機器學習課程的一個實驗，整理出來共享。
原理很簡單，優化方法是用的梯度下降。後面有測試結果。

# coding=utf-8
from math import exp

import matplotlib.pyplot as plt
import numpy as np
from sklearn.datasets.samples_generator import make_blobs


def sigmoid(num):
    '''

    :param num: 待計算的x
    :return: sigmoid之後的數值
    '''
    if type(num) == int or type(num) == float:
        return 1.0 / (1 + exp(-1 * num))
    else:
        raise ValueError, 'only int or float data can compute sigmoid'


class logistic():
    def __init__(self, x, y): 
        if type(x) == type(y) == list:
            self.x = np.array(x)
            self.y = np.array(y)
        elif type(x) == type(y) == np.ndarray:
            self.x = x
            self.y = y
        else:
            raise ValueError, 'input data error'

    def sigmoid(self, x):
        '''

        :param x: 輸入向量
        :return: 對輸入向量整體進行simgoid計算後的向量結果
        '''
        s = np.frompyfunc(lambda x: sigmoid(x), 1, 1)
        return s(x)

    def train_with_punish(self, alpha, errors, punish=0.0001):
        '''

        :param alpha: alpha為學習速率
        :param errors: 誤差小於多少時停止迭代的閾值
        :param punish: 懲罰係數
        :param times: 最大迭代次數
        :return:
        '''
        self.punish = punish
        dimension = self.x.shape[1]
        self.theta = np.random.random(dimension)
        compute_error = 100000000
        times = 0
        while compute_error > errors:
            res = np.dot(self.x, self.theta)
            delta = self.sigmoid(res) - self.y
            self.theta = self.theta - alpha * np.dot(self.x.T, delta) - punish * self.theta  # 帶懲罰的梯度下降方法
            compute_error = np.sum(delta)
            times += 1

    def predict(self, x):
        '''

        :param x: 給入新的未標註的向量
        :return: 按照計算出的引數返回判定的類別
        '''
        x = np.array(x)
        if self.sigmoid(np.dot(x, self.theta)) > 0.5:
            return 1
        else:
            return 0


def test1():
    '''
    用來進行測試和畫圖，展現效果
    :return:
    '''
    x, y = make_blobs(n_samples=200, centers=2, n_features=2, random_state=0, center_box=(10, 20))
    x1 = []
    y1 = []
    x2 = []
    y2 = []
    for i in range(len(y)):
        if y[i] == 0:
            x1.append(x[i][0])
            y1.append(x[i][1])
        elif y[i] == 1:
            x2.append(x[i][0])
            y2.append(x[i][1])
    # 以上均為處理資料，生成出兩類資料
    p = logistic(x, y)
    p.train_with_punish(alpha=0.00001, errors=0.005, punish=0.01)  # 步長是0.00001，最大允許誤差是0.005，懲罰係數是0.01
    x_test = np.arange(10, 20, 0.01)
    y_test = (-1 * p.theta[0] / p.theta[1]) * x_test
    plt.plot(x_test, y_test, c='g', label='logistic_line')
    plt.scatter(x1, y1, c='r', label='positive')
    plt.scatter(x2, y2, c='b', label='negative')
    plt.legend(loc=2)
    plt.title('punish value = ' + p.punish.__str__())
    plt.show()


if __name__ == '__main__':
    test1()

 

執行結果如下圖

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