Network Embedding via Coupled Kernelized Multi-Dimensional Array Factorization

Network embedding has been widely employed in networked data mining applications as it can learn low-dimensional and dense node representations from the high-dimensional and sparse network structure. While most existing network embedding methods only model the proximity between two nodes regardless of the order of the proximity, this paper proposes to explicitly model multi-node proximities which can be widely observed in practice, e.g., multiple researchers coauthor a paper, and multiple genes co-express a protein. Explicitly modeling multi-node proximities is important because some two-node interactions may not come into existence without a third node. By proving that LINE(1st), a recent network embedding method, is equivalent to kernelized matrix factorization, this paper proposes coupled kernelized multi-dimensional array factorization (Cetera) which jointly factorizes multiple multi-dimensional arrays by enforcing a consensus representation for each node. In this way, node representations can be more comprehensive and effective, which is demonstrated on three real-world networks through link prediction and multi-label classification.