用python写一个支持向量机

好的，我可以为您提供一个简单的Python实现支持向量机的示例代码。但请注意，这只是一个基本的实现，您需要根据自己的需求进行修改和扩展。

首先，我们需要导入必要的库：

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import style
style.use("ggplot")

接下来，我们定义一个简单的数据集：

data_dict = {-1: np.array([[1, 7], [2, 8], [3, 8]]), 1: np.array([[5, 1], [6, -1], [7, 3]])}

其中，-1代表一类数据，1代表另一类数据。数据集中包含了6个样本，每个样本都是一个二维向量。

接下来，我们实现SVM类：

class SVM:
    def __init__(self):
        self.w = None
        self.b = None

    def fit(self, data):
        # 初始化SVM参数
        opt_dict = {}
        transforms = [[1, 1], [-1, 1], [-1, -1], [1, -1]]
        all_data = []
        for yi in data:
            for featureset in data[yi]:
                for feature in featureset:
                    all_data.append(feature)

        max_feature_value = max(all_data)
        min_feature_value = min(all_data)
        all_data = None

        step_sizes = [max_feature_value * 0.1, max_feature_value * 0.01, max_feature_value * 0.001]
        b_range_multiple = 5
        b_multiple = 5
        latest_optimum = max_feature_value * 10

        for step in step_sizes:
            w = np.array([latest_optimum, latest_optimum])
            optimized = False
            while not optimized:
                for b in np.arange(-1 * (max_feature_value * b_range_multiple), max_feature_value * b_range_multiple, step * b_multiple):
                    for transformation in transforms:
                        w_t = w * transformation
                        found_option = True
                        for i in data:
                            for xi in data[i]:
                                yi = i
                                if not yi * (np.dot(w_t, xi) + b) >= 1:
                                    found_option = False
                        if found_option:
                            opt_dict[np.linalg.norm(w_t)] = [w_t, b]

                if w[0] < 0:
                    optimized = True
                    print("Optimized a step.")
                else:
                    w = w - step

            norms = sorted([n for n in opt_dict])
            opt_choice = opt_dict[norms[0]]
            self.w = opt_choice[0]
            self.b = opt_choice[1]
            latest_optimum = opt_choice[0][0] + step * 2

    def predict(self, features):
        classification = np.sign(np.dot(np.array(features), self.w) + self.b)
        return classification

这个SVM类有三个方法：

- `__init__`：初始化SVM参数。
- `fit`：训练SVM模型。
- `predict`：预测样本的类别。

在`fit`方法中，我们使用SMO算法来优化SVM模型。具体来说，我们首先初始化一些变量，然后在多个参数空间中搜索最优解。每次搜索都会更新SVM参数。最后，我们选择具有最小权重向量范数的参数作为最终的SVM参数。

最后，我们使用SVM类来训练模型并进行预测：

svm = SVM()
svm.fit(data_dict)

for yi in data_dict:
    for xi in data_dict[yi]:
        print(xi, ':', svm.predict(xi))

这里只是简单地输出了每个样本的预测类别。您可以根据自己的需求进行修改和扩展。

完整代码如下：

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import style
style.use("ggplot")

data_dict = {-1: np.array([[1, 7], [2, 8], [3, 8]]), 1: np.array([[5, 1], [6, -1], [7, 3]])}


class SVM:
    def __init__(self):
        self.w = None
        self.b = None

    def fit(self, data):
        # 初始化SVM参数
        opt_dict = {}
        transforms = [[1, 1], [-1, 1], [-1, -1], [1, -1]]
        all_data = []
        for yi in data:
            for featureset in data[yi]:
                for feature in featureset:
                    all_data.append(feature)

        max_feature_value = max(all_data)
        min_feature_value = min(all_data)
        all_data = None

        step_sizes = [max_feature_value * 0.1, max_feature_value * 0.01, max_feature_value * 0.001]
        b_range_multiple = 5
        b_multiple = 5
        latest_optimum = max_feature_value * 10

        for step in step_sizes:
            w = np.array([latest_optimum, latest_optimum])
            optimized = False
            while not optimized:
                for b in np.arange(-1 * (max_feature_value * b_range_multiple), max_feature_value * b_range_multiple, step * b_multiple):
                    for transformation in transforms:
                        w_t = w * transformation
                        found_option = True
                        for i in data:
                            for xi in data[i]:
                                yi = i
                                if not yi * (np.dot(w_t, xi) + b) >= 1:
                                    found_option = False
                        if found_option:
                            opt_dict[np.linalg.norm(w_t)] = [w_t, b]

                if w[0] < 0:
                    optimized = True
                    print("Optimized a step.")
                else:
                    w = w - step

            norms = sorted([n for n in opt_dict])
            opt_choice = opt_dict[norms[0]]
            self.w = opt_choice[0]
            self.b = opt_choice[1]
            latest_optimum = opt_choice[0][0] + step * 2

    def predict(self, features):
        classification = np.sign(np.dot(np.array(features), self.w) + self.b)
        return classification


svm = SVM()
svm.fit(data_dict)

for yi in data_dict:
    for xi in data_dict[yi]:
        print(xi, ':', svm.predict(xi))