如果我没有cvxopt,有没有其他办法可以实现svm的手写数字识别
时间: 2024-03-27 13:36:03 浏览: 7
如果您没有cvxopt,也可以使用scipy库中的优化函数来求解SVM的对偶问题。下面是一个使用scipy库的示例代码:
```python
import numpy as np
from scipy.optimize import minimize
# 读入mnist数据集
data = np.genfromtxt('mnist.csv', delimiter=',')
X = data[:, 1:] # 特征
y = data[:, 0] # 标签
# 将数据集分为训练集和测试集
n_train = 6000
X_train, y_train = X[:n_train], y[:n_train]
X_test, y_test = X[n_train:], y[n_train:]
# 定义径向基函数
def rbf_kernel(x, y, gamma=0.1):
return np.exp(-gamma * np.linalg.norm(x - y) ** 2)
# 定义支持向量机分类器
class SVM:
def __init__(self, kernel=rbf_kernel, C=1.0):
self.kernel = kernel
self.C = C
def fit(self, X, y):
n_samples, n_features = X.shape
# 计算核矩阵
K = np.zeros((n_samples, n_samples))
for i in range(n_samples):
for j in range(n_samples):
K[i, j] = self.kernel(X[i], X[j])
# 定义目标函数
def objective(alpha):
return 0.5 * np.sum(alpha * alpha * y.reshape((-1, 1)) * y.reshape((1, -1)) * K) - np.sum(alpha)
# 定义约束条件
def constraint(alpha):
return np.sum(alpha * y)
# 定义不等式约束条件
def inequality_constraint(alpha):
return self.C - alpha
# 初始化alpha
alpha0 = np.zeros(n_samples)
# 定义优化问题
bounds = [(0, self.C) for i in range(n_samples)]
constraints = [{'type': 'eq', 'fun': constraint},
{'type': 'ineq', 'fun': inequality_constraint}]
solution = minimize(objective, alpha0, bounds=bounds, constraints=constraints)
self.a = solution.x
self.sv = self.a > 1e-5
self.b = np.mean(y[self.sv] - np.sum(self.a[self.sv] * y[self.sv].reshape((-1, 1)) * K[self.sv][:, self.sv], axis=0))
def predict(self, X):
y_pred = np.zeros(len(X))
for i in range(len(X)):
s = 0
for a, sv_y, sv in zip(self.a[self.sv], y_train[self.sv], X_train[self.sv]):
s += a * sv_y * self.kernel(X[i], sv)
y_pred[i] = s
return np.sign(y_pred + self.b)
# 训练支持向量机分类器
svm = SVM(kernel=rbf_kernel, C=1.0)
svm.fit(X_train, y_train)
# 在测试集上评估分类器
y_pred = svm.predict(X_test)
accuracy = np.mean(y_pred == y_test)
print('Accuracy:', accuracy)
```
请注意,这只是一个简单的示例代码。实际上,支持向量机分类器的实现可能会更加复杂,需要进行参数调整和模型选择等工作。