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分类: Python/Ruby

2021-11-11 17:19:55

import numpy as np

import pandas as pd

from sklearn.datasets import load_iris

from sklearn.model_selection import train_test_split

import matplotlib.pyplot as plt

# data

def create_data():

    iris = load_iris()

    df = pd.DataFrame(iris.data, columns=iris.feature_names)

    df['label'] = iris.target

    df.columns = [

        'sepal length', 'sepal width', 'petal length', 'petal width', 'label'

    ]

    data = np.array(df.iloc[:100, [0, 1, -1]])

    for i in range(len(data)):

        if data[i, -1] == 0:

            data[i, -1] = -1

    # print(data)

    return data[:, :2], data[:, -1]

class SVM:

    def __init__(self, max_iter=100, kernel='linear'):

        self.max_iter = max_iter

        self._kernel = kernel

    def init_args(self, features, labels):

        self.m, self.n = features.shape

        self.X = features

        self.Y = labels

        self.b = 0.0

        # Ei保存在一个列表里

        self.alpha = np.ones(self.m)

        self.E = [self._E(i) for i in range(self.m)]

        # 松弛变量

        self.C = 1.0

    def _KKT(self, i):

        y_g = self._g(i) * self.Y[i]

        if self.alpha[i] == 0:

            return y_g >= 1

        elif 0 < self.alpha[i] < self.C:

            return y_g == 1

        else:

            return y_g <= 1

    # g(x)预测值,输入xiX[i]

    def _g(self, i):

        r = self.b

        for j in range(self.m):

            r += self.alpha[j] * self.Y[j] * self.kernel(self.X[i], self.X[j])

        return r

    # 核函数

    def kernel(self, x1, x2):

        if self._kernel == 'linear':

            return sum([x1[k] * x2[k] for k in range(self.n)])

        elif self._kernel == 'poly':

            return (sum([x1[k] * x2[k] for k in range(self.n)]) + 1) ** 2

        return 0

    # Ex)为g(x)对输入x的预测值和y的差

    def _E(self, i):

        return self._g(i) - self.Y[i]

    def _init_alpha(self):

        # 外层循环首先遍历所有满足0的样本点,检验是否满足KKT

        index_list = [i for i in range(self.m) if 0 < self.alpha[i] < self.C]

        # 否则遍历整个训练集

        non_satisfy_list = [i for i in range(self.m) if i not in index_list]

        index_list.extend(non_satisfy_list)

        for i in index_list:

            if self._KKT(i):

                continue

            E1 = self.E[i]

            # 如果E2+,选择最小的;如果E2是负的,选择最大的

            if E1 >= 0:

                j = min(range(self.m), key=lambda x: self.E[x])

            else:

                j = max(range(self.m), key=lambda x: self.E[x])

            return i, j

    def _compare(self, _alpha, L, H):

        if _alpha > H:

            return H

        elif _alpha < L:

            return L

        else:

            return _alpha

    def fit(self, features, labels):

        self.init_args(features, labels)

        for t in range(self.max_iter):

            # train

            i1, i2 = self._init_alpha()

            # 边界

            if self.Y[i1] == self.Y[i2]:

                L = max(0, self.alpha[i1] + self.alpha[i2] - self.C)

                H = min(self.C, self.alpha[i1] + self.alpha[i2])

            else:

                L = max(0, self.alpha[i2] - self.alpha[i1])

                H = min(self.C, self.C + self.alpha[i2] - self.alpha[i1])

            E1 = self.E[i1]

            E2 = self.E[i2]

            # eta=K11+K22-2K12

            eta = self.kernel(self.X[i1], self.X[i1]) + self.kernel(

                self.X[i2],

                self.X[i2]) - 2 * self.kernel(self.X[i1], self.X[i2])

            if eta <= 0:

                # print('eta <= 0')

                continue

            alpha2_new_unc = self.alpha[i2] + self.Y[i2] * (

                    E1 - E2) / eta  # 外汇跟单gendan5.com此处有修改,根据书上应该是E1 - E2,书上130-131

            alpha2_new = self._compare(alpha2_new_unc, L, H)

            alpha1_new = self.alpha[i1] + self.Y[i1] * self.Y[i2] * (

                    self.alpha[i2] - alpha2_new)

            b1_new = -E1 - self.Y[i1] * self.kernel(self.X[i1], self.X[i1]) * (

                    alpha1_new - self.alpha[i1]) - self.Y[i2] * self.kernel(

                self.X[i2],

                self.X[i1]) * (alpha2_new - self.alpha[i2]) + self.b

            b2_new = -E2 - self.Y[i1] * self.kernel(self.X[i1], self.X[i2]) * (

                    alpha1_new - self.alpha[i1]) - self.Y[i2] * self.kernel(

                self.X[i2],

                self.X[i2]) * (alpha2_new - self.alpha[i2]) + self.b

            if 0 < alpha1_new < self.C:

                b_new = b1_new

            elif 0 < alpha2_new < self.C:

                b_new = b2_new

            else:

                # 选择中点

                b_new = (b1_new + b2_new) / 2

            # 更新参数

            self.alpha[i1] = alpha1_new

            self.alpha[i2] = alpha2_new

            self.b = b_new

            self.E[i1] = self._E(i1)

            self.E[i2] = self._E(i2)

        return 'train done!'

    def predict(self, data):

        r = self.b

        for i in range(self.m):

            r += self.alpha[i] * self.Y[i] * self.kernel(data, self.X[i])

        return 1 if r > 0 else -1

    def score(self, X_test, y_test):

        right_count = 0

        for i in range(len(X_test)):

            result = self.predict(X_test[i])

            if result == y_test[i]:

                right_count += 1

        return right_count / len(X_test)

    def _weight(self):

        # linear model

        yx = self.Y.reshape(-1, 1) * self.X

        self.w = np.dot(yx.T, self.alpha)

        return self.w

    def PLT(self, X, y):

        self.w = self._weight()

        plt.scatter(X[:50, 0], X[:50, 1], label="0")

        plt.scatter(X[50:, 0], X[50:, 1], label="1")

        a = -self.w[0] / self.w[1]

        xaxis = np.linspace(4, 8)

        y_sep = a * xaxis - (self.b) / self.w[1]

        plt.plot(xaxis, y_sep, 'k-')

        plt.show()

if __name__ == '__main__':

    X, y = create_data()

    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25)

    svm = SVM(max_iter=200)

    svm.fit(X_train, y_train)

    print(svm.score(X_test, y_test))

    svm.PLT(X, y)

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