In modern database systems, a large portion of data naturally exists in the form of attributed graphs, such as knowledge graphs, social networks, and recommender systems. Although common, these data types remain underexplored, particularly in learning expressive representations that support effective clustering. However, Graph Convolutional Networks (GCNs) often suffer from the Over-Smoothing (OS) effect, which homogenizes node embeddings, while existing OS solutions mainly focus on topology information rather than attribute learning, which is inconsistent with the objective of attributed graph clustering. To address this limitation, we propose Hyper-complex space Representation Learning (HyReaL), a generalized framework that introduces hyper-complex (quaternion) feature transformation to enhance attribute representation. The HyReaL bridges arbitrary-dimensional attributes to quaternion algebra and connects the learned embeddings to a generalized clustering objective without being restricted to a specific number of clusters k. By strengthening attribute coupling and reducing the need for deep graph convolution layers, HyReaL alleviates the OS problem and produces more discriminative node representations. Extensive experiments, including significance tests and ablation studies, demonstrate that HyReaL achieves superior and scalable performance for attributed graph clustering in modern database systems. The source code is here https://github.com/Juny-Chen/HyReaL.git .