Sparse multinomial logistic regression has recently received widespread attention. It provides a useful tool for solving multi-classification problems in various fields, such as signal and image processing, machine learning and disease diagnosis. In this paper, we first study the group sparse multinomial logistic regression model and establish its optimality conditions. Based on the theoretical results of this model, we hence propose an efficient algorithm called the subspace quadratic regularization algorithm to compute a stationary point of a given problem. This algorithm enjoys excellent convergence properties, including the global convergence and locally quadratic convergence. Finally, our numerical results on standard benchmark data clearly demonstrate the superior performance of our proposed algorithm in terms of logistic loss value, sparsity recovery and computational time.

稀疏多项式逻辑回归最近受到广泛关注。它为解决信号和图像处理、机器学习和疾病诊断等各个领域的多分类问题提供了有用的工具。在本文中，我们首先研究了群稀疏多项式逻辑回归模型，并建立了其最优性条件。因此，基于该模型的理论结果，我们提出了一种称为子空间二次正则化算法的有效算法来计算给定问题的驻点。该算法具有优良的收敛特性，包括全局收敛和局部二次收敛。最后，我们在标准基准数据上的数值结果清楚地证明了我们提出的算法在逻辑损失值方面的优越性能，