中文摘要：

介绍了一种基于密度的逻辑回归（Density-based logistic regression，DLR）分类模型以解决逻辑回归中非线性分类的问题，其主要思想是根据Nadarays-Watson密度估计将训练数据映射到特定的特征空间，然后组建优化模模型优化特征权重以及Nadarays—Watson密度估计算法的宽度，其主要优点在于：它不仅优于标准的逻辑回归，而且优于基于径向基函数（R．adialbasisfnction，RBF）内核的核逻辑回归（Kernel logistic regression，KLR），特别是与核逻辑回归分析和支持向量机（Supporr vector machine,SVM）相比，该方法不仅达到更好的分类精度，而且有更好的时间效率．该方法的另一个显著优点墨蔓可唑j艮皂然地扩展到数值类型和分类型混合的数据集中,除此之外，该方法和逻辑回归（Logistic regression，LR）一样，有同样的模型可解释的优点，这恰恰是其他如核逻辑回归分析和支持向量机所不具备的．

英文摘要：

We propose a density-based logistic regression （DLR） model for classification to address the challenge of the nonlinear classification problem in this domain. Based on a Nadarays-Watson density estimator, the training data is mapped into a particular feature space. Then, an optimization model is set up to optimize the feature weights and the width in the Nadaraya-Watson density estimation algorithm. We show that it is superior to not only standard logistic regression but also kernel logistic regression （KLR） with radial basis function （RBF） kernels. The results show that DLR compares favorably against other nonlinear methods including KLR and support vector machine （SVM）. The introduced approach achieves not only better classification accuracy but also better time efficiency. Another major advantage of our method is that it can be naturally extended to cope with hybrid data with both categorical features and numerical features. Moveover, our approach shares with logistic regression the same advantage of interpretability of the model, which is not obtained by kernel based methods such as KLR and SVM.