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Learning predictive models in new domains with scarce training data is a growing challenge in modern supervised learning scenarios. This incentivizes developing domain adaptation methods that leverage the knowledge in known domains (source) and adapt to new domains (target) with a different probability distribution. This becomes more challenging when the source and target domains are in heterogeneous feature spaces, known as heterogeneous domain adaptation (HDA). While most HDA methods utilize mathematical optimization to map source and target data to a common space, they suffer from low transferability. Neural representations have proven to be more transferable; however, they are mainly designed for homogeneous environments. Drawing on the theory of domain adaptation, we propose a novel framework, Heterogeneous Adversarial Neural Domain Adaptation (HANDA), to effectively maximize the transferability in heterogeneous environments. HANDA conducts feature and distribution alignment in a unified neural network architecture and achieves domain invariance through adversarial kernel learning. Three experiments were conducted to evaluate the performance against the state-of-the-art HDA methods on major image and text e-commerce benchmarks. HANDA shows statistically significant improvement in predictive performance. The practical utility of HANDA was shown in real-world dark web online markets. HANDA is an important step towards successful domain adaptation in e-commerce applications.