机器学习-支撑向量机SVM

Support Vector Machine

离分类样本尽可能远

Soft Margin SVM

scikit-learn中的SVM

和kNN一样,要做数据标准化处理!

涉及距离!

加载数据集

python 复制代码
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets

iris = datasets.load_iris()

X = iris.data
y = iris.target

X = X[y<2,:2]
y = y[y<2]
plt.scatter(X[y==0,0], X[y==0,1], color='red')
plt.scatter(X[y==1,0], X[y==1,1], color='blue')
plt.show()

数据标准化

python 复制代码
from sklearn.preprocessing import StandardScaler

standardScaler = StandardScaler()
standardScaler.fit(X)
X_standard = standardScaler.transform(X)

svm

python 复制代码
from sklearn.svm import LinearSVC

svc = LinearSVC(C=1e9)
svc.fit(X_standard, y)

可视化

python 复制代码
def plot_decision_boundary(model, axis):
    
    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)
python 复制代码
plot_decision_boundary(svc, axis=[-3, 3, -3, 3])
plt.scatter(X_standard[y==0,0], X_standard[y==0,1])
plt.scatter(X_standard[y==1,0], X_standard[y==1,1])
plt.show()
python 复制代码
svc2 = LinearSVC(C=0.01)
svc2.fit(X_standard, y)
python 复制代码
plot_decision_boundary(svc2, axis=[-3, 3, -3, 3])
plt.scatter(X_standard[y==0,0], X_standard[y==0,1])
plt.scatter(X_standard[y==1,0], X_standard[y==1,1])
plt.show()

绘制上下对应的两条线

python 复制代码
def plot_svc_decision_boundary(model, axis):
    
    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)
    
    w = model.coef_[0]
    b = model.intercept_[0]
    
    # w0*x0 + w1*x1 + b = 0
    # => x1 = -w0/w1 * x0 - b/w1
    plot_x = np.linspace(axis[0], axis[1], 200)
    up_y = -w[0]/w[1] * plot_x - b/w[1] + 1/w[1]
    down_y = -w[0]/w[1] * plot_x - b/w[1] - 1/w[1]
    
    up_index = (up_y >= axis[2]) & (up_y <= axis[3])
    down_index = (down_y >= axis[2]) & (down_y <= axis[3])
    plt.plot(plot_x[up_index], up_y[up_index], color='black')
    plt.plot(plot_x[down_index], down_y[down_index], color='black')
python 复制代码
plot_svc_decision_boundary(svc, axis=[-3, 3, -3, 3])
plt.scatter(X_standard[y==0,0], X_standard[y==0,1])
plt.scatter(X_standard[y==1,0], X_standard[y==1,1])
plt.show()

SVM中使用多项式特征

生成数据集

python 复制代码
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets

X, y = datasets.make_moons()
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()
python 复制代码
X, y = datasets.make_moons(noise=0.15, random_state=666)

plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()

使用多项式特征的SVM

python 复制代码
from sklearn.preprocessing import PolynomialFeatures, StandardScaler
from sklearn.svm import LinearSVC
from sklearn.pipeline import Pipeline

def PolynomialSVC(degree, C=1.0):
    return Pipeline([
        ("poly", PolynomialFeatures(degree=degree)),
        ("std_scaler", StandardScaler()),
        ("linearSVC", LinearSVC(C=C))
    ])
python 复制代码
poly_svc = PolynomialSVC(degree=3)
poly_svc.fit(X, y)
python 复制代码
def plot_decision_boundary(model, axis):
    
    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)
python 复制代码
plot_decision_boundary(poly_svc, axis=[-1.5, 2.5, -1.0, 1.5])
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()

使用多项式核函数的SVM

python 复制代码
from sklearn.svm import SVC

def PolynomialKernelSVC(degree, C=1.0):
    return Pipeline([
        ("std_scaler", StandardScaler()),
        ("kernelSVC", SVC(kernel="poly", degree=degree, C=C))
    ])
python 复制代码
poly_kernel_svc = PolynomialKernelSVC(degree=3)
poly_kernel_svc.fit(X, y)
python 复制代码
plot_decision_boundary(poly_kernel_svc, axis=[-1.5, 2.5, -1.0, 1.5])
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()

什么是核函数

多项式核函数

高斯核函数

RBF核 Radial Basis Function Kernel

将每一个样本点映射到一个无穷维的特征空间

多项式特征

高斯核

python 复制代码
import numpy as np
import matplotlib.pyplot as plt
x = np.arange(-4, 5, 1)
y = np.array((x >= -2) & (x <= 2), dtype='int')
plt.scatter(x[y==0], [0]*len(x[y==0]))
plt.scatter(x[y==1], [0]*len(x[y==1]))
plt.show()

