Motivation In many biomedical studies, there arises the need to integrate data from multiple directly or indirectly related sources. Collective matrix factorization (CMF) and its variants are models designed to collectively learn from arbitrary collections of matrices. The latent factors learnt are rich integrative representations that can be used in downstream tasks such as clustering or relation prediction with standard machine learning models. Previous CMF-based methods have numerous modeling limitations. They do not adequately capture complex non-linear interactions and do not explicitly model varying sparsity and noise levels in the inputs, and some cannot model inputs with multiple datatypes. These inadequacies limit their use on many biomedical datasets. Results To address these limitations, we develop Neural Collective Matrix Factorization (NCMF), the first fully neural approach to CMF. We evaluate NCMF on relation prediction tasks of gene-disease association prediction and adverse drug event prediction, using multiple datasets. In each case, data is obtained from heterogeneous publicly available databases, and used to learn representations to build predictive models. NCMF is found to outperform previous CMF-based methods and several state-of-the-art graph embedding methods for representation learning in our experiments. Our experiments illustrate the versatility and efficacy of NCMF in representation learning for seamless integration of heterogeneous data. Availability https://github.com/ajayago/NCMF_bioinformatics