Eunho Koo

Eunho Koo, Tongseok Lim

Considering higher-order interactions allows for a more comprehensive understanding of network structures beyond simple pairwise connections. While leveraging all cliques in a network to handle higher-order interactions is intuitive, it often leads to computational inefficiencies due to overlapping information between higher-order and lower-order cliques. To address this issue, we propose an augmented maximal clique strategy. Although using only maximal cliques can reduce unnecessary overlap and provide a concise representation of the network, certain nodes may still appear in multiple maximal cliques, resulting in imbalanced training data. Therefore, our augmented maximal clique approach selectively includes some non-maximal cliques to mitigate the overrepresentation of specific nodes and promote more balanced learning across the network. Comparative analyses on synthetic networks and real-world citation datasets demonstrate that our method outperforms approaches based on pairwise interactions, all cliques, or only maximal cliques. Finally, by integrating this strategy into GNN-based semi-supervised learning, we establish a link between maximal clique-based methods and GNNs, showing that incorporating higher-order structures improves predictive accuracy. As a result, the augmented maximal clique strategy offers a computationally efficient and effective solution for higher-order network learning.

Eunho Koo, Hyungjun Kim

In regression analysis under artificial neural networks, the prediction performance depends on determining the appropriate weights between layers. As randomly initialized weights are updated during back-propagation using the gradient descent procedure under a given loss function, the loss function structure can affect the performance significantly. In this study, we considered the distribution error, i.e., the inconsistency of two distributions (those of the predicted values and label), as the prediction error, and proposed weighted empirical stretching (WES) as a novel loss function to increase the overlap area of the two distributions. The function depends on the distribution of a given label, thus, it is applicable to any distribution shape. Moreover, it contains a scaling hyperparameter such that the appropriate parameter value maximizes the common section of the two distributions. To test the function capability, we generated ideal distributed curves (unimodal, skewed unimodal, bimodal, and skewed bimodal) as the labels, and used the Fourier-extracted input data from the curves under a feedforward neural network. In general, WES outperformed loss functions in wide use, and the performance was robust to the various noise levels. The improved results in RMSE for the extreme domain (i.e., both tail regions of the distribution) are expected to be utilized for prediction of abnormal events in non-linear complex systems such as natural disaster and financial crisis.