高斯核

python 复制代码
def gaussian(x, l):
    gamma = 1.0
    return np.exp(-gamma * (x-l)**2)
l1, l2 = -1, 1

X_new = np.empty((len(x), 2))
for i, data in enumerate(x):
    X_new[i, 0] = gaussian(data, l1)
    X_new[i, 1] = gaussian(data, l2)
plt.scatter(X_new[y==0,0], X_new[y==0,1])
plt.scatter(X_new[y==1,0], X_new[y==1,1])
plt.show()

scikit-learn中的高斯核函数

python 复制代码
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets

X, y = datasets.make_moons(noise=0.15, random_state=666)

plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()

预处理

python 复制代码
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline
from sklearn.svm import SVC

def RBFKernelSVC(gamma):
    return Pipeline([
        ("std_scaler", StandardScaler()),
        ("svc", SVC(kernel="rbf", gamma=gamma))
    ])
python 复制代码
svc = RBFKernelSVC(gamma=1)
svc.fit(X, y)

可视化

python 复制代码
def plot_decision_boundary(model, axis):
    
    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)
python 复制代码
plot_decision_boundary(svc, axis=[-1.5, 2.5, -1.0, 1.5])
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()
python 复制代码
svc_gamma100 = RBFKernelSVC(gamma=100)
svc_gamma100.fit(X, y)
python 复制代码
plot_decision_boundary(svc_gamma100, axis=[-1.5, 2.5, -1.0, 1.5])
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()
python 复制代码
svc_gamma10 = RBFKernelSVC(gamma=10)
svc_gamma10.fit(X, y)
plot_decision_boundary(svc_gamma10, axis=[-1.5, 2.5, -1.0, 1.5])
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()
python 复制代码
svc_gamma05 = RBFKernelSVC(gamma=0.5)
svc_gamma05.fit(X, y)
plot_decision_boundary(svc_gamma05, axis=[-1.5, 2.5, -1.0, 1.5])
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()
python 复制代码
svc_gamma01 = RBFKernelSVC(gamma=0.1)
svc_gamma01.fit(X, y)
plot_decision_boundary(svc_gamma01, axis=[-1.5, 2.5, -1.0, 1.5])
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()

SVM思路解决回归问题

python 复制代码
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets

boston = datasets.load_boston()
X = boston.data
y = boston.target
from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=666)
python 复制代码
from sklearn.svm import LinearSVR
from sklearn.svm import SVR
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline

def StandardLinearSVR(epsilon=0.1):
    return Pipeline([
        ('std_scaler', StandardScaler()),
        ('linearSVR', LinearSVR(epsilon=epsilon))
    ])
python 复制代码
svr = StandardLinearSVR()
svr.fit(X_train, y_train)
python 复制代码
svr.score(X_test, y_test)
相关推荐
m0_7513363922 分钟前
突破性进展:超短等离子体脉冲实现单电子量子干涉,为飞行量子比特奠定基础
人工智能·深度学习·量子计算·材料科学·光子器件·光子学·无线电电子
美狐美颜sdk3 小时前
跨平台直播美颜SDK集成实录:Android/iOS如何适配贴纸功能
android·人工智能·ios·架构·音视频·美颜sdk·第三方美颜sdk
DeepSeek-大模型系统教程4 小时前
推荐 7 个本周 yyds 的 GitHub 项目。
人工智能·ai·语言模型·大模型·github·ai大模型·大模型学习
郭庆汝4 小时前
pytorch、torchvision与python版本对应关系
人工智能·pytorch·python
IT古董4 小时前
【第二章:机器学习与神经网络概述】03.类算法理论与实践-(3)决策树分类器
神经网络·算法·机器学习
小雷FansUnion6 小时前
深入理解MCP架构:智能服务编排、上下文管理与动态路由实战
人工智能·架构·大模型·mcp
资讯分享周6 小时前
扣子空间PPT生产力升级:AI智能生成与多模态创作新时代
人工智能·powerpoint
叶子爱分享7 小时前
计算机视觉与图像处理的关系
图像处理·人工智能·计算机视觉
鱼摆摆拜拜7 小时前
第 3 章:神经网络如何学习
人工智能·神经网络·学习
一只鹿鹿鹿7 小时前
信息化项目验收,软件工程评审和检查表单
大数据·人工智能·后端·智慧城市·软件工程