As the simplest structure of interval neural networks (INNs), the single-layer interval perceptron (SIP) has the advantages of uncomplicated structure and fast computation, making it well-suited for handling various uncertain data. While \(L_0\) regularization yields the sparsest solution among all \(L_n\) regularization methods, optimizing \(L_0\) regularization poses a challenge as it is an NP-hard problem. Therefore, \(L_0\) regularization is approximated using smoothing functions. The incorporation of smoothing Group \(L_0\) regularization retains the sparse solution characteristics of \(L_0\) regularization and effectively resolves its NP-hard problem. Building upon the aforementioned content, a modified learning algorithm based on smoothing Group \(L_0\) regularization for interval perceptron with interval weights (MIPSG \(L_0\) ) is proposed, where the interval perceptron take real numbers as inputs, weights and outputs are represented as intervals. The radius of each interval weight is expressed through a quadratic term rather than an absolute value function, ensuring a positive radius and preventing oscillations phenomenon. The monotonicity, the strong and weak convergence of the proposed algorithm is rigorously demonstrated under moderate assumptions. Moreover, experimental results on one-class approximation and one-class classification simulations reveal that the proposed algorithm exhibits superior performance in terms of training and testing mean squared error (MSE), pruning weights and accuracy.
