This paper introduces a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlations using a hypergraph structure. HGNN addresses the challenge of learning representations for complex data by incorporating data structures into hypergraphs, which are more flexible for modeling complex data. The proposed method includes a hyperedge convolution operation to handle data correlations during representation learning, making it efficient for traditional hypergraph learning procedures. HGNN is designed to learn hidden layer representations considering the high-order data structure, making it a general framework for complex data correlations. Experiments on citation network classification and visual object recognition tasks demonstrate that HGNN outperforms recent state-of-the-art methods, particularly when dealing with multi-modal data. The main contributions of the paper are the proposal of HGNN and its effectiveness in handling complex and high-order data correlations, as well as its superior performance in multi-modal data tasks.This paper introduces a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlations using a hypergraph structure. HGNN addresses the challenge of learning representations for complex data by incorporating data structures into hypergraphs, which are more flexible for modeling complex data. The proposed method includes a hyperedge convolution operation to handle data correlations during representation learning, making it efficient for traditional hypergraph learning procedures. HGNN is designed to learn hidden layer representations considering the high-order data structure, making it a general framework for complex data correlations. Experiments on citation network classification and visual object recognition tasks demonstrate that HGNN outperforms recent state-of-the-art methods, particularly when dealing with multi-modal data. The main contributions of the paper are the proposal of HGNN and its effectiveness in handling complex and high-order data correlations, as well as its superior performance in multi-modal data tasks.