支持向量机

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.model_selection import train_test_split
from cvxopt import matrix, solvers  # 凸优化求解库
from sklearn.metrics import accuracy_score

# 生成模拟二分类数据集
X, y = make_blobs(n_samples=150, n_features=2, centers=2, cluster_std=1.2, random_state=40)
colors = {0: 'r', 1: 'g'}
plt.scatter(X[:, 0], X[:, 1], marker='o', c=pd.Series(y).map(colors))
plt.show()

# 将标签转换为1/-1
y_ = y.copy()
y_[y_ == 0] = -1
y_ = y_.astype(float)

X_train, X_test, y_train, y_test = train_test_split(X, y_, test_size=0.3, random_state=43)
print(X_train.shape, y_train.shape, X_test.shape, y_test.shape)

# cvxopt库的使用示例
# 1. 定义二次规划参数
P = matrix([[1.0, 0.0], [0.0, 0.0]])
q = matrix([3.0, 4.0])
G = matrix([[-1.0, 0.0, -1.0, 2.0, 3.0], [0.0, -1.0, -3.0, 5.0, 4.0]])
h = matrix([0.0, 0.0, -15.0, 100.0, 80.0])
# 2. 构建求解
sol = solvers.qp(P, q, G, h)
# 3. 获取最优值
print(sol['x'], sol['primal objective'])


# 实现线性可分支持向量机
class Hard_Margin_SVM:
    # 线性可分支持向量机拟合方法
    def fit(self, X, y):
        # 训练样本数和特征数
        m, n = X.shape

        # 初始化二次规划相关变量：P/q/G/h
        self.P = matrix(np.identity(n + 1, dtype=np.float))
        self.q = matrix(np.zeros((n + 1,), dtype=np.float))
        self.G = matrix(np.zeros((m, n + 1), dtype=np.float))
        self.h = -matrix(np.ones((m,), dtype=np.float))

        # 将数据转为变量
        self.P[0, 0] = 0
        for i in range(m):
            self.G[i, 0] = -y[i]
            self.G[i, 1:] = -X[i, :] * y[i]

        sol = solvers.qp(self.P, self.q, self.G, self.h)  # 构建二次规划求解

        # 对权重和偏置寻优
        self.w = np.zeros(n, )
        self.b = sol['x'][0]
        for i in range(1, n + 1):
            self.w[i - 1] = sol['x'][i]
        return self.w, self.b

    # 定义模型预测函数
    def predict(self, X):
        return np.sign(np.dot(self.w, X.T) + self.b)


hard_margin_svm = Hard_Margin_SVM()  # 创建线性可分支持向量机模型实例
hard_margin_svm.fit(X_train, y_train)  # 执行训练
y_pred = hard_margin_svm.predict(X_test)  # 模型预测
print(accuracy_score(y_test, y_pred))  # 计算测试集准确率

import numpy as np
import matplotlib.pyplot as plt
from sklearn.svm import SVC, LinearSVC
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report


def plot_decision_boundary(model, axis):
    """
    在axis范围内绘制模型model的决策边界
    :param model: classification model which must have 'predict' function
    :param axis: [left, right, down, up]
    """
    x0, x1 = np.meshgrid(
        np.linspace(axis[0], axis[1], int((axis[1] - axis[0]) * 100)).reshape(-1, 1),
        np.linspace(axis[2], axis[3], int((axis[3] - axis[2]) * 100)).reshape(-1, 1),
    )
    X_new = np.c_[x0.ravel(), x1.ravel()]

    y_predict = model.predict(X_new)
    zz = y_predict.reshape(x0.shape)

    from matplotlib.colors import ListedColormap
    custom_cmap = ListedColormap(['#EF9A9A', '#FFF59D', '#90CAF9'])

    plt.contourf(x0, x1, zz, linewidth=5, cmap=custom_cmap)


X, y = load_iris(return_X_y=True)
X = X[:, :2]  # 仅选择前两个特征，便于绘制决策边界
X_train, X_test, y_train, y_test = train_test_split(X, y)
print(X_train.shape, X_test.shape, y_train.shape, y_test.shape)  # (112, 2) (38, 2) (112,) (38,)

lin_svc = LinearSVC()
lin_svc.fit(X_train, y_train)
print('classification accuracy of LinearSVC: ', lin_svc.score(X_test, y_test))

svc_rf = SVC(kernel='rbf', degree=5)
svc_rf.fit(X_train, y_train)
print('classification accuracy of SVC with RBF kernel: ', svc_rf.score(X_test, y_test))

plt.subplot(1, 2, 1)
plot_decision_boundary(lin_svc, axis=[3, 8, 1, 5])
plt.scatter(X_test[y_test == 0, 0], X_test[y_test == 0, 1])
plt.scatter(X_test[y_test == 1, 0], X_test[y_test == 1, 1])
plt.scatter(X_test[y_test == 2, 0], X_test[y_test == 2, 1])

plt.subplot(1, 2, 2)
plot_decision_boundary(svc_rf, axis=[3, 8, 1, 5])
plt.scatter(X_test[y_test == 0, 0], X_test[y_test == 0, 1])
plt.scatter(X_test[y_test == 1, 0], X_test[y_test == 1, 1])
plt.scatter(X_test[y_test == 2, 0], X_test[y_test == 2, 1])

plt.show()