In the node classification task, it is natural to presume that densely connected nodes tend to exhibit similar attributes. Given this, it is crucial to first define what constitutes a dense connection and to develop a reliable mathematical tool for assessing node cohesiveness. In this paper, we propose a probability-based objective function for semi-supervised node classification that takes advantage of higher-order networks' capabilities. The proposed function reflects the philosophy aligned with the intuition behind classifying within higher order networks, as it is designed to reduce the likelihood of nodes interconnected through higher-order networks bearing different labels. Additionally, we propose the Stochastic Block Tensor Model (SBTM) as a graph generation model designed specifically to address a significant limitation of the traditional stochastic block model, which does not adequately represent the distribution of higher-order structures in real networks. We evaluate the objective function using networks generated by the SBTM, which include both balanced and imbalanced scenarios. Furthermore, we present an approach that integrates the objective function with graph neural network (GNN)-based semi-supervised node classification methodologies, aiming for additional performance gains. Our results demonstrate that in challenging classification scenarios--characterized by a low probability of homo-connections, a high probability of hetero-connections, and limited prior node information--models based on the higher-order network outperform pairwise interaction-based models. Furthermore, experimental results suggest that integrating our proposed objective function with existing GNN-based node classification approaches enhances classification performance by efficiently learning higher-order structures distributed in the network.