【Stanford-ML-Discussion】非线性分类问题理解

最新推荐文章于 2025-01-22 08:30:00 发布

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#非线性分类 #机器学习

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本文探讨了三种解决非线性分类问题的方法：通过构造多项式特征提升逻辑回归的表达能力；利用带有非线性激活函数的神经网络进行复杂模式识别；采用支持向量机的核技巧将低维非线性问题映射到高维空间实现线性可分。

利用Logistic Regression, SVM, Neural Network解决非线性分类问题

（1）Logistic Regression
Creating some polynomial features based on the original features to map the original examples into a high-dimensional feature space (like the polynomial kernel in SVM)，such as quadratic, cubic features, to solve the non-linear classification problems.

（2）Neural Network
Theoretically, Neural Network with nonlinear activation function is as a non-linear classifier to be able to deal with the nonlinear classification problems.

The Neural Network is same as logistic regression when the number of hidden layer is 0 and the activation function in output layer is sigmoid function.

（3） Support Vector Machine
SVM introduces kernel function to dispose of the non-linear classification problems. Kernel function is able to map the original examples into a high-dimensional feature space so as to solve it by linear classifiers.

Though SVM with linear or polynomial functions is similar to logistic regression, The differences between logistic regression and SVM include:
-The hypothesis is different
-the optimization objective is different
Maybe, the optimization method could be same.