支持向量机（SVM）-R

1、损失函数

损失函数.PNG

在实际应用中，可能不存在这样一条最大间隔线，将样本分开，这个时候就出现了损失函数，每一个被错分的训练集到直线（模型）的距离都是一个损失量，我们要使这些损失量达到最小。模型是由关键的样本决定的（异常），也是由错分样本决定的，错分样本和关键样本都是对模型的建立造成干扰比较大的样本，都是难以区分的样本。

2、分类模板

这个分类模板只适用于处理这个案例，我们做的只是替换分类器。
代码：

# Support Vector Machine (SVM)

# Importing the dataset
dataset = read.csv('Social_Network_Ads.csv')
dataset = dataset[3:5]

# Splitting the dataset into the Training set and Test set
# install.packages('caTools')
library(caTools)
set.seed(123)
split = sample.split(dataset$Purchased, SplitRatio = 0.75)
training_set = subset(dataset, split == TRUE)
test_set = subset(dataset, split == FALSE)

# Feature Scaling
training_set[-3] = scale(training_set[-3])
test_set[-3] = scale(test_set[-3])

# Fitting Kernel SVM to the Training set
#install.packages('e1071')
library(e1071)
classifier = svm(formula = Purchased ~ .,
                 data = training_set,
                 type = 'C-classification',
                 kernel = 'linear')

# Predicting the Test set results
y_pred = predict(classifier, newdata = test_set[-3])

# Making the Confusion Matrix
cm = table(test_set[, 3], y_pred)

# Visualising the Training set results
library(ElemStatLearn)
set = training_set
X1 = seq(min(set[, 1]) - 1, max(set[, 1]) + 1, by = 0.0075)
X2 = seq(min(set[, 2]) - 1, max(set[, 2]) + 1, by = 0.0075)
grid_set = expand.grid(X1, X2)
colnames(grid_set) = c('Age', 'EstimatedSalary')
y_grid = predict(classifier, newdata = grid_set)
plot(set[, -3],
     main = 'Classifier (Training set)',
     xlab = 'Age', ylab = 'Estimated Salary',
     xlim = range(X1), ylim = range(X2))
contour(X1, X2, matrix(as.numeric(y_grid), length(X1), length(X2)), add = TRUE)
points(grid_set, pch = '.', col = ifelse(y_grid == 1, 'springgreen3', 'tomato'))
points(set, pch = 21, bg = ifelse(set[, 3] == 1, 'green4', 'red3'))

# Visualising the Test set results
library(ElemStatLearn)
set = test_set
X1 = seq(min(set[, 1]) - 1, max(set[, 1]) + 1, by = 0.0075)
X2 = seq(min(set[, 2]) - 1, max(set[, 2]) + 1, by = 0.0075)
grid_set = expand.grid(X1, X2)
colnames(grid_set) = c('Age', 'EstimatedSalary')
y_grid = predict(classifier, newdata = grid_set)
plot(set[, -3], main = 'Classifier (Test set)',
     xlab = 'Age', ylab = 'Estimated Salary',
     xlim = range(X1), ylim = range(X2))
contour(X1, X2, matrix(as.numeric(y_grid), length(X1), length(X2)), add = TRUE)
points(grid_set, pch = '.', col = ifelse(y_grid == 1, 'springgreen3', 'tomato'))
points(set, pch = 21, bg = ifelse(set[, 3] == 1, 'green4', 'red3'))

关键代码：
install.packages('e1071')
library(e1071)
classifier = svm(formula = Purchased ~ .,
data = training_set,
type = 'C-classification',
kernel = 'linear')
代码解释：
SVM不仅可以用于分类还可以用于回归，这里指定用于分类，核函数是线性。

3、执行结果

混淆矩阵.PNG 训练集.PNG y_pred.PNG
测试集.PNG

这里跟程序稍有差别，测试集为了提高运行速度，我们将点的密度降到0.01。原理简单，就是少画几个红绿点，速度快些。