SVM决策边界

理解SVM的决策边界

最新推荐文章于 2024-12-30 12:47:22 发布

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本文探讨了支持向量机（SVM）的决策边界，包括线性可分情况和线性不可分情况的处理，深入解析SVM如何构建最优分类超平面。

SVM决策边界

一、线性可分

w = clf.coef_[0]
#调用coef_取得w值
a = -w[0] / w[1]
xx = np.linspace(-2, 2) # x轴范围
yy = a * xx - (clf.intercept_[0] / w[1])
b = clf.support_vectors_[0]
yy_down = a * xx + (b[1] - a * b[0])
b = clf.support_vectors_[-1]
yy_up = a * xx + (b[1] - a * b[0])
#得到分界线上方和下方与之平行的边际直线的xx和yy后面一并画出
plt.figure()
plt.plot(xx, yy, 'g-')
plt.plot(xx, yy_down, 'g--')
plt.plot(xx, yy_up, 'g--')
plt.ylim(0.75,1.1) # y轴范围

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)

    plt.show()

二、线性不可分

from matplotlib.colors import ListedColormap
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()]                 #c_[]将两个数组以列的形式拼接起来，形成矩阵。
    y_predict = model.predict(X_new)

    zz = y_predict.reshape(x0.shape)                      #通过训练好的模型，预测平面上这些点的分类

    custom_cmap = ListedColormap(['#EF9A9A', '#FFF59D', '#90CAF9'])

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

def visualize_boundary(model):
    x_min, x_max = 0, 1
    y_min, y_max = 0.4, 1

    xx, yy = np.meshgrid(np.linspace(x_min, x_max, 500),
                         np.linspace(y_min, y_max, 500))

    z = model.predict(np.c_[xx.flatten(), yy.flatten()])
    zz = z.reshape(xx.shape)
    plt.contour(xx, yy, zz)

def make_meshgrid(x, y, h=.02):
    x_min, x_max = x.min()-0.05, x.max()+0.05
    y_min, y_max = y.min()-0.05, y.max()+0.05
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
    return xx, yy

def plot_contours(ax, clf, xx, yy, **params):
    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)
    out = ax.contourf(xx, yy, Z, **params)
    return out

fig, ax = plt.subplots()
title = ('Decision surface of linear SVC ')
X0, X1 = X_norm[:, 0], X_norm[:, 1]
xx, yy = make_meshgrid(X0, X1)

plot_contours(ax, clf, xx, yy, cmap=plt.cm.coolwarm, alpha=0.8)
ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')
ax.set_ylabel('F1')
ax.set_xlabel('F2')
ax.set_xticks(())
ax.set_yticks(())
ax.set_title('Decison surface using the features')
plt.show()