sklearn求解支持向量机

小鱼儿 2023-06-23 04:52 50阅读 0赞

%matplotlib inline
    import numpy as np
    import matplotlib.pyplot as plt
    from scipy import stats
    
    # use seaborn plotting defaults
    import seaborn as sns; sns.set()

### 支持向量基本原理 ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70]  
如何解决这个线性不可分问题呢？咱们给它映射到高维来试试

z = x 2 + y 2 z=x^2+y^2 z=x2\+y2.

## 例子 ##

make\_blobs函数是为聚类产生数据集  
产生一个数据集和相应的标签  
n\_samples:表示数据样本点个数,默认值100  
n\_features:表示数据的维度，默认值是2  
centers:产生数据的中心点，默认值3  
cluster\_std：数据集的标准差，浮点数或者浮点数序列，默认值1.0  
center\_box：中心确定之后的数据边界，默认值(-10.0, 10.0)  
shuffle ：洗乱，默认值是True  
random\_state:官网解释是随机生成器的种子

#随机来点数据
    from sklearn.datasets.samples_generator import make_blobs
    X, y = make_blobs(n_samples=50, centers=2,
                      random_state=0, cluster_std=0.60)
    plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 1]  
随便画几条线进行分割

xfit = np.linspace(-1, 3.5)
    plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')
    plt.plot([0.6], [2.1], 'x', color='red', markeredgewidth=2, markersize=10)
    
    for m, b in [(1, 0.65), (0.5, 1.6), (-0.2, 2.9)]:
        plt.plot(xfit, m * xfit + b, '-k')
    
    plt.xlim(-1, 3.5);

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 2]

### Support Vector Machines: 最小化 *雷区* ###

xfit = np.linspace(-1, 3.5)
    plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')
    
    for m, b, d in [(1, 0.65, 0.33), (0.5, 1.6, 0.55), (-0.2, 2.9, 0.2)]:
        yfit = m * xfit + b
        plt.plot(xfit, yfit, '-k')
        plt.fill_between(xfit, yfit - d, yfit + d, edgecolor='none',
                         color='#AAAAAA', alpha=0.4)
    
    plt.xlim(-1, 3.5);

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 3]

### 训练一个基本的SVM ###

from sklearn.svm import SVC # "Support vector classifier"
    model = SVC(kernel='linear')
    model.fit(X, y)

![在这里插入图片描述][20191217151350114.png]

#绘图函数
    def plot_svc_decision_function(model, ax=None, plot_support=True):
        """Plot the decision function for a 2D SVC"""
        if ax is None:
            ax = plt.gca()
        xlim = ax.get_xlim()
        ylim = ax.get_ylim()
        
        # create grid to evaluate model
        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)
        
        # plot decision boundary and margins
        ax.contour(X, Y, P, colors='k',
                   levels=[-1, 0, 1], alpha=0.5,
                   linestyles=['--', '-', '--'])
        
        # plot support vectors
        if plot_support:
            ax.scatter(model.support_vectors_[:, 0],
                       model.support_vectors_[:, 1],
                       s=300, linewidth=1, facecolors='none');
        ax.set_xlim(xlim)
        ax.set_ylim(ylim)

plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')
    plot_svc_decision_function(model);

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 4]

*  这条线就是我们希望得到的决策边界啦
 *  有3个点恰好都是边界上的点
 *  它们就是我们的*support vectors*（支持向量）
 *  在Scikit-Learn中, 它们存储在这个位置 `support_vectors_`（一个属性）

model.support_vectors_

![在这里插入图片描述][20191217153005237.png]

*  观察可以发现，只需要支持向量我们就可以把模型构建出来
 *  接下来我们尝试一下，用不同多的数据点，看看效果会不会发生变化
 *  分别使用60个和120个数据点

def plot_svm(N=10, ax=None):
        X, y = make_blobs(n_samples=200, centers=2,
                          random_state=0, cluster_std=0.60)
        X = X[:N]
        y = y[:N]
        model = SVC(kernel='linear', C=1E10)
        model.fit(X, y)
        
        ax = ax or plt.gca()
        ax.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')
        ax.set_xlim(-1, 4)
        ax.set_ylim(-1, 6)
        plot_svc_decision_function(model, ax)
    
    fig, ax = plt.subplots(1, 2, figsize=(16, 6))
    fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)
    for axi, N in zip(ax, [60, 120]):
        plot_svm(N, axi)
        axi.set_title('N = {0}'.format(N))

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 5]

*  左边是60个点的结果，右边的是120个点的结果
 *  观察发现，只要支持向量没变，其他的数据怎么加无所谓！

### 引入核函数的SVM ###

*  首先我们先用线性的核来看一下在下面这样比较难的数据集上还能分了吗？

from sklearn.datasets.samples_generator import make_circles
    X, y = make_circles(100, factor=.1, noise=.1)
    # datasets.make_circles()专门用来生成圆圈形状的二维样本.factor表示里圈和外圈的距离之比.
    clf = SVC(kernel='linear').fit(X, y)
    
    plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')
    plot_svc_decision_function(clf, plot_support=False);

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 6]

*  分不了了，那咋办呢？试试高维核变换吧！

#加入了新的维度r
    from mpl_toolkits import mplot3d
    r = np.exp(-(X ** 2).sum(1))
    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='autumn')
        ax.view_init(elev=elev, azim=azim)
        ax.set_xlabel('x')
        ax.set_ylabel('y')
        ax.set_zlabel('r')
    
    plot_3D(elev=45, azim=45, X=X, y=y)

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 7]

#加入径向基函数
    clf = SVC(kernel='rbf', C=1E6)
    clf.fit(X, y)

![在这里插入图片描述][20191217154059229.png]

plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')
    plot_svc_decision_function(clf)
    plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],
                s=300, lw=1, facecolors='none');

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 8]  
使用这种核支持向量机，我们学习一个合适的非线性决策边界。这种核变换策略在机器学习中经常被使用！

### 调节SVM参数: Soft Margin问题 ###

### 调节C参数 ###

*  当C趋近于无穷大时：意味着分类严格不能有错误
 *  当C趋近于很小的时：意味着可以有更大的错误容忍

X, y = make_blobs(n_samples=100, centers=2,
                      random_state=0, cluster_std=0.8)
    plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn');

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 9]

X, y = make_blobs(n_samples=100, centers=2,
                      random_state=0, cluster_std=0.8)
    
    fig, ax = plt.subplots(1, 2, figsize=(16, 6))
    fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)
    
    for axi, C in zip(ax, [10.0, 0.1]):
        model = SVC(kernel='linear', C=C).fit(X, y)
        axi.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')
        plot_svc_decision_function(model, axi)
        axi.scatter(model.support_vectors_[:, 0],
                    model.support_vectors_[:, 1],
                    s=300, lw=1, facecolors='none');
        axi.set_title('C = {0:.1f}'.format(C), size=14)

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 10]

X, y = make_blobs(n_samples=100, centers=2,
                      random_state=0, cluster_std=1.1)
    
    fig, ax = plt.subplots(1, 2, figsize=(16, 6))
    fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)
    
    for axi, gamma in zip(ax, [10.0, 0.1]):
        model = SVC(kernel='rbf', gamma=gamma).fit(X, y)
        axi.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')
        plot_svc_decision_function(model, axi)
        axi.scatter(model.support_vectors_[:, 0],
                    model.support_vectors_[:, 1],
                    s=300, lw=1, facecolors='none');
        axi.set_title('gamma = {0:.1f}'.format(gamma), size=14)

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 11]

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