scikit learn 中的 SVC 与 LinearSVC：损失函数的差异

Question

根据这篇文章，scikit learn 中的 SVC 和 LinearSVC 有很大不同。但是当阅读官方 scikit learn 文档时，并没有那么清楚。

特别是对于损失函数，似乎存在等价关系：

并且这篇文章说le损失函数是不同的：

• SVC：

  1/2||w||^2 + C SUM xi_i

• 线性SVC：

  1/2||[w b]||^2 + C SUM xi_i

看起来在LinearSVC的情况下，截距是正则化的，但官方文档却另有说法。

有人有更多信息吗？

Answer 1

SVC

是LIBSVM库的包装，而

LinearSVC

是LIBLINEAR

的包装

LinearSVC

通常比

SVC

更快，并且可以处理更大的数据集，但它只能使用线性内核，因此得名。所以区别不在于表述，而在于实施方式。

引用

LIBLINEAR

常见问题解答：

When to use LIBLINEAR but not LIBSVM

There are some large data for which with/without nonlinear mappings gives similar performances. 
Without using kernels, one can quickly train a much larger set via a linear classifier. 
Document classification is one such application. 
In the following example (20,242 instances and 47,236 features; available on LIBSVM data sets), 
the cross-validation time is significantly reduced by using LIBLINEAR:

% time libsvm-2.85/svm-train -c 4 -t 0 -e 0.1 -m 800 -v 5 rcv1_train.binary
Cross Validation Accuracy = 96.8136%
345.569s

% time liblinear-1.21/train -c 4 -e 0.1 -v 5 rcv1_train.binary
Cross Validation Accuracy = 97.0161%
2.944s

Warning:While LIBLINEAR's default solver is very fast for document classification, it may be slow in other situations. See Appendix C of our SVM guide about using other solvers in LIBLINEAR.
Warning:If you are a beginner and your data sets are not large, you should consider LIBSVM first.