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A gradient-based learning method with smoothing group L0 regularization for interval perceptron and interval weights
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AI
DOI：10.1007/s40314-025-03180-4.png)
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Abstract
En 中文
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 L-0 of regularization and effectively resolves its NP-hard problem. Building upon the aforementioned content, a modified learning algorithm based on smoothing Group regularization for interval perceptron with interval weights (MIPSGL(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.
Keywords:
Smoothing approximation
Group L-0 regularization
Interval perceptron
Interval weights
Convergence
Journal
IF:
4.3
Papers:
354
Citations:
593