specifically designed for partial co-occurrence data (HTCPC). It is superior to the existing methods in three facets. First, HTCPC fully uses the partial co-occurrence data in both source and target domains to learn a latent space, maximally extracting useful knowledge for clustering from limited information. Second, it incorporates multi-layer hidden representations, accurately preserving the complex hierarchical structure of data. Third, it enforces approximately orthogonal constraint in representations, effectively characterizing the latent subspace with minimal redundancy. An efficient algorithm has been derived and implemented to realize the proposed HTCPC. A series of experiments on the real datasets have illustrated the advantage of the proposed approach compared with state-of-the-art methods.