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A real recommender system can usually make use of more than one type of user feedback--for example, numerical ratings and binary ratings-to learn a user's true preferences. Recent work has proposed a transfer learning algorithm called transfer by collective factorization (TCF) to exploit such heterogeneous user feedback. TCF performs via sharing data-independent knowledge and modeling data-dependent effects simultaneously. However, TCF is a batch algorithm and updates the model parameters only once after scanning all data, which might not be efficient enough for real systems. This article proposes a novel and efficient transfer learning algorithm called interaction-rich transfer by collective factorization (iTCF), which extends the efficient collective matrix factorization (CMF) algorithm by providing more interactions between the user-specific latent features. The assumption under iTCF is that the predictability with regards to the same user's rating behaviors in two related data is likely to be similar. Considering the shared predictability, the authors derive novel update rules for iTCF in a stochastic algorithmic framework. The advantages of iTCF include its efficiency compared with TCF, and its higher prediction accuracy compared with CMF. Experimental results on three real-world datasets show the effectiveness of iTCF over the state-of-the-art methods.