pyhon实现使用梯形模糊隶属函数改进支持向量机
时间: 2023-12-10 16:41:42 浏览: 35
使用梯形模糊隶属函数改进支持向量机可以提高分类器的性能和鲁棒性。下面是Python实现的步骤:
1. 导入必要的库
```python
import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.svm import SVC
```
2. 生成模拟数据
```python
X, y = make_classification(n_samples=1000, n_features=2, n_informative=2,
n_redundant=0, n_classes=2, random_state=42)
```
3. 对数据进行预处理,将特征缩放到区间[0, 1]
```python
X = (X - X.min()) / (X.max() - X.min())
```
4. 定义梯形模糊隶属函数
```python
def trapezoid(x, a, b, c, d):
if x <= a or x >= d:
return 0
elif a < x <= b:
return (x - a) / (b - a)
elif b < x <= c:
return 1
elif c < x < d:
return (d - x) / (d - c)
```
5. 将特征映射到高维空间
```python
def phi(x):
x1, x2 = x
return np.array([trapezoid(x1, 0.2, 0.3, 0.7, 0.8),
trapezoid(x1, 0.4, 0.5, 0.9, 1.0),
trapezoid(x2, 0.2, 0.3, 0.7, 0.8),
trapezoid(x2, 0.4, 0.5, 0.9, 1.0)])
```
6. 将数据映射到高维空间
```python
X_mapped = np.apply_along_axis(phi, axis=1, arr=X)
```
7. 划分训练集和测试集
```python
X_train, X_test, y_train, y_test = train_test_split(X_mapped, y, test_size=0.2, random_state=42)
```
8. 定义支持向量机模型
```python
svm = SVC(kernel='linear', C=1)
```
9. 训练模型
```python
svm.fit(X_train, y_train)
```
10. 预测测试集
```python
y_pred = svm.predict(X_test)
```
11. 计算准确率
```python
accuracy = np.mean(y_pred == y_test)
print('Accuracy:', accuracy)
```
完整代码如下:
```python
import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.svm import SVC
def trapezoid(x, a, b, c, d):
if x <= a or x >= d:
return 0
elif a < x <= b:
return (x - a) / (b - a)
elif b < x <= c:
return 1
elif c < x < d:
return (d - x) / (d - c)
def phi(x):
x1, x2 = x
return np.array([trapezoid(x1, 0.2, 0.3, 0.7, 0.8),
trapezoid(x1, 0.4, 0.5, 0.9, 1.0),
trapezoid(x2, 0.2, 0.3, 0.7, 0.8),
trapezoid(x2, 0.4, 0.5, 0.9, 1.0)])
X, y = make_classification(n_samples=1000, n_features=2, n_informative=2,
n_redundant=0, n_classes=2, random_state=42)
X = (X - X.min()) / (X.max() - X.min())
X_mapped = np.apply_along_axis(phi, axis=1, arr=X)
X_train, X_test, y_train, y_test = train_test_split(X_mapped, y, test_size=0.2, random_state=42)
svm = SVC(kernel='linear', C=1)
svm.fit(X_train, y_train)
y_pred = svm.predict(X_test)
accuracy = np.mean(y_pred == y_test)
print('Accuracy:', accuracy)
```
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