1. Libsvm-2.6使用介绍

2. Libsvm-2.6特点 Support multi-class classification
Different SVM formulation
Cross-validation for model selection
Probability estimate
Weighted SVM for unbalanced data
Both C++ and Java sources
Version 2.8 released on April fool’s day,2005

3. Libsvm-2.6程序结构
Kernel 类
Solver类：Generalized SMO和SVMLight algorithm 解二次规划问题
采用one-against-one 解决多类分类

4. Format of training and testing data file
<label> <index1>:<value1> <index2>:<value2> ...
+1 1: :1 3:1 4: : :-1 7:1
-1 1: :-1 3: : :1 6:-1 7:1
+1 1: :1 3:-1 4: : :-1 7:-1
-1 1: :1 3:1 4: : :-1 7:-1

5. Data scaling svmscale –l -1 –u 1 –s range train.1>train.1.scale
Avoid attributes in greater numeric ranges dominate those in smaller number ranges.
Usually scale each attribute to [0,1] or[-1,+1].
svmscale –l -1 –u 1 –s range train.1>train.1.scale
svmscale –r range test.1>test.1.scale

6. Svmtrain
One-class:Here a hyperplane is placed such that it separates the dataset from the origin with maximal margin. The regularization parameter nu(0,1), is a user defined parameter indicating the fraction of the data that should be accepted by the description.
nu-SVR: nu回归机。引入能够自动计算epsilon的参数nu。若记错误样本的个数为q ,则nu大于等于q/l,即nu是错误样本的个数所占总样本数的份额的上界；若记支持向量的个数为p,则nu小于等于p/l,即nu是支持向量的个数所占总样本数的份额的下界。首先选择参数nu和C,然后求解最优化问题。
Shrinking： 优化求解过程中是否采用shrinking. 边界支持向量BSVs（ai＝C的SV）在迭代过程中ai不会变化，如果找到这些点，并把它们固定为C，可以减少QP的规模。
Probability estimate: 是否训练SVC和SVR获得概率输出
-wi 不平衡样本的加权参数

7. Output of training C-SVM
optimization finished, #iter = 219 nu = :nu-SVM is a somewhat equivalent form of C-SVM where C is replaced by nu.
obj = :optimal objective value of the dual problme.
rho = :bias term of the decision function. nSV = 132,
nBSV = 107: number of the bounded support vectors Total nSV = 132

8. Model file svm_type c_svc kernel_type rbf gamma 0.0769231
nr_class 2:number of classes. For regression and one-class model, this number is 2.
total_sv 132
rho
label 1 -1
nr_sv 64 68: number of support vector for each class. SV

9. Two tools for Model Selection
Easy.py: does everything automatically-from data scaling to parameter selection
Grid.py: uses grid search to find the best model parameters
Grid.py的输出文件
-out: 搜索过程。每个参数取值及此时精度
-png: 搜索过程等高线图

10. Proposed procedure Transform data to the format of Libsvm.
Conduct simple scaling on the data.
Consider the RBF kernel.
Using the cross-validate to find the best model parameters.
Using the best parameters to train the whole training set.
Test

11. Experiments Original sets with default parameters Accuracy=9.7561%
Scaled sets with default parameters
Accuracy= %
Scaled sets with parameter selection
Accuracy=95.123%
Using an automatic script
Accuracy=95.122%

12. Remark Recommend Python 2.3
Recommend Gnuplot version Vesion has a bug.

13. References A practical guide to support vector machines classification
LIBSVM: a Library for Support Vector Machines
FAQ and Readme in Libsvm-2.6