Objective. Domain adaptation has been recognized as a potent solution to the challenge of limited training data for electroencephalography (EEG) classification tasks. Existing studies primarily focus on homogeneous environments, however, the heterogeneous properties of EEG data arising from device diversity cannot be overlooked. This motivates the development of heterogeneous domain adaptation methods that can fully exploit the knowledge from an auxiliary heterogeneous domain for EEG classification. Approach. In this article, we propose a novel model named informative representation fusion (IRF) to tackle the problem of unsupervised heterogeneous domain adaptation in the context of EEG data. In IRF, we consider different perspectives of data, i.e. independent identically distributed (iid) and non-iid, to learn different representations. Specifically, from the non-iid perspective, IRF models high-order correlations among data by hypergraphs and develops hypergraph encoders to obtain data representations of each domain. From the non-iid perspective, by applying multi-layer perceptron networks to the source and target domain data, we achieve another type of representation for both domains. Subsequently, an attention mechanism is used to fuse these two types of representations to yield informative features. To learn transferable representations, the maximum mean discrepancy is utilized to align the distributions of the source and target domains based on the fused features. Main results. Experimental results on several real-world datasets demonstrate the effectiveness of the proposed model. Significance. This article handles an EEG classification situation where the source and target EEG data lie in different spaces, and what’s more, under an unsupervised learning setting. This situation is practical in the real world but barely studied in the literature. The proposed model achieves high classification accuracy, and this study is important for the commercial applications of EEG-based BCIs.