A Hierarchical Graph Convolution Network for Representation Learning of Gene Expression Data

The curse of dimensionality, which is caused by high-dimensionality and low-sample-size, is a major challenge in gene expression data analysis. However, the real situation is even worse: labelling data is laborious and time-consuming, so only a small part of the limited samples will be labelled. Having such few labelled samples further increases the difficulty of training deep learning models. Interpretability is an important requirement in biomedicine. Many existing deep learning methods are trying to provide interpretability, but rarely apply to gene expression data. Recent semi-supervised graph convolution network methods try to address these problems by smoothing the label information over a graph. However, to the best of our knowledge, these methods only utilize graphs in either the feature space or sample space, which restrict their performance. We propose a transductive semi-supervised representation learning method called a hierarchical graph convolution network (HiGCN) to aggregate the information of gene expression data in both feature and sample spaces. HiGCN first utilizes external knowledge to construct a feature graph and a similarity kernel to construct a sample graph. Then, two spatial-based GCNs are used to aggregate information on these graphs. To validate the model's performance, synthetic and real datasets are provided to lend empirical support. Compared with two recent models and three traditional models, HiGCN learns better representations of gene expression data, and these representations improve the performance of downstream tasks, especially when the model is trained on a few labelled samples. Important features can be extracted from our model to provide reliable interpretability.