线性 SVM 决策过程的可视化
导入模块
from sklearn.datasets import make_blobs
from sklearn.svm import SVC
import matplotlib.pyplot as plt
import numpy as np
实例化数据集，可视化数据集
x, y = make_blobs(n_samples=50, centers=2, random_state=0, cluster_std=0.5)
# plt.scatter(x[:, 0], x[:, 1], c=y, cmap="rainbow")
# plt.xticks([])
# plt.yticks([])
画决策边界
# 首先要有散点图
plt.scatter(x[:, 0], x[:, 1], c=y, s=50, cmap="rainbow")
# 获取当前的子图，如果不存在，则创建新的子图
ax = plt.gca()
# 获取平面上两条坐标轴的最大值和最小值
xlim = ax.get_xlim() # (-0.46507821433712176, 3.1616962549275827)
ylim = ax.get_ylim() # (-0.22771027454251097, 5.541407658378895)
# 在最大值和最小值之间形成30个规律的数据
axisx = np.linspace(xlim[0], xlim[1], 30) # shape(30,)
axisy = np.linspace(ylim[0], ylim[1], 30) # shape(30,)
# 将axis（x, y）转换成二维数组
axisx, axisy = np.meshgrid(axisx, axisy) # axisx, axisy = shape((30, 30)
# 将axisx, axisy 组成 900 * 2 的数组
xy = np.vstack([axisx.ravel(), axisy.ravel()]).T # shape(900, 2)
# 展示xy画出的网格图
# plt.scatter(xy[:, 0], xy[:, 1], s=1, c="grey", alpha=0.3)
建模，计算决策边界并找出网格上每个点到决策边界的距离
# 建模，通过fit计算出对应的决策边界
clf = SVC(kernel="linear").fit(x, y)
# 重要接口decision_function，返回每个输入的样本所对应的到决策边界的距离
z = clf.decision_function(xy).reshape(axisx.shape) # shape(30, 30)
plt.scatter(x[:, 0], x[:, 1], c=y, s=50, cmap="rainbow")
ax = plt.gca()
# 画决策边界和平行于决策边界的超平面
ax.contour(
axisx,
axisy,
z,
colors="k",
levels=[-1, 0, 1],
linestyles=["--", "-", "--"],
alpha=0.5,
)
# 设置xyk刻度
ax.set_xlim(xlim)
ax.set_ylim(ylim)
(-0.22771027454251097, 5.541407658378895)
将绘图过程包装成函数
# 将上述过程包装成函数：
def plot_svc_decision_function(model: SVC, ax=None):
"""画出线性数据中策边界和平行于决策边界的超平面
Args:
model (SVC): 模型
ax (_type_, optional): 子图. Defaults to None.
"""
if ax is None:
ax = plt.gca() # 获取子图或新建子图
xlim = ax.get_xlim() # 获取子图x轴最大值和最小值
ylim = ax.get_ylim() # 获取子图y轴最大值和最小值
# 在最大值和最小值之间形成30个规律的数据
x = np.linspace(xlim[0], xlim[1], 30)
y = np.linspace(ylim[0], ylim[1], 30)
# 将x,y转换成x^2, y^2的二维数组
Y, X = np.meshgrid(y, x)
# 组成 xy * 2 的数组
xy = np.vstack([X.ravel(), Y.ravel()]).T
# 获取每个输入的样本所对应的到决策边界的距离
P = model.decision_function(xy).reshape(X.shape)
# 画图
ax.contour(
X, Y, P, colors="k", levels=[-1, 0, 1], alpha=0.5, linestyles=["--", "-", "--"]
)
ax.set_xlim(xlim)
ax.set_ylim(ylim)
clf = SVC(kernel="linear").fit(x, y)
plt.scatter(x[:, 0], x[:, 1], s=50, cmap="rainbow", c=y)
plot_svc_decision_function(clf)
# 测试
x1, y1 = make_blobs(n_samples=500, centers=2, cluster_std=0.9)
clf1 = SVC(kernel="linear").fit(x1, y1)
plt.scatter(x1[:, 0], x1[:, 1], c=y1, s=25, cmap="rainbow")
plot_svc_decision_function(clf1)
探索模型
# 根据决策边界，对X中的样本进行分类，返回的结构为n_samples
clf.predict(x)
array([1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1,
1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1,
0, 1, 1, 0, 1, 0])
# 返回给定测试数据和标签的平均准确度
clf.score(x, y)
1.0
# 返回支持向量
clf.support_vectors_
array([[0.5323772 , 3.31338909],
[2.11114739, 3.57660449],
[2.06051753, 1.79059891]])
# 返回每个类中支持向量的个数
clf.n_support_
array([2, 1], dtype=int32)
推广到非线性情况
from sklearn.datasets import make_circles
x, y = make_circles(n_samples=300, factor=0.1, noise=0.1)
# x.shape(300, 2)
# y.shape(300,)
plt.scatter(x[:, 0], x[:, 1], c=y, s=50, cmap="rainbow")
plt.show()
# 测试plot_svc_decision_function
clf = SVC(kernel="linear").fit(x, y)
plt.scatter(x[:, 0], x[:, 1], s=50, cmap="rainbow", c=y)
plot_svc_decision_function(clf)
clf.score(x, y)
0.6733333333333333
为非线性数据增加维度并绘制 3D 图像
r = np.exp(-(x**2).sum(1)) # r.shape(300,)
rlim = np.linspace(min(r), max(r), 100)
from mpl_toolkits import mplot3d
# 定义一个绘制三维图像的函数
# elev表示上下旋转的角度
# azim表示平行旋转的角度
def plot_3D(elev=30, azim=30, x=x, y=y):
ax = plt.subplot(projection="3d")
ax.scatter3D(x[:, 0], x[:, 1], r, c=y, s=50, cmap="rainbow")
ax.view_init(elev=elev, azim=azim)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("r")
plt.show()
plot_3D()
将上述过程放到 Jupyter Notebook 中运行
# 如果放到jupyter notebook中运行
from sklearn.svm import SVC
import matplotlib.pyplot as plt
import numpy as np
from sklearn.datasets import make_circles
X, y = make_circles(100, factor=0.1, noise=0.1)
plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap="rainbow")
def plot_svc_decision_function(model, ax=None):
if ax is None:
ax = plt.gca()
xlim = ax.get_xlim()
ylim = ax.get_ylim()
x = np.linspace(xlim[0], xlim[1], 30)
y = np.linspace(ylim[0], ylim[1], 30)
Y, X = np.meshgrid(y, x)
xy = np.vstack([X.ravel(), Y.ravel()]).T
P = model.decision_function(xy).reshape(X.shape)
ax.contour(
X, Y, P, colors="k", levels=[-1, 0, 1], alpha=0.5, linestyles=["--", "-", "--"]
)
ax.set_xlim(xlim)
ax.set_ylim(ylim)
clf = SVC(kernel="linear").fit(X, y)
plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap="rainbow")
plot_svc_decision_function(clf)
r = np.exp(-(X**2).sum(1))
rlim = np.linspace(min(r), max(r), 100)
from mpl_toolkits import mplot3d
def plot_3D(elev=30, azim=30, X=X, y=y):
ax = plt.subplot(projection="3d")
ax.scatter3D(X[:, 0], X[:, 1], r, c=y, s=50, cmap="rainbow")
ax.view_init(elev=elev, azim=azim)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("r")
plt.show()
from ipywidgets import interact, fixed
interact(plot_3D, elev=[0, 30], azip=(-180, 180), X=fixed(X), y=fixed(y))
plt.show()
interactive(children=(Dropdown(description='elev', index=1, options=(0, 30), value=30), IntSlider(value=30, de